added the dijkstra algorithm (#704)

graphs/dijkstra.py

@@ -0,0 +1,47 @@
+"""pseudo-code"""
+
+"""
+DIJKSTRA(graph G, start vertex s,destination vertex d):
+// all nodes initially unexplored
+let H = min heap data structure, initialized with 0 and s [here 0 indicates the distance from start vertex]
+while H is non-empty:
+    remove the first node and cost of H, call it U and cost
+    if U is not explored
+    mark U as explored
+    if U is d:
+        return cost // total cost from start to destination vertex
+    for each edge(U, V): c=cost of edge(u,V) // for V in graph[U]
+        if V unexplored:
+            next=cost+c
+            add next,V to H (at the end)
+"""
+import heapq
+
+
+def dijkstra(graph, start, end):
+    heap = [(0, start)]  # cost from start node,end node
+    visited = []
+    while heap:
+        (cost, u) = heapq.heappop(heap)
+        if u in visited:
+            continue
+        visited.append(u)
+        if u == end:
+            return cost
+        for v, c in G[u]:
+            if v in visited:
+                continue
+            next = cost + c
+            heapq.heappush(heap, (next, v))
+    return (-1, -1)
+
+
+G = {'A': [['B', 2], ['C', 5]],
+     'B': [['A', 2], ['D', 3], ['E', 1]],
+     'C': [['A', 5], ['F', 3]],
+     'D': [['B', 3]],
+     'E': [['B', 1], ['F', 3]],
+     'F': [['C', 3], ['E', 3]]}
+
+shortDistance = dijkstra(G, 'E', 'C')
+print(shortDistance)