Added Dijkstra Algorithm [Python] (iiitv#291)

Author: Monal5031

README.md

@@ -20,7 +20,7 @@ Community (college) maintained list of Algorithms and Data Structures implementa
 | [Coin Change Problem](http://www.algorithmist.com/index.php/Coin_Change) | [:white_check_mark:](coin_change_problem/coin_change_problem.c) | | [:white_check_mark:](coin_change_problem/CoinChange.java) | [:white_check_mark:](coin_change_problem/coin_change_problem.py) | | |
 | [Counting Sort](http://www.geeksforgeeks.org/counting-sort/)| [:white_check_mark:](counting_sort/counting_sort.c) | | [:white_check_mark:](counting_sort/CountingSort.java) | | | |
 | [Depth First Traversal](http://www.geeksforgeeks.org/depth-first-traversal-for-a-graph/) | | | [:white_check_mark:](depth_first_traversal/DepthFirstTraversal.java) | | | |
-| [Dijkstra Algorithm](https://en.wikipedia.org/wiki/Dijkstra's_algorithm/) | [:white_check_mark:](dijkstra/dijkstra.c) | | [:white_check_mark:](dijkstra/Dijkstra.java) | | | |
+| [Dijkstra Algorithm](https://en.wikipedia.org/wiki/Dijkstra's_algorithm/) | [:white_check_mark:](dijkstra/dijkstra.c) | | [:white_check_mark:](dijkstra/Dijkstra.java) | [:white_check_mark:](dijkstra/dijkstra.py) | | |
 | [Euclidean GCD](https://en.wikipedia.org/wiki/Euclidean_algorithm) | [:white_check_mark:](euclidean_gcd/euclidean_gcd.c) | | [:white_check_mark:](euclidean_gcd/EuclideanGCD.java) | [:white_check_mark:](euclidean_gcd/euclidean_gcd.py) | | |
 | [Exponentation by Squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring) | [:white_check_mark:](exponentation_by_squaring/exponentation_by_squaring.c) | | | [:white_check_mark:](exponentation_by_squaring/exponentation_by_squaring.py) | | |
 | [Heap Sort](https://en.wikipedia.org/wiki/Heapsort) | [:white_check_mark:](heap_sort/heap_sort.c) | | [:white_check_mark:](heap_sort/HeapSort.java) | [:white_check_mark:](heap_sort/heap_sort.py) | | |

dijkstra/dijkstra.py

@@ -0,0 +1,75 @@
+"""
+Dijktra's shortest path algorithm. Finds the path and distance from source to target.
+To add an edge between vertex a and b with distance dist:
+    graph[a].append((b, dist)) and graph[b].append((a, dist)).
+"""
+
+
+import heapq
+
+
+def dijkstra(graph, source, target):
+    """
+    Finds the shortest path and shortest distance from source to target
+
+    :param graph: Dictionary linking the vertices using list of tuples
+    :param source: The vertex to start the path.
+    :param target: The vertex to end the path.
+    :return: shortest path and distance from source to target
+    """
+    INF = float('Inf')
+    predecessors = {x: x for x in graph}
+    distances = {x: INF for x in graph}
+    distances[source] = 0
+    temp = []
+    heapq.heappush(temp, [source, distances[source]])
+
+    while temp:
+        u = heapq.heappop(temp)
+        u_dist = u[1]
+        u_idx = u[0]
+        if u_dist == distances[u_idx]:
+            for v in graph[u_idx]:
+                v_idx = v[0]
+                u2v = v[1]
+                if distances[u_idx] + u2v < distances[v_idx]:
+                    distances[v_idx] = distances[u_idx] + u2v
+                    heapq.heappush(temp, [v_idx, distances[v_idx]])
+                    predecessors[v_idx] = u_idx
+
+    if distances[target] == INF:
+        return None, None
+    else:
+        path = []
+        vertex = target
+        while True:
+            path.append(str(vertex))
+            if vertex == predecessors[vertex]:
+                break
+            vertex = predecessors[vertex]
+        return path[::-1], distances[target]
+
+
+def main():
+    """
+    driver function to test the dijkstra's algorithm
+    """
+    graph = {'s': [('a', 2), ('b', 1)],
+             'a': [('s', 3), ('b', 4), ('c', 8)],
+             'b': [('s', 4), ('a', 2), ('d', 2)],
+             'c': [('a', 2), ('d', 7), ('t', 4)],
+             'd': [('b', 1), ('c', 11), ('t', 5)],
+             't': [('c', 3), ('d', 5)]
+             }
+    source = 'a'
+    target = 't'
+    path, cost = dijkstra(graph, source, target)
+    print('The path from ' + source + ' to ' + target + ' :')
+    if path is None or cost is None:
+        print('does not exist')
+    else:
+        print(str(path) + ' with cost: ' + str(cost))
+
+
+if __name__ == "__main__":
+    main()