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"<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">num_legal_values</span><span class=\"p\">(</span><span class=\"n\">csp</span><span class=\"p\">,</span> <span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">):</span>\n",
" <span class=\"k\">if</span> <span class=\"n\">csp</span><span class=\"o\">.</span><span class=\"n\">curr_domains</span><span class=\"p\">:</span>\n",
" <span class=\"k\">return</span> <span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"n\">csp</span><span class=\"o\">.</span><span class=\"n\">curr_domains</span><span class=\"p\">[</span><span class=\"n\">var</span><span class=\"p\">])</span>\n",
" <span class=\"k\">else</span><span class=\"p\">:</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">count</span><span class=\"p\">(</span><span class=\"n\">csp</span><span class=\"o\">.</span><span class=\"n\">nconflicts</span><span class=\"p\">(</span><span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">val</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">)</span> <span class=\"o\">==</span> <span class=\"mi\">0</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">val</span> <span class=\"ow\">in</span> <span class=\"n\">csp</span><span class=\"o\">.</span><span class=\"n\">domains</span><span class=\"p\">[</span><span class=\"n\">var</span><span class=\"p\">])</span>\n",
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{
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"<div class=\"highlight\"><pre><span></span> <span class=\"k\">def</span> <span class=\"nf\">nconflicts</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">val</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Return the number of conflicts var=val has with other variables."""</span>\n",
" <span class=\"c1\"># Subclasses may implement this more efficiently</span>\n",
" <span class=\"k\">def</span> <span class=\"nf\">conflict</span><span class=\"p\">(</span><span class=\"n\">var2</span><span class=\"p\">):</span>\n",
" <span class=\"k\">return</span> <span class=\"p\">(</span><span class=\"n\">var2</span> <span class=\"ow\">in</span> <span class=\"n\">assignment</span> <span class=\"ow\">and</span>\n",
" <span class=\"ow\">not</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">constraints</span><span class=\"p\">(</span><span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">val</span><span class=\"p\">,</span> <span class=\"n\">var2</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">[</span><span class=\"n\">var2</span><span class=\"p\">]))</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">count</span><span class=\"p\">(</span><span class=\"n\">conflict</span><span class=\"p\">(</span><span class=\"n\">v</span><span class=\"p\">)</span> <span class=\"k\">for</span> <span class=\"n\">v</span> <span class=\"ow\">in</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">neighbors</span><span class=\"p\">[</span><span class=\"n\">var</span><span class=\"p\">])</span>\n",
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"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"
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"execution_count": 34,
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"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">lcv</span><span class=\"p\">(</span><span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">,</span> <span class=\"n\">csp</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Least-constraining-values heuristic."""</span>\n",
" <span class=\"k\">return</span> <span class=\"nb\">sorted</span><span class=\"p\">(</span><span class=\"n\">csp</span><span class=\"o\">.</span><span class=\"n\">choices</span><span class=\"p\">(</span><span class=\"n\">var</span><span class=\"p\">),</span>\n",
" <span class=\"n\">key</span><span class=\"o\">=</span><span class=\"k\">lambda</span> <span class=\"n\">val</span><span class=\"p\">:</span> <span class=\"n\">csp</span><span class=\"o\">.</span><span class=\"n\">nconflicts</span><span class=\"p\">(</span><span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">val</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">))</span>\n",
"</pre></div>\n",
"</body>\n",
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"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."
]
},
{
"cell_type": "markdown",
"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."
