From 568e11793cbb9c46f4000d34ef61cae0fa0ac6a4 Mon Sep 17 00:00:00 2001 From: Muhammad Junaid <34795347+mkhalid1@users.noreply.github.com> Date: Mon, 1 Oct 2018 03:41:28 +0500 Subject: [PATCH 1/2] Revamped the notebook --- csp.ipynb | 364 ++++++++++++++++++++++++------------------------------ 1 file changed, 160 insertions(+), 204 deletions(-) diff --git a/csp.ipynb b/csp.ipynb index d9254ef0e..17978cf75 100644 --- a/csp.ipynb +++ b/csp.ipynb @@ -12,9 +12,7 @@ { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "from csp import *\n", @@ -306,7 +304,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The __ _ _init_ _ __ method parameters specify the CSP. Variable can be passed as a list of strings or integers. Domains are passed as dict where key specify the variables and value specify the domains. The variables are passed as an empty list. Variables are extracted from the keys of the domain dictionary. Neighbor is a dict of variables that essentially describes the constraint graph. Here each variable key has a list its value which are the variables that are constraint along with it. The constraint parameter should be a function **f(A, a, B, b**) that **returns true** if neighbors A, B **satisfy the constraint** when they have values **A=a, B=b**. We have additional parameters like nassings which is incremented each time an assignment is made when calling the assign method. You can read more about the methods and parameters in the class doc string. We will talk more about them as we encounter their use. Let us jump to an example." + "The __ _ _init_ _ __ method parameters specify the CSP. Variables can be passed as a list of strings or integers. Domains are passed as dict (dictionary datatpye) where \"key\" specifies the variables and \"value\" specifies the domains. The variables are passed as an empty list. Variables are extracted from the keys of the domain dictionary. Neighbor is a dict of variables that essentially describes the constraint graph. Here each variable key has a list of its values which are the variables that are constraint along with it. The constraint parameter should be a function **f(A, a, B, b**) that **returns true** if neighbors A, B **satisfy the constraint** when they have values **A=a, B=b**. We have additional parameters like nassings which is incremented each time an assignment is made when calling the assign method. You can read more about the methods and parameters in the class doc string. We will talk more about them as we encounter their use. Let us jump to an example." ] }, { @@ -315,7 +313,7 @@ "source": [ "## GRAPH COLORING\n", "\n", - "We use the graph coloring problem as our running example for demonstrating the different algorithms in the **csp module**. The idea of map coloring problem is that the adjacent nodes (those connected by edges) should not have the same color throughout the graph. The graph can be colored using a fixed number of colors. Here each node is a variable and the values are the colors that can be assigned to them. Given that the domain will be the same for all our nodes we use a custom dict defined by the **UniversalDict** class. The **UniversalDict** Class takes in a parameter which it returns as value for all the keys of the dict. It is very similar to **defaultdict** in Python except that it does not support item assignment." + "We use the graph coloring problem as our running example for demonstrating the different algorithms in the **csp module**. The idea of map coloring problem is that the adjacent nodes (those connected by edges) should not have the same color throughout the graph. The graph can be colored using a fixed number of colors. Here each node is a variable and the values are the colors that can be assigned to them. Given that the domain will be the same for all our nodes we use a custom dict defined by the **UniversalDict** class. The **UniversalDict** Class takes in a parameter and returns it as a value for all the keys of the dict. It is very similar to **defaultdict** in Python except that it does not support item assignment." ] }, { @@ -343,7 +341,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "For our CSP we also need to define a constraint function **f(A, a, B, b)**. In this what we need is that the neighbors must not have the same color. This is defined in the function **different_values_constraint** of the module." + "For our CSP we also need to define a constraint function **f(A, a, B, b)**. In this, we need to ensure that the neighbors don't have the same color. This is defined in the function **different_values_constraint** of the module." ] }, { @@ -463,15 +461,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The CSP class takes neighbors in the form of a Dict. The module specifies a simple helper function named **parse_neighbors** which allows us to take input in the form of strings and return a Dict of a form compatible with the **CSP Class**." + "The CSP class takes neighbors in the form of a Dict. The module specifies a simple helper function named **parse_neighbors** which allows us to take input in the form of strings and return a Dict of a form that is compatible with the **CSP Class**." ] }, { "cell_type": "code", "execution_count": 5, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "%pdoc parse_neighbors" @@ -481,7 +477,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The **MapColoringCSP** function creates and returns a CSP with the above constraint function and states. The variables are the keys of the neighbors dict and the constraint is the one specified by the **different_values_constratint** function. **australia**, **usa** and **france** are three CSPs that have been created using **MapColoringCSP**. **australia** corresponds to ** Figure 6.1 ** in the book." + "The **MapColoringCSP** function creates