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IMAGE_LICENSE.md

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+("Chess qdt45.svg")[https://commons.wikimedia.org/wiki/File:Chess_qdt45.svg] by [Colin M.L. Burnett](https://en.wikipedia.org/wiki/User:Cburnett) is licensed under [CC Attribution-Share Alike 3.0 Unported](https://creativecommons.org/licenses/by-sa/3.0/deed.en).

README.md

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+In this exercise you will explore Constraint Satisfaction Problems by implementing the N-Queens problem using symbolic constraints in a Jupyter notebook, and solving it using the Backtracking Search algorithm from AIMA.
+
+To launch the notebook, run the following command from a terminal with anaconda3 installed and on the application path:
+
+    jupyter notebook AIND-Constraint_Satisfaction.ipynb

util.py

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+
+import matplotlib as mpl
+import matplotlib.pyplot as plt
+import numpy as np
+
+from sympy import *
+
+
+def constraint(name, expr):
+    """Augment the sympy Function class by attaching a symbolic expression
+    and making the function evaluatable by patching the .subs() method.
+
+    Parameters
+    ----------
+    name : str
+        A string defining the name of the function
+
+    expr : sympy.Expr
+        A symbolic expression that can be evaluated for a particular
+        assignment to determine whether the constraint is True, False,
+        or undetermined
+
+    Returns
+    -------
+    sympy.Function or sympy.Expr
+        If the expression still has unassigned free variables, then a
+        Function is returned with an attached Expr object; otherwise
+        the expression is returned unchanged
+    """
+    if not len(expr.free_symbols):
+        return expr
+    func = Function(name)(*expr.free_symbols)
+    setattr(func, "expr", expr)
+    setattr(func, "subs", lambda *a, **b: constraint(name, expr.subs(*a, **b)))
+    setattr(func, "_subs", lambda *a, **b: expr.subs(*a, **b))
+    return func
+
+
+def displayBoard(locations, shape):
+    """Draw a chessboard with queens placed at each position specified
+    by the assignment.
+
+    Parameters
+    ----------
+    locations : list
+        The locations list should contain one element for each queen
+        of the chessboard containing a tuple (r, c) indicating the
+        row and column coordinates of a queen to draw on the board.
+
+    shape : integer
+        The number of cells in each dimension of the board (e.g.,
+        shape=3 indicates a 3x3 board)
+
+    Returns
+    -------
+    matplotlib.figure.Figure
+        The handle to the figure containing the board and queens
+    """
+    r = c = shape
+    cmap = mpl.colors.ListedColormap(['#f5ecce', '#614532'])
+    img = mpl.image.imread('queen.png').astype(np.float)
+    boxprops = {"facecolor": "none", "edgecolor": "none"}
+
+    x, y = np.meshgrid(range(c), range(r))
+    plt.matshow(x % 2 ^ y % 2, cmap=cmap)
+    plt.axis("off")  # eliminate borders from plot
+
+    fig = plt.gcf()
+    fig.set_size_inches([r, c])
+    scale = fig.get_dpi() / max(img.shape)
+    ax = plt.gca()
+    for y, x in set(locations):
+        box = mpl.offsetbox.OffsetImage(img, zoom=scale)
+        ab = mpl.offsetbox.AnnotationBbox(box, (y, x), bboxprops=boxprops)
+        ax.add_artist(ab)
+
+    plt.show()
+    return fig