]
},
{
"cell_type": "code",
},
"outputs": [],
"source": [
"solve_simple = copy.deepcopy(usa)\n",
"solve_parameters = copy.deepcopy(usa)"
]
},
{
"cell_type": "code",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'AL': 'G',\n",
" 'AR': 'G',\n",
" 'AZ': '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",
" 'MI': 'G',\n",
" 'MN': 'R',\n",
" 'MO': 'B',\n",
" 'MS': 'B',\n",
" 'MT': 'R',\n",
" 'NC': 'G',\n",
" 'ND': 'G',\n",
" 'NE': 'R',\n",
" 'NJ': 'R',\n",
" 'NM': 'G',\n",
" 'NV': 'G',\n",
" 'OH': 'R',\n",
" 'OK': 'R',\n",
" 'OR': 'R',\n",
" 'PA': 'G',\n",
" 'SC': 'R',\n",
" 'SD': 'B',\n",
" 'TN': 'R',\n",
" 'TX': 'B',\n",
" 'UT': 'R',\n",
" 'VA': 'B',\n",
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"backtracking_search(solve_simple)\n",
"backtracking_search(solve_parameters, order_domain_values=lcv, select_unassigned_variable=mrv, inference=mac)"
]
},
{
"cell_type": "code",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"metadata": {},
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"source": [
"solve_simple.nassigns"
]
},
{
"cell_type": "code",
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"outputs": [
{
"data": {
"text/plain": [
"49"
]
},
"metadata": {},
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}
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"source": [
"solve_parameters.nassigns"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"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",
"\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",
"\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",
"\n",
"The implementation of the algorithm:"
]
},
{
"cell_type": "code",
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"execution_count": 39,
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"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">tree_csp_solver</span><span class=\"p\">(</span><span class=\"n\">csp</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""[Figure 6.11]"""</span>\n",
" <span class=\"n\">assignment</span> <span class=\"o\">=</span> <span class=\"p\">{}</span>\n",
" <span class=\"n\">root</span> <span class=\"o\">=</span> <span class=\"n\">csp</span><span class=\"o\">.</span><span class=\"n\">variables</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span>\n",
" <span class=\"n\">X</span><span class=\"p\">,</span> <span class=\"n\">parent</span> <span class=\"o\">=</span> <span class=\"n\">topological_sort</span><span class=\"p\">(</span><span class=\"n\">csp</span><span class=\"p\">,</span> <span class=\"n\">root</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"n\">csp</span><span class=\"o\">.</span><span class=\"n\">support_pruning</span><span class=\"p\">()</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">Xj</span> <span class=\"ow\">in</span> <span class=\"nb\">reversed</span><span class=\"p\">(</span><span class=\"n\">X</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">:]):</span>\n",
" <span class=\"k\">if</span> <span class=\"ow\">not</span> <span class=\"n\">make_arc_consistent</span><span class=\"p\">(</span><span class=\"n\">parent</span><span class=\"p\">[</span><span class=\"n\">Xj</span><span class=\"p\">],</span> <span class=\"n\">Xj</span><span class=\"p\">,</span> <span class=\"n\">csp</span><span class=\"p\">):</span>\n",
" <span class=\"k\">return</span> <span class=\"bp\">None</span>\n",
"\n",
" <span class=\"n\">assignment</span><span class=\"p\">[</span><span class=\"n\">root</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">csp</span><span class=\"o\">.</span><span class=\"n\">curr_domains</span><span class=\"p\">[</span><span class=\"n\">root</span><span class=\"p\">][</span><span class=\"mi\">0</span><span class=\"p\">]</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">Xi</span> <span class=\"ow\">in</span> <span class=\"n\">X</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">:]:</span>\n",
" <span class=\"n\">assignment</span><span class=\"p\">[</span><span class=\"n\">Xi</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">assign_value</span><span class=\"p\">(</span><span class=\"n\">parent</span><span class=\"p\">[</span><span class=\"n\">Xi</span><span class=\"p\">],</span> <span class=\"n\">Xi</span><span class=\"p\">,</span> <span class=\"n\">csp</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">)</span>\n",
" <span class=\"k\">if</span> <span class=\"ow\">not</span> <span class=\"n\">assignment</span><span class=\"p\">[</span><span class=\"n\">Xi</span><span class=\"p\">]:</span>\n",
" <span class=\"k\">return</span> <span class=\"bp\">None</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">assignment</span>\n",
"</pre></div>\n",
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"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",
"\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:"
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"australia_small = MapColoringCSP(list('RB'),\n",
" 'NT: WA Q; NSW: Q V')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will input `australia_small` to the `tree_csp_solver` and we will print the given assignment."