and returns a CSP with the above constraint function and states. The variables are the keys of the neighbors dict and the constraint is the one specified by the **different_values_constratint** function. **Australia**, **USA** and **France** are three CSPs that have been created using **MapColoringCSP**. **Australia** corresponds to ** Figure 6.1 ** in the book." ] }, { @@ -611,9 +607,7 @@ { "data": { "text/plain": [ - "(,\n", - " ,\n", - " )" + "(, , )" ] }, "execution_count": 7, @@ -631,7 +625,7 @@ "source": [ "## N-QUEENS\n", "\n", - "The N-queens puzzle is the problem of placing N chess queens on an N×N chessboard so that no two queens threaten each other. Here N is a natural number. Like the graph coloring problem, NQueens is also implemented in the csp module. The **NQueensCSP** class inherits from the **CSP** class. It makes some modifications in the methods to suit the particular problem. The queens are assumed to be placed one per column, from left to right. That means position (x, y) represents (var, val) in the CSP. The constraint that needs to be passed on the CSP is defined in the **queen_constraint** function. The constraint is satisfied (true) if A, B are really the same variable, or if they are not in the same row, down diagonal, or up diagonal. " + "The N-queens puzzle is the problem of placing N chess queens on an N×N chessboard in a way such that no two queens threaten each other. Here N is a natural number. Like the graph coloring problem, NQueens is also implemented in the csp module. The **NQueensCSP** class inherits from the **CSP** class. It makes some modifications in the methods to suit this particular problem. The queens are assumed to be placed one per column, from left to right. That means position (x, y) represents (var, val) in the CSP. The constraint that needs to be passed to the CSP is defined in the **queen_constraint** function. The constraint is satisfied (true) if A, B are really the same variable, or if they are not in the same row, down diagonal, or up diagonal. " ] }, { @@ -752,7 +746,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The **NQueensCSP** method implements methods that support solving the problem via **min_conflicts** which is one of the techniques for solving CSPs. Because **min_conflicts** hill climbs the number of conflicts to solve, the CSP **assign** and **unassign** are modified to record conflicts. More details about the structures **rows**, **downs**, **ups** which help in recording conflicts are explained in the docstring." + "The **NQueensCSP** method implements methods that support solving the problem via **min_conflicts** which is one of the many popular techniques for solving CSPs. Because **min_conflicts** hill climbs the number of conflicts to solve, the CSP **assign** and **unassign** are modified to record conflicts. More details about the structures: **rows**, **downs**, **ups** which help in recording conflicts are explained in the docstring." ] }, { @@ -950,15 +944,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The _ ___init___ _ method takes only one parameter **n** the size of the problem. To create an instance we just pass the required n into the constructor." + "The _ ___init___ _ method takes only one parameter **n** i.e. the size of the problem. To create an instance, we simply just pass the required value of n into the constructor." ] }, { "cell_type": "code", "execution_count": 10, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "eight_queens = NQueensCSP(8)" @@ -969,18 +961,18 @@ "metadata": {}, "source": [ "We have defined our CSP. \n", - "We now need to solve this.\n", + "Now, we need to solve this.\n", "\n", "### Min-conflicts\n", "As stated above, the `min_conflicts` algorithm is an efficient method to solve such a problem.\n", "
\n", - "To begin with, all the variables of the CSP are _randomly_ initialized. \n", + "In the start, all the variables of the CSP are _randomly_ initialized. \n", "
\n", "The algorithm then randomly selects a variable that has conflicts and violates some constraints of the CSP.\n", "
\n", "The selected variable is then assigned a value that _minimizes_ the number of conflicts.\n", "
\n", - "This is a simple stochastic algorithm which works on a principle similar to **Hill-climbing**.\n", + "This is a simple **stochastic algorithm** which works on a principle similar to **Hill-climbing**.\n", "The conflicting state is repeatedly changed into a state with fewer conflicts in an attempt to reach an approximate solution.\n", "
\n", "This algorithm sometimes benefits from having a good initial assignment.\n", @@ -1123,9 +1115,7 @@ { "cell_type": "code", "execution_count": 12, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "solution = min_conflicts(eight_queens)" @@ -1147,9 +1137,9 @@ "outputs": [ { "data": { - "image/png": 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qvMrfn7uovnoCQLshYCM2zZ5Xfv1w8L5XXvOejx4PThO2LwpmjANoZwRstNTC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\nYrfnP4SxJKkAAAAASUVORK5CYII=\n", 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\n", 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7ogjrfS+8pLm8AQBoVlsG7JM7/bc/uq619Sh5eK3/9refaW09AADF1RYBe9L4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\nAUlr8AXRtSNBAAAAAElFTkSuQmCC\n", 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\n", 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" ] }, "metadata": {}, @@ -1194,9 +1184,9 @@ "metadata": {}, "source": [ "The solution is a bit different this time. \n", - "Running the above cell several times should give you various valid solutions.\n", + "Running the above cell several times should give you different valid solutions.\n", "
