Added A* algorithm (#1913)

* a* algorithm

* changes after build error

* intent changes

* fix after review

* ImportMissmatchError

* Build failed fix

* doctest changes

* doctest changes

machine_learning/astar.py

@@ -0,0 +1,152 @@
+import numpy as np
+
+'''
+The A* algorithm combines features of uniform-cost search and pure
+heuristic search to efficiently compute optimal solutions.
+A* algorithm is a best-first search algorithm in which the cost
+associated with a node is f(n) = g(n) + h(n),
+where g(n) is the cost of the path from the initial state to node n and
+h(n) is the heuristic estimate or the cost or a path
+from node n to a goal.A* algorithm introduces a heuristic into a
+regular graph-searching algorithm,
+essentially planning ahead at each step so a more optimal decision
+is made.A* also known as the algorithm with brains
+'''
+
+
+class Cell(object):
+    '''
+    Class cell represents a cell in the world which have the property
+    position : The position of the represented by  tupleof x and y
+    co-ordinates initially set to (0,0)
+    parent : This contains the parent cell object which we visited
+    before arrinving this cell
+    g,h,f : The parameters for constructing the heuristic function
+    which can be any function. for simplicity used line
+    distance
+    '''
+    def __init__(self):
+        self.position = (0, 0)
+        self.parent = None
+
+        self.g = 0
+        self.h = 0
+        self.f = 0
+    '''
+    overrides equals method because otherwise cell assign will give
+    wrong results
+    '''
+    def __eq__(self, cell):
+        return self.position == cell.position
+
+    def showcell(self):
+        print(self.position)
+
+
+class Gridworld(object):
+
+    '''
+    Gridworld class represents the  external world here a grid M*M
+    matrix
+    w    : create a numpy array with the given world_size default is 5
+    '''
+
+    def __init__(self, world_size=(5, 5)):
+        self.w = np.zeros(world_size)
+        self.world_x_limit = world_size[0]
+        self.world_y_limit = world_size[1]
+
+    def show(self):
+        print(self.w)
+
+    '''
+    get_neighbours
+    As the name suggests this function will return the neighbours of
+    the a particular cell
+    '''
+    def get_neigbours(self, cell):
+        neughbour_cord = [
+            (-1, -1), (-1, 0), (-1, 1), (0, -1),
+            (0, 1), (1, -1), (1, 0), (1, 1)]
+        current_x = cell.position[0]
+        current_y = cell.position[1]
+        neighbours = []
+        for n in neughbour_cord:
+            x = current_x + n[0]
+            y = current_y + n[1]
+            if (
+               (x >= 0 and x < self.world_x_limit) and
+               (y >= 0 and y < self.world_y_limit)):
+                c = Cell()
+                c.position = (x, y)
+                c.parent = cell
+                neighbours.append(c)
+        return neighbours
+
+'''
+Implementation of a start algorithm
+world : Object of the world object
+start : Object of the cell as  start position
+stop  : Object of the cell as goal position
+'''
+
+
+def astar(world, start, goal):
+    '''
+    >>> p = Gridworld()
+    >>> start = Cell()
+    >>> start.position = (0,0)
+    >>> goal = Cell()
+    >>> goal.position = (4,4)
+    >>> astar(p, start, goal)
+    [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4)]
+    '''
+    _open = []
+    _closed = []
+    _open.append(start)
+
+    while _open:
+        min_f = np.argmin([n.f for n in _open])
+        current = _open[min_f]
+        _closed.append(_open.pop(min_f))
+        if current == goal:
+            break
+        for n in world.get_neigbours(current):
+            for c in _closed:
+                if c == n:
+                    continue
+            n.g = current.g + 1
+            x1, y1 = n.position
+            x2, y2 = goal.position
+            n.h = (y2 - y1)**2 + (x2 - x1)**2
+            n.f = n.h + n.g
+
+            for c in _open:
+                if c == n and c.f < n.f:
+                    continue
+            _open.append(n)
+    path = []
+    while current.parent is not None:
+        path.append(current.position)
+        current = current.parent
+    path.append(current.position)
+    path = path[::-1]
+    return path
+
+if __name__ == '__main__':
+    '''
+    sample run
+    '''
+#   object for the world
+    p = Gridworld()
+#   stat position and Goal
+    start = Cell()
+    start.position = (0, 0)
+    goal = Cell()
+    goal.position = (4, 4)
+    print("path from {} to {} ".format(start.position, goal.position))
+    s = astar(p, start, goal)
+#   Just for visual Purpose
+    for i in s:
+        p.w[i] = 1
+    print(p.w)