]
},
{
"cell_type": "code",
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'NT': 'R', 'Q': 'B', 'NSW': 'R', 'V': 'B', 'WA': 'B'}\n"
]
}
],
"source": [
"assignment = tree_csp_solver(australia_small)\n",
"print(assignment)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`WA`, `Q` and `V` got painted with the same color and `NT` and `NSW` got painted with the other."
{
"cell_type": "markdown",
"## GRAPH COLORING VISUALIZATION\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"
]
},
{
"cell_type": "code",
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import networkx as nx\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib\n",
"import time"
]
},
{
"cell_type": "markdown",
"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."
]
},
{
"cell_type": "code",
},
"outputs": [],
"source": [
"def make_update_step_function(graph, instru_csp):\n",
" \n",
" def draw_graph(graph):\n",
" # create networkx graph\n",
" G=nx.Graph(graph)\n",
" # draw graph\n",
" pos = nx.spring_layout(G,k=0.15)\n",
" return (G, pos)\n",
" \n",
" G, pos = draw_graph(graph)\n",
" \n",
" def update_step(iteration):\n",
" # here iteration is the index of the assignment_history we want to visualize.\n",
" current = instru_csp.assignment_history[iteration]\n",
" # We convert the particular assignment to a default dict so that the color for nodes which \n",
" # have not been assigned defaults to black.\n",
" current = defaultdict(lambda: 'Black', current)\n",
"\n",
" # Now we use colors in the list and default to black otherwise.\n",
" colors = [current[node] for node in G.node.keys()]\n",
" # Finally drawing the nodes.\n",
" 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",
" 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",
" plt.show()\n",
"\n",
" return update_step # <-- this is a function\n",
"\n",
"def make_visualize(slider):\n",
" ''' Takes an input a slider and returns \n",
" callback function for timer and animation\n",
" '''\n",
" \n",
" def visualize_callback(Visualize, time_step):\n",
" if Visualize is True:\n",
" for i in range(slider.min, slider.max + 1):\n",
" slider.value = i\n",
" time.sleep(float(time_step))\n",
" \n",
" return visualize_callback\n",
" "
]
},
{
"cell_type": "markdown",
"source": [
"Finally let us plot our problem. We first use the function above to obtain a step function."
]
},
{
"cell_type": "code",
},
"outputs": [],
"source": [
"step_func = make_update_step_function(neighbors, coloring_problem1)"
]
},
{
"cell_type": "markdown",
"source": [
"Next we set the canvas size."
]
},
{
"cell_type": "code",
},
"outputs": [],
"source": [
"matplotlib.rcParams['figure.figsize'] = (18.0, 18.0)"
]
},
{
"cell_type": "markdown",
"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."
]
},
{
"cell_type": "code",
"metadata": {},
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RN6EdAicAAADQFXET2iJwAgAAAN0QN6E9AicAAADQBXET2iRwAgAAAM0TN6FdAicAAADQ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\nRK5CYII=\n",
]
},
"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"
}
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import ipywidgets as widgets\n",
"from IPython.display import display\n",
"\n",
"iteration_slider = widgets.IntSlider(min=0, max=len(coloring_problem1.assignment_history)-1, step=1, value=0)\n",
"w=widgets.interactive(step_func,iteration=iteration_slider)\n",
"display(w)\n",
"\n",
"visualize_callback = make_visualize(iteration_slider)\n",
"\n",
"visualize_button = widgets.ToggleButton(description = \"Visualize\", value = False)\n",
"time_select = widgets.ToggleButtons(description='Extra Delay:',options=['0', '0.1', '0.2', '0.5', '0.7', '1.0'])\n",
"\n",
"a = widgets.interactive(visualize_callback, Visualize = visualize_button, time_step=time_select)\n",
"display(a)"
"## 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."