\n", - "In the `search.ipynb` notebook, we will see how NQueensProblem can be solved using a heuristic search method such as `uniform_cost_search` and `astar_search`." + "In the `search.ipynb` notebook, we will see how NQueensProblem can be solved using a **heuristic search method** such as `uniform_cost_search` and `astar_search`." ] }, { @@ -1205,15 +1195,13 @@ "source": [ "### Helper Functions\n", "\n", - "We will now implement a few helper functions that will help us visualize the Coloring Problem. We will make some modifications to the existing Classes and Functions for additional book keeping. To begin we modify the **assign** and **unassign** methods in the **CSP** to add a copy of the assignment to the **assignment_history**. We call this new class **InstruCSP**. This will allow us to see how the assignment evolves over time." + "Now we will implement a few helper functions that will allow us to visualize the Coloring Problem; we'll also make a few modifications to the exisiting classes and functions for additional record keeping. To start with, we modify the **assign** and **unassign** methods in the **CSP** in order to add a copy of the assignment to the **assignment_history**. We name this new class as **InstruCSP**; it will allow us to see how the assignment evolves over the time. " ] }, { "cell_type": "code", "execution_count": 15, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "import copy\n", @@ -1236,15 +1224,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Next, we define **make_instru** which takes an instance of **CSP** and returns a **InstruCSP** instance. " + "Next, we define **make_instru** which takes an instance of **CSP** and returns an instance of **InstruCSP**." ] }, { "cell_type": "code", "execution_count": 16, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "def make_instru(csp):\n", @@ -1255,15 +1241,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We will now use a graph defined as a dictionary for plotting purposes in our Graph Coloring Problem. The keys are the nodes and their corresponding values are the nodes they are connected to." + "We will now use a graph defined as a dictionary for plotting purposes in our Graph Coloring Problem. The keys are the nodes and their values are the corresponding nodes they are connected to." ] }, { "cell_type": "code", "execution_count": 17, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "neighbors = {\n", @@ -1295,15 +1279,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we are ready to create an InstruCSP instance for our problem. We are doing this for an instance of **MapColoringProblem** class which inherits from the **CSP** Class. This means that our **make_instru** function will work perfectly for it." + "Now we are ready to create an InstruCSP instance for our problem. We are doing this for an instance of **MapColoringProblem** class which inherits from the **CSP** Class. This means that our **make_instru** function should work perfectly for it." ] }, { "cell_type": "code", "execution_count": 18, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "coloring_problem = MapColoringCSP('RGBY', neighbors)" @@ -1312,9 +1294,7 @@ { "cell_type": "code", "execution_count": 19, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "coloring_problem1 = make_instru(coloring_problem)" @@ -1325,14 +1305,14 @@ "metadata": {}, "source": [ "### CONSTRAINT PROPAGATION\n", - "Algorithms that solve CSPs have a choice between searching and or do a _constraint propagation_, a specific type of inference.\n", - "The constraints can be used to reduce the number of legal values for a another variable, which in turn can reduce the legal values for another variable, and so on.\n", + "Algorithms that solve CSPs have a choice between searching and or doing a _constraint propagation_, a specific type of inference.\n", + "The constraints can be used to reduce the number of legal values for another variable, which in turn can reduce the legal values for some other variable, and so on. \n", "
\n", "Constraint propagation tries to enforce _local consistency_.\n", "Consider each variable as a node in a graph and each binary constraint as an arc.\n", "Enforcing local consistency causes inconsistent values to be eliminated throughout the graph, \n", "a lot like the `GraphPlan` algorithm in planning, where mutex links are removed from a planning graph.\n", - "There are different types of local consistency:\n", + "There are different types of local consistencies:\n", "1. Node consistency\n", "2. Arc consistency\n", "3. Path consistency\n", @@ -1638,9 +1618,7 @@ { "cell_type": "code", "execution_count": 22, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "neighbors = parse_neighbors('A: B; B: ')\n", @@ -1659,9 +1637,7 @@ { "cell_type": "code", "execution_count": 23, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "csp = CSP(variables=None, domains=domains, neighbors=neighbors, constraints=constraints)" @@ -1697,9 +1673,7 @@ { "cell_type": "code", "execution_count": 25, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "constraints = lambda X, x, Y, y: (x % 2) == 0 and (x + y) == 4\n", @@ -1740,15 +1714,13 @@ "source": [ "## BACKTRACKING SEARCH\n", "\n", - "For solving a CSP the main issue with Naive search algorithms is that they can continue expanding obviously wrong paths. In backtracking search, we check constraints as we go. Backtracking is just the above idea combined with the fact that we are dealing with one variable at a time. Backtracking Search is implemented in the repository as the function **backtracking_search**. This is the same as **Figure 6.5** in the book. The function takes as input a CSP and few other optional parameters which can be used to further speed it up. The function returns the correct assignment if it satisfies the goal. We will discuss these later. Let us solve our **coloring_problem1** with **backtracking_search**." + "The main issue with using