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Helper Functions & Backtracking Search
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‎csp.ipynb

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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"collapsed": false
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"['R', 'G', 'B']"
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]
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},
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"metadata": {},
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"output_type": "execute_result"
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"cell_type": "code",
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{
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"cell_type": "code",
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"execution_count": 5,
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"%pdoc parse_neighbors"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The **MapColoringCSP** function creates and returns a CSP with the above constraint function and states. The variables our 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."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"%psource MapColoringCSP"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(<csp.CSP at 0x7f9da0d9aa58>,\n",
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" <csp.CSP at 0x7f9da0da0ac8>,\n",
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" <csp.CSP at 0x7f9da0d2a080>)"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"australia, usa, france"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Helper Functions\n",
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"\n",
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"We will now implement 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 with we modify the **assign** and **unassign** methods in the **CSP** to add a copy of the assignment to the **assingment_history**. We call this new class **InstruCSP**. This would allow us to see how the assignment evolves over time."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"import copy\n",
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"class InstruCSP(CSP):\n",
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" \n",
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" def __init__(self, variables, domains, neighbors, constraints):\n",
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" super().__init__(variables, domains, neighbors, constraints)\n",
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" self.assingment_history = []\n",
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" \n",
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" def assign(self, var, val, assignment):\n",
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" super().assign(var,val, assignment)\n",
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" self.assingment_history.append(copy.deepcopy(assignment))\n",
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" \n",
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" def unassign(self, var, assignment):\n",
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" super().unassign(var,assignment)\n",
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" self.assingment_history.append(copy.deepcopy(assignment)) "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Next, we modify the **MapColoringCSP** function to use the **InstruCSP**. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"def ModMapColoringCSP(colors, neighbors):\n",
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" if isinstance(neighbors, str):\n",
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" neighbors = parse_neighbors(neighbors)\n",
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" return InstruCSP(list(neighbors.keys()), UniversalDict(colors), neighbors,\n",
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" different_values_constraint)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We will now use the france graph for plotting purposes. The **parse_neighbors** function is used for parsing them."
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]
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},
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"cell_type": "code",
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"execution_count": 10,
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"collapsed": true
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"outputs": [],
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"source": []
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"source": [
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"neighbors = parse_neighbors(\"\"\"AL: LO FC; AQ: MP LI PC; AU: LI CE BO RA LR MP; BO: CE IF CA FC RA\n",
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" AU; BR: NB PL; CA: IF PI LO FC BO; CE: PL NB NH IF BO AU LI PC; FC: BO\n",
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" CA LO AL RA; IF: NH PI CA BO CE; LI: PC CE AU MP AQ; LO: CA AL FC; LR:\n",
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" MP AU RA PA; MP: AQ LI AU LR; NB: NH CE PL BR; NH: PI IF CE NB; NO:\n",
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" PI; PA: LR RA; PC: PL CE LI AQ; PI: NH NO CA IF; PL: BR NB CE PC; RA:\n",
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" AU BO FC PA LR\"\"\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Now we are ready to create an InstruCSP instance for our problem."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"coloring_problem1 = ModMapColoringCSP('RGBY', neighbors)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Backtracking Search\n",
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"\n",
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"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**.\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"result = backtracking_search(coloring_problem1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"{'AL': 'R',\n",
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" 'AQ': 'B',\n",
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" 'AU': 'G',\n",
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" 'BO': 'B',\n",
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" 'BR': 'Y',\n",
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" 'CA': 'R',\n",
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" 'CE': 'R',\n",
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" 'FC': 'Y',\n",
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" 'IF': 'G',\n",
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" 'LI': 'Y',\n",
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" 'LO': 'G',\n",
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" 'LR': 'Y',\n",
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" 'MP': 'R',\n",
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" 'NB': 'G',\n",
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" 'NH': 'B',\n",
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" 'NO': 'R',\n",
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" 'PA': 'G',\n",
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" 'PC': 'G',\n",
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" 'PI': 'Y',\n",
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" 'PL': 'B',\n",
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" 'RA': 'R'}"
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]
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},
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"execution_count": 13,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"result # A dictonary of assingments."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Let us also check the number of assingments made."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"37"
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]
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},
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"execution_count": 14,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"coloring_problem1.nassigns"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Now let us check the total number of assingments and unassingments which is the lentgh ofour assingment history."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {
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"collapsed": false
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"outputs": [
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{
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"data": {
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"text/plain": [
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"53"
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},
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"execution_count": 15,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"len(coloring_problem1.assingment_history)"
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]
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}
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],
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"metadata": {

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