]
},
{
"cell_type": "code",
"def label_queen_conflicts(assignment,grid):\n",
" ''' Mark grid with queens that are under conflict. '''\n",
" for col, row in assignment.items(): # check each queen for conflict\n",
" row_conflicts = {temp_col:temp_row for temp_col,temp_row in assignment.items() \n",
" up_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",
" down_conflicts = {temp_col:temp_row for temp_col,temp_row in assignment.items() \n",
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" if temp_row-temp_col == row-col and temp_col != col}\n",
" \n",
" # Now marking the grid.\n",
" for col, row in row_conflicts.items():\n",
" grid[col][row] = 3\n",
" for col, row in up_conflicts.items():\n",
" grid[col][row] = 3\n",
" for col, row in down_conflicts.items():\n",
" grid[col][row] = 3\n",
"\n",
" return grid\n",
"\n",
"def make_plot_board_step_function(instru_csp):\n",
" '''ipywidgets interactive function supports\n",
" single parameter as input. This function\n",
" creates and return such a function by taking\n",
" in input other parameters.\n",
" '''\n",
" n = len(instru_csp.variables)\n",
" \n",
" \n",
" def plot_board_step(iteration):\n",
" ''' Add Queens to the Board.'''\n",
" data = instru_csp.assignment_history[iteration]\n",
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" \n",
" grid = [[(col+row+1)%2 for col in range(n)] for row in range(n)]\n",
" grid = label_queen_conflicts(data, grid) # Update grid with conflict labels.\n",
" \n",
" # color map of fixed colors\n",
" cmap = matplotlib.colors.ListedColormap(['white','lightsteelblue','red'])\n",
" bounds=[0,1,2,3] # 0 for white 1 for black 2 onwards for conflict labels (red).\n",
" norm = matplotlib.colors.BoundaryNorm(bounds, cmap.N)\n",
" \n",
" fig = plt.imshow(grid, interpolation='nearest', cmap = cmap,norm=norm)\n",
"\n",
" plt.axis('off')\n",
" fig.axes.get_xaxis().set_visible(False)\n",
" fig.axes.get_yaxis().set_visible(False)\n",
"\n",
" # Place the Queens Unicode Symbol\n",
" for col, row in data.items():\n",
" fig.axes.text(row, col, u\"\\u265B\", va='center', ha='center', family='Dejavu Sans', fontsize=32)\n",
" plt.show()\n",
" \n",
" return plot_board_step"
]
},
{
"cell_type": "markdown",
"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."
]
},
{
"cell_type": "code",
"twelve_queens_csp = NQueensCSP(12)\n",
"backtracking_instru_queen = make_instru(twelve_queens_csp)\n",
"result = backtracking_search(backtracking_instru_queen)"
]
},
{
"cell_type": "code",
},
"outputs": [],
"source": [
"backtrack_queen_step = make_plot_board_step_function(backtracking_instru_queen) # Step Function for Widgets"
]
},
{
"cell_type": "markdown",
"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"
"metadata": {},
"outputs": [
{
"data": {
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]
},
"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"
}
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"matplotlib.rcParams['figure.figsize'] = (8.0, 8.0)\n",
"matplotlib.rcParams['font.family'].append(u'Dejavu Sans')\n",
"\n",
"iteration_slider = widgets.IntSlider(min=0, max=len(backtracking_instru_queen.assignment_history)-1, step=0, value=0)\n",
"w=widgets.interactive(backtrack_queen_step,iteration=iteration_slider)\n",
"display(w)\n",
"\n",
"visualize_callback = make_visualize(iteration_slider)\n",
"\n",
"visualize_button = widgets.ToggleButton(description = \"Visualize\", value = False)\n",
"time_select = widgets.ToggleButtons(description='Extra Delay:',options=['0', '0.1', '0.2', '0.5', '0.7', '1.0'])\n",
"\n",
"a = widgets.interactive(visualize_callback, Visualize = visualize_button, time_step=time_select)\n",
"display(a)"