Naive Search Algorithms to solve a CSP is that they can continue to expand obviously wrong paths; whereas, in **backtracking search**, we check the constraints as we go and we deal with only one variable at a time. Backtracking Search is implemented in the repository as the function **backtracking_search**. This is the same as **Figure 6.5** in the book. The function takes as input a CSP and a few other optional parameters which can be used to speed it up further. The function returns the correct assignment if it satisfies the goal. However, we will discuss these later. For now, let us solve our **coloring_problem1** with **backtracking_search**." ] }, { "cell_type": "code", "execution_count": 27, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "result = backtracking_search(coloring_problem1)" @@ -1825,7 +1797,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now let us check the total number of assignments and unassignments which is the length of our assignment history." + "Now, let us check the total number of assignments and unassignments, which would be the length of our assignment history. We can see it by using the command below. " ] }, { @@ -1852,9 +1824,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now let us explore the optional keyword arguments that the **backtracking_search** function takes. These optional arguments help speed up the assignment further. Along with these, we will also point out to methods in the CSP class that help make this work. \n", + "Now let us explore the optional keyword arguments that the **backtracking_search** function takes. These optional arguments help speed up the assignment further. Along with these, we will also point out the methods in the CSP class that help to make this work. \n", "\n", - "The first of these is **select_unassigned_variable**. It takes in a function that helps in deciding the order in which variables will be selected for assignment. We use a heuristic called Most Restricted Variable which is implemented by the function **mrv**. The idea behind **mrv** is to choose the variable with the fewest legal values left in its domain. The intuition behind selecting the **mrv** or the most constrained variable is that it allows us to encounter failure quickly before going too deep into a tree if we have selected a wrong step before. The **mrv** implementation makes use of another function **num_legal_values** to sort out the variables by a number of legal values left in its domain. This function, in turn, calls the **nconflicts** method of the **CSP** to return such values.\n" + "The first one is **select_unassigned_variable**. It takes in, as a parameter, a function that helps in deciding the order in which the variables will be selected for assignment. We use a heuristic called Most Restricted Variable which is implemented by the function **mrv**. The idea behind **mrv** is to choose the variable with the least legal values left in its domain. The intuition behind selecting the **mrv** or the most constrained variable is that it allows us to encounter failure quickly before going too deep into a tree if we have selected a wrong step before. The **mrv** implementation makes use of another function **num_legal_values** to sort out the variables by the number of legal values left in its domain. This function, in turn, calls the **nconflicts** method of the **CSP** to return such values." ] }, { @@ -2209,7 +2181,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Another ordering related parameter **order_domain_values** governs the value ordering. Here we select the Least Constraining Value which is implemented by the function **lcv**. The idea is to select the value which rules out the fewest values in the remaining variables. The intuition behind selecting the **lcv** is that it leaves a lot of freedom to assign values later. The idea behind selecting the mrc and lcv makes sense because we need to do all variables but for values, we might better try the ones that are likely. So for vars, we face the hard ones first.\n" + "Another ordering related parameter **order_domain_values** governs the value ordering. Here we select the Least Constraining Value which is implemented by the function **lcv**. The idea is to select the value which rules out least number of values in the remaining variables. The intuition behind selecting the **lcv** is that it allows a lot of freedom to assign values later. The idea behind selecting the mrc and lcv makes sense because we need to do all variables but for values, and it's better to try the ones that are likely. So for vars, we face the hard ones first." ] }, { @@ -2330,22 +2302,20 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Finally, the third parameter **inference** can make use of one of the two techniques called Arc Consistency or Forward Checking. The details of these methods can be found in the **Section 6.3.2** of the book. In short the idea of inference is to detect the possible failure before it occurs and to look ahead to not make mistakes. **mac** and **forward_checking** implement these two techniques. The **CSP** methods **support_pruning**, **suppose**, **prune**, **choices**, **infer_assignment** and **restore** help in using these techniques. You can know more about these by looking up the source code." + "Finally, the third parameter **inference** can make use of one of the two techniques called Arc Consistency or Forward Checking. The details of these methods can be found in the **Section 6.3.2** of the book. In short the idea of inference is to detect the possible failure before it occurs and to look ahead to not make mistakes. **mac** and **forward_checking** implement these two techniques. The **CSP** methods **support_pruning**, **suppose**, **prune**, **choices**, **infer_assignment** and **restore** help in using these techniques. You can find out more about these by looking up the source code." