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Notebook: Grid #459

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Apr 6, 2017
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Notebook: Grid #459

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162 changes: 157 additions & 5 deletions grid.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -10,8 +10,150 @@
"source": [
"# Grid\n",
"\n",
"The functions here are used often when dealing with 2D grids (like in TicTacToe).\n",
"The functions here are used often when dealing with 2D grids (like in TicTacToe)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Heading\n",
"\n",
"With the `turn_heading`, `turn_left` and `turn_right` functions an agent can turn around in a grid. In a 2D grid the orientations normally are:\n",
"\n",
"* North: (0,1)\n",
"* South: (0,-1)\n",
"* East: (1,0)\n",
"* West: (-1,0)\n",
"\n",
"In code:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"orientations = [(1, 0), (0, 1), (-1, 0), (0, -1)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We signify a left turn with a +1 and a right turn with a -1.\n",
"\n",
"The functions `turn_left` and `turn_right` call `turn_heading`, which then turns the agent around according to the input.\n",
"\n",
"First the code for `turn_heading`:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def turn_heading(heading, inc, headings=orientations):\n",
" return headings[(headings.index(heading) + inc) % len(headings)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now use the function to turn left:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(-1, 0)\n"
]
}
],
"source": [
"print(turn_heading((0, 1), 1))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We were facing north and we turned left, so we are now facing west.\n",
"\n",
"Let's now take a look at the other two functions, which automate this process:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def turn_right(heading):\n",
" return turn_heading(heading, -1)\n",
"\n",
"def turn_left(heading):\n",
" return turn_heading(heading, +1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first one turns the agent right, so it passes -1 to `turn_heading`, while the second one turns the agent left, so it passes +1.\n",
"\n",
"Let's see what happens when we are facing north and want to turn left and right:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(-1, 0)\n",
"(1, 0)\n"
]
}
],
"source": [
"print(turn_left((0, 1)))\n",
"print(turn_right((0, 1)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"When we turn left from north we end up facing west, while on the other hand if we turn right we end up facing east."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Distance\n",
"\n",
"The function returns the Euclidean Distance between two points in the 2D space."
Expand Down Expand Up @@ -139,7 +281,9 @@
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
Expand All @@ -154,7 +298,10 @@
},
{
"cell_type": "markdown",
"metadata": {},
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"For example:"
]
Expand All @@ -163,7 +310,9 @@
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
Expand All @@ -180,7 +329,10 @@
},
{
"cell_type": "markdown",
"metadata": {},
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"The vector we wanted to clip was the tuple (-1, 10). The lowest allowed values were (0, 0) and the highest (9, 9). So, the result is the tuple (0,9)."
]
Expand Down