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now let us compare the performance with these parameters enabled vs the default parameters. We will use the Graph Coloring problem instance usa for comparison. We will call the instances **solve_simple** and **solve_parameters** and solve them using backtracking and compare the number of assignments." + "Now let us compare the performance with these parameters enabled vs the default parameters. We will use the Graph Coloring problem instance 'usa' for comparison. We will call the instances **solve_simple** and **solve_parameters** and solve them using backtracking and compare the number of assignments." ] }, { "cell_type": "code", "execution_count": 35, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "solve_simple = copy.deepcopy(usa)\n", @@ -2360,55 +2330,55 @@ { "data": { "text/plain": [ - "{'AL': 'G',\n", - " 'AR': 'G',\n", - " 'AZ': 'B',\n", - " 'CA': 'Y',\n", - " 'CO': 'B',\n", - " 'CT': 'R',\n", - " 'DC': 'G',\n", - " 'DE': 'B',\n", - " 'FL': 'R',\n", - " 'GA': 'B',\n", - " 'IA': 'G',\n", - " 'ID': 'B',\n", - " 'IL': 'R',\n", - " 'IN': 'B',\n", - " 'KA': 'G',\n", - " 'KY': 'G',\n", - " 'LA': 'R',\n", - " 'MA': 'G',\n", + "{'NJ': 'R',\n", + " 'DE': 'G',\n", + " 'PA': 'B',\n", " 'MD': 'R',\n", - " 'ME': 'R',\n", - " 'MI': 'G',\n", - " 'MN': 'R',\n", - " 'MO': 'B',\n", - " 'MS': 'B',\n", - " 'MT': 'R',\n", - " 'NC': 'G',\n", - " 'ND': 'G',\n", - " 'NE': 'R',\n", - " 'NH': 'B',\n", - " 'NJ': 'R',\n", - " 'NM': 'G',\n", - " 'NV': 'G',\n", - " 'NY': 'B',\n", + " 'NY': 'G',\n", + " 'WV': 'G',\n", + " 'VA': 'B',\n", " 'OH': 'R',\n", + " 'KY': 'Y',\n", + " 'IN': 'G',\n", + " 'IL': 'R',\n", + " 'MO': 'G',\n", + " 'TN': 'R',\n", + " 'AR': 'B',\n", " 'OK': 'R',\n", - " 'OR': 'R',\n", - " 'PA': 'G',\n", - " 'RI': 'B',\n", + " 'IA': 'B',\n", + " 'NE': 'R',\n", + " 'MI': 'B',\n", + " 'TX': 'G',\n", + " 'NM': 'B',\n", + " 'LA': 'R',\n", + " 'KA': 'B',\n", + " 'NC': 'G',\n", + " 'GA': 'B',\n", + " 'MS': 'G',\n", + " 'AL': 'Y',\n", + " 'CO': 'G',\n", + " 'WY': 'B',\n", " 'SC': 'R',\n", - " 'SD': 'B',\n", - " 'TN': 'R',\n", - " 'TX': 'B',\n", + " 'FL': 'R',\n", " 'UT': 'R',\n", - " 'VA': 'B',\n", + " 'ID': 'G',\n", + " 'SD': 'G',\n", + " 'MT': 'R',\n", + " 'ND': 'B',\n", + " 'DC': 'G',\n", + " 'NV': 'B',\n", + " 'OR': 'R',\n", + " 'MN': 'R',\n", + " 'CA': 'G',\n", + " 'AZ': 'Y',\n", + " 'WA': 'B',\n", + " 'WI': 'G',\n", + " 'CT': 'R',\n", + " 'MA': 'B',\n", " 'VT': 'R',\n", - " 'WA': 'G',\n", - " 'WI': 'B',\n", - " 'WV': 'Y',\n", - " 'WY': 'G'}" + " 'NH': 'G',\n", + " 'RI': 'G',\n", + " 'ME': 'R'}" ] }, "execution_count": 36, @@ -2469,15 +2439,15 @@ "\n", "The `tree_csp_solver` function (**Figure 6.11** in the book) can be used to solve problems whose constraint graph is a tree. Given a CSP, with `neighbors` forming a tree, it returns an assignment that satisfies the given constraints. The algorithm works as follows:\n", "\n", - "First it finds the *topological sort* of the tree. This is an ordering of the tree where each variable/node comes after its parent in the tree. The function that accomplishes this is `topological_sort`, which builds the topological sort using the recursive function `build_topological`. That function is an augmented DFS, where each newly visited node of the tree is pushed on a stack. The stack in the end holds the variables topologically sorted.\n", + "First it finds the *topological sort* of the tree. This is an ordering of the tree where each variable/node comes after its parent in the tree. The function that accomplishes this is `topological_sort`; it builds the topological sort using the recursive function `build_topological`. That function is an augmented DFS (Depth First Search), where each newly visited node of the tree is pushed on a stack. The stack in the end holds the variables topologically sorted.\n", "\n", - "Then the algorithm makes arcs between each parent and child consistent. *Arc-consistency* between two variables, *a* and *b*, occurs when for every possible value of *a* there is an assignment in *b* that satisfies the problem's constraints. If such an assignment cannot be found, then the problematic value is removed from *a*'s possible values. This is done with the use of the function `make_arc_consistent` which takes as arguments a variable `Xj` and its parent, and makes the arc between them consistent by removing any values from the parent which do not allow for a consistent assignment in `Xj`.\n", + "Then the algorithm makes arcs between each parent and child consistent. *Arc-consistency* between two variables, *a* and *b*, occurs when for every possible value of *a* there is an assignment in *b* that satisfies the problem's constraints. If such an assignment cannot be found, the problematic value is removed from *a*'s possible values. This is done with the use of the function `make_arc_consistent`, which takes as arguments a variable `Xj` and its parent, and makes the arc between them consistent by removing any values from the parent which do not allow for a consistent assignment in `Xj`.\n", "\n", "If an arc cannot be made consistent, the solver fails. If every arc is made consistent, we move to assigning values.\n", "\n", - "First we assign a random value to the root from its domain and then we start assigning values to the rest of the variables. Since the graph is now arc-consistent, we can simply move from variable to variable picking any remaining consistent values. At the end we are left with a valid assignment. If at any point though we find a variable where no consistent value is left in its domain, the solver fails.\n", + "First we assign a random value to the root from its domain and then we assign values to the rest of the variables. Since the graph is now arc-consistent, we can simply move from variable to variable picking any remaining consistent values. At the end we are left with a valid assignment. If at any point though we find a variable where no consistent value is left in its domain, the solver fails.\n", "\n", - "The implementation of the algorithm:" + "Run the cell below to see the implementation of the algorithm:" ] }, { @@ -2611,19 +2581,17 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We will now use the above function to solve a problem. More specifically, we will solve the problem of coloring the map of Australia. At our disposal we have two colors: Red and Blue. As a reminder, this is the graph of Australia:\n", + "We will now use the above function to solve a problem. More specifically, we will solve the problem of coloring Australia's map. We have two colors at our disposal: Red and Blue. As a reminder, this is the graph of Australia:\n", "\n", "`\"SA: WA NT Q NSW V; NT: WA Q; NSW: Q V; T: \"`\n", "\n", - "Unfortunately as you can see the above is not a tree. If, though, we remove `SA`, which has arcs to `WA`, `NT`, `Q`, `NSW` and `V`, we are left with a tree (we also remove `T`, since it has no in-or-out arcs). We can now solve this using our algorithm. Let's define the map coloring problem at hand:" + "Unfortunately, as you can see, the above is not a tree. However, if we remove `SA`, which has arcs to `WA`, `NT`, `Q`, `NSW` and `V`, we are left with a tree (we also remove `T`, since it has no in-or-out arcs). We can now solve this using our algorithm. Let's define the map coloring problem at hand:" ] }, { "cell_type": "code", "execution_count": 40, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "australia_small = MapColoringCSP(list('RB'),\n", @@ -2634,7 +2602,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We will input `australia_small` to the `tree_csp_solver` and we will print the given assignment." + "We will input `australia_small` to the `tree_csp_solver` and print the given assignment." ] }, { @@ -2668,15 +2636,13 @@ "source": [ "## GRAPH COLORING VISUALIZATION\n", "\n", - "Next, we define some functions to create the visualisation from the assignment_history of **coloring_problem1**. The reader need not concern himself with the code that immediately follows as it is the usage of Matplotib with IPython Widgets. If you are interested in reading more about these visit [ipywidgets.readthedocs.io](http://ipywidgets.readthedocs.io). We will be using the **networkx** library to generate graphs. These graphs can be treated as the graph that needs to be colored or as a constraint graph for this problem. If interested you can read a dead simple tutorial [here](https://www.udacity.com/wiki/creating-network-graphs-with-python). We start by importing the necessary libraries and initializing matplotlib inline.\n" + "Next, we define some functions to create the visualisation from the assignment_history of **coloring_problem1**. The readers need not concern themselves with the code that immediately follows as it is the usage of Matplotib with IPython Widgets. If you are interested in reading more about these, visit [ipywidgets.readthedocs.io](http://ipywidgets.readthedocs.io). We will be using the **networkx** library to generate graphs. These graphs can be treated as graphs that need to be colored or as constraint graphs for this problem. If interested you can check out a fairly simple tutorial [here](https://www.udacity.com/wiki/creating-network-graphs-with-python). We start by importing the necessary libraries and initializing matplotlib inline.\n" ] }, { "cell_type": "code", "execution_count": 42, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", @@ -2690,23 +2656,21 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The ipython widgets we will be using require the plots in the form of a step function such that there is a graph corresponding to each value. We define the **make_update_step_function** which return such a function. It takes in as inputs the neighbors/graph along with an instance of the **InstruCSP**. This will be more clear with the example below. If this sounds confusing do not worry this is not the part of the core material and our only goal is to help you visualize how the process works." + "The ipython widgets we will be using require the plots in the form of a step function such that there is a graph corresponding to each value. We define the **make_update_step_function** which returns such a function. It takes in as inputs the neighbors/graph along with an instance of the **InstruCSP**. The example below will elaborate it further. If this sounds confusing, don't worry. This is not part of the core material and our only goal is to help you visualize how the process works." ] }, { "cell_type": "code", "execution_count": 43, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "def make_update_step_function(graph, instru_csp):\n", " \n", + " #define a function to draw the graphs\n", " def draw_graph(graph):\n", - " # create networkx graph\n", + " \n", " G=nx.Graph(graph)\n", - " # draw graph\n", " pos = nx.spring_layout(G,k=0.15)\n", " return (G, pos)\n", " \n", @@ -2725,11 +2689,11 @@ " nx.draw(G, pos, node_color=colors, node_size=500)\n", "\n", " labels = {label:label for label in G.node}\n", - " # Labels shifted by offset so as to not overlap nodes.\n", + " # Labels shifted by offset so that nodes don't overlap\n", " label_pos = {key:[value[0], value[1]+0.03] for key, value in pos.items()}\n", " nx.draw_networkx_labels(G, label_pos, labels, font_size=20)\n", "\n", - " # show graph\n", + " # display the graph\n", " plt.show()\n", "\n", " return update_step # <-- this is a function\n", @@ -2753,15 +2717,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Finally let us plot our problem. We first use the function above to obtain a step function." + "Finally let us plot our problem. We first use the function below to obtain a step function." ] }, { "cell_type": "code", "execution_count": 44, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "step_func = make_update_step_function(neighbors, coloring_problem1)" @@ -2771,15 +2733,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Next we set the canvas size." + "Next, we set the canvas size." ] }, { "cell_type": "code", "execution_count": 45, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "matplotlib.rcParams['figure.figsize'] = (18.0, 18.0)" @@ -2789,7 +2749,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Finally our plot using ipywidget slider and matplotib. You can move the slider to experiment and see the coloring change. It is also possible to move the slider using arrow keys or to jump to the value by directly editing the number with a double click. The **Visualize Button** will automatically animate the slider for you. The **Extra Delay Box** allows you to set time delay in seconds upto one second for each time step." + "Finally, our plot using ipywidget slider and matplotib. You can move the slider to experiment and see the colors change. It is also possible to move the slider using arrow keys or to jump to the value by directly editing the number with a double click. The **Visualize Button** will automatically animate the slider for you. The **Extra Delay Box** allows you to set time delay in seconds (upto one second) for each time step." ] }, { @@ -2799,26 +2759,28 @@ "outputs": [ { "data": { - "image/png": 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RN6EdAicAAADQFXET2iJwAgAAAN0QN6E9AicAAADQBXET2iRwAgAAAM0TN6FdAicAAADQ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\n6JLACcBgxE0AAAC6JnACMAh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+ "application/vnd.jupyter.widget-view+json": { + "model_id": "26b425b8fade4789a075632715b1afcd", + "version_major": 2, + "version_minor": 0 + }, "text/plain": [ - "" + "interactive(children=(IntSlider(value=0, description='iteration', max=20), Output()), _dom_classes=('widget-in…" ] }, "metadata": {}, "output_type": "display_data" }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "The installed widget Javascript is the wrong version. It must satisfy the semver range ~2.1.4.\n" - ] - }, { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "0a993a2fa8864b4d984f41784f8e1e8f" - } + "model_id": "179048eb3f8e41a1afc1ec22343dece4", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(ToggleButton(value=False, description='Visualize'), ToggleButtons(description='Extra Del…" + ] }, "metadata": {}, "output_type": "display_data" @@ -2847,15 +2809,13 @@ "source": [ "## N-QUEENS VISUALIZATION\n", "\n", - "Just like the Graph Coloring Problem we will start with defining a few helper functions to help us visualize the assignments as they evolve over time. The **make_plot_board_step_function** behaves similar to the **make_update_step_function** introduced earlier. It initializes a chess board in the form of a 2D grid with alternating 0s and 1s. This is used by **plot_board_step** function which draws the board using matplotlib and adds queens to it. This function also calls the **label_queen_conflicts** which modifies the grid placing 3 in positions in a position where there is a conflict." + "Just like the Graph Coloring Problem, we will start with defining a few helper functions to help us visualize the assignments as they evolve over time. The **make_plot_board_step_function** behaves similar to the **make_update_step_function** introduced earlier. It initializes a chess board in the form of a 2D grid with alternating 0s and 1s. This is used by **plot_board_step** function which draws the board using matplotlib and adds queens to it. This function also calls the **label_queen_conflicts** which modifies the grid placing a 3 in any position where there is a conflict." ] }, { "cell_type": "code", "execution_count": 47, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "def label_queen_conflicts(assignment,grid):\n", @@ -2868,7 +2828,7 @@ " down_conflicts = {temp_col:temp_row for temp_col,temp_row in assignment.items() \n", " if temp_row-temp_col == row-col and temp_col != col}\n", " \n", - " # Now marking the grid.\n", + " # Place a 3 in positions where this is a conflict\n", " for col, row in row_conflicts.items():\n", " grid[col][row] = 3\n", " for col, row in up_conflicts.items():\n", @@ -2917,15 +2877,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now let us visualize a solution obtained via backtracking. We use of the previosuly defined **make_instru** function for keeping a history of steps." + "Now let us visualize a solution obtained via backtracking. We make use of the previosuly defined **make_instru** function for keeping a history of steps." ] }, { "cell_type": "code", "execution_count": 48, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "twelve_queens_csp = NQueensCSP(12)\n", @@ -2936,9 +2894,7 @@ { "cell_type": "code", "execution_count": 49, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "backtrack_queen_step = make_plot_board_step_function(backtracking_instru_queen) # Step Function for Widgets" @@ -2948,7 +2904,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now finally we set some matplotlib parameters to adjust how our plot will look. The font is necessary because the Black Queen Unicode character is not a part of all fonts. You can move the slider to experiment and observe the how queens are assigned. It is also possible to move the slider using arrow keys or to jump to the value by directly editing the number with a double click.The **Visualize Button** will automatically animate the slider for you. The **Extra Delay Box** allows you to set time delay in seconds upto one second for each time step.\n" + "Now finally we set some matplotlib parameters to adjust how our plot will look like. The font is necessary because the Black Queen Unicode character is not a part of all fonts. You can move the slider to experiment and observe how the queens are assigned. It is also possible to move the slider using arrow keys or to jump to the value by directly editing the number with a double click. The **Visualize Button** will automatically animate the slider for you. The **Extra Delay Box** allows you to set time delay in seconds of upto one second for each time step." ] }, { @@ -2958,26 +2914,28 @@ "outputs": [ { "data": { - "image/png": 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+ "application/vnd.jupyter.widget-view+json": { + "model_id": "fa243795d27f47c0af2cd12cbefa5e52", + "version_major": 2, + "version_minor": 0 + }, "text/plain": [ - "" + "interactive(children=(IntSlider(value=0, description='iteration', max=473, step=0), Output()), _dom_classes=('…" ] }, "metadata": {}, "output_type": "display_data" }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "The installed widget Javascript is the wrong version. It must satisfy the semver range ~2.1.4.\n" - ] - }, { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "516a8bb7f00d48a0b208c3f69a6f887d" - } + "model_id": "bdea801600cb441697ea3a810cb747a9", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(ToggleButton(value=False, description='Visualize'), ToggleButtons(description='Extra Del…" + ] }, "metadata": {}, "output_type": "display_data" @@ -3010,9 +2968,7 @@ { "cell_type": "code", "execution_count": 51, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "conflicts_instru_queen = make_instru(twelve_queens_csp)\n", @@ -3022,9 +2978,7 @@ { "cell_type": "code", "execution_count": 52, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "conflicts_step = make_plot_board_step_function(conflicts_instru_queen)" @@ -3034,7 +2988,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The visualization has same features as the above. But here it also highlights the conflicts by labeling the conflicted queens with a red background." + "This visualization has same features as the one above; however, this one also highlights the conflicts by labeling the conflicted queens with a red background." ] }, { @@ -3044,26 +2998,28 @@ "outputs": [ { "data": { - "image/png": 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+ "application/vnd.jupyter.widget-view+json": { + "model_id": "3bf64b599e5e4f128da23ecce08f3f53", + "version_major": 2, + "version_minor": 0 + }, "text/plain": [ - "" + "interactive(children=(IntSlider(value=0, description='iteration', max=52, step=0), Output()), _dom_classes=('w…" ] }, "metadata": {}, "output_type": "display_data" }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "The installed widget Javascript is the wrong version. It must satisfy the semver range ~2.1.4.\n" - ] - }, { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "29f5dba226b3492383ad768b54876588" - } + "model_id": "e4ccaba569f34a78857f2de8af4f01f2", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(ToggleButton(value=False, description='Visualize'), ToggleButtons(description='Extra Del…" + ] }, "metadata": {}, "output_type": "display_data" @@ -3100,7 +3056,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.6.5" } }, "nbformat": 4, From 6ecf664cd3bb89eed9c9cab5d6f122710ea15d6b Mon Sep 17 00:00:00 2001 From: Muhammad Junaid <34795347+mkhalid1@users.noreply.github.com> Date: Tue, 2 Oct 2018 01:17:04 +0500 Subject: [PATCH 2/2] A few changes reversed Changed a few things from my original PR after a review from ad71. --- csp.ipynb | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/csp.ipynb b/csp.ipynb index 17978cf75..fcf8b5867 100644 --- a/csp.ipynb +++ b/csp.ipynb @@ -944,7 +944,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The _ ___init___ _ method takes only one parameter **n** i.e. the size of the problem. To create an instance, we simply just pass the required value of n into the constructor." + "The _ ___init___ _ method takes only one parameter **n** i.e. the size of the problem. To create an instance, we just pass the required value of n into the constructor." ] }, { @@ -1195,7 +1195,7 @@ "source": [ "### Helper Functions\n", "\n", - "Now we will implement a few helper functions that will allow us to visualize the Coloring Problem; we'll also make a few modifications to the exisiting classes and functions for additional record keeping. To start with, we modify the **assign** and **unassign** methods in the **CSP** in order to add a copy of the assignment to the **assignment_history**. We name this new class as **InstruCSP**; it will allow us to see how the assignment evolves over the time. " + "We will now implement a few helper functions that will allow us to visualize the Coloring Problem; we'll also make a few modifications to the existing classes and functions for additional record keeping. To begin, we modify the **assign** and **unassign** methods in the **CSP** in order to add a copy of the assignment to the **assignment_history**. We name this new class as **InstruCSP**; it will allow us to see how the assignment evolves over time. " ] }, { @@ -1279,7 +1279,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we are ready to create an InstruCSP instance for our problem. We are doing this for an instance of **MapColoringProblem** class which inherits from the **CSP** Class. This means that our **make_instru** function should work perfectly for it." + "Now we are ready to create an InstruCSP instance for our problem. We are doing this for an instance of **MapColoringProblem** class which inherits from the **CSP** Class. This means that our **make_instru** function will work perfectly for it." ] }, {