Python Dijsktra's algorithm using adjacency matrix

algorithms/Python/graphs/python-dijkstra.py

@@ -0,0 +1,111 @@
+# A Dijkstra's algorithm implementation in Python
+# using adjacency matrix
+# Time complexity: O(V+E)*O(logV)
+
+from math import inf
+
+wmat = [[0, 2, 0, 0, 0, 1, 0, 0],
+        [2, 0, 2, 2, 4, 0, 0, 0],
+        [0, 2, 0, 0, 3, 0, 0, 1],
+        [0, 2, 0, 0, 4, 3, 0, 0],
+        [0, 4, 3, 4, 0, 0, 7, 0],
+        [1, 0, 0, 3, 0, 0, 5, 0],
+        [0, 0, 0, 0, 7, 5, 0, 6],
+        [0, 0, 1, 0, 0, 0, 6, 0]]
+
+
+def find_all(wmat, start, end=-1):
+    """
+    Returns a tuple with a distances' list and paths' list of
+    all remaining vertices with the same indexing.
+
+        (distances, paths)
+
+    For example, distances[x] are the shortest distances from x
+    vertex which shortest path is paths[x]. x is an element of
+    {0, 1, ..., n-1} where n is the number of vertices
+
+    Args:
+    wmat    --  weighted graph's adjacency matrix
+    start   --  paths' first vertex
+    end     --  (optional) path's end vertex. Return just the 
+                distance and its path
+
+    Exceptions:
+    Index out of range, Be careful with start and end vertices
+    """
+    n = len(wmat)
+
+    dist = [inf]*n
+    dist[start] = wmat[start][start]  # 0
+
+    spVertex = [False]*n
+    parent = [-1]*n
+
+    path = [{}]*n
+
+    for count in range(n-1):
+        minix = inf
+        u = 0
+
+        for v in range(len(spVertex)):
+            if spVertex[v] == False and dist[v] <= minix:
+                minix = dist[v]
+                u = v
+
+        spVertex[u] = True
+        for v in range(n):
+            if not(spVertex[v]) and wmat[u][v] != 0 and dist[u] + wmat[u][v] < dist[v]:
+                parent[v] = u
+                dist[v] = dist[u] + wmat[u][v]
+
+    for i in range(n):
+        j = i
+        s = []
+        while parent[j] != -1:
+            s.append(j)
+            j = parent[j]
+        s.append(start)
+        path[i] = s[::-1]
+
+    return (dist[end], path[end]) if end >= 0 else (dist, path)
+
+
+def find_shortest_path(wmat, start, end=-1):
+    """
+    Returns paths' list of all remaining vertices.
+
+    Args:
+    wmat    --  weigthted graph's adjacency matrix
+    start   --  paths' first vertex
+    end     --  (optional) path's end vertex. Return just
+                the path
+
+    Exceptions:
+    Index out of range, Be careful with start and end vertices.
+    """
+    return find_all(wmat, start, end)[1]
+
+
+def find_shortest_distance(wmat, start, end=-1):
+    """
+    Returns distances' list of all remaining vertices.
+
+    Args:
+    wmat    --  weigthted graph's adjacency matrix
+    start   --  paths' first vertex
+    end     --  (optional) path's end vertex. Return just
+                the distance
+
+    Exceptions:
+    Index out of range, Be careful with start and end vertices.
+    """
+    return find_all(wmat, start, end)[0]
+
+if __name__ == "__main__":
+    i = 0
+    for D, P in zip(*find_all(wmat, 0)):
+        print("Target: {}, Distance: {}, Path: {}".format(i, D, P))
+        i += 1
+    print("\nshortest path to last node", find_shortest_path(wmat, 0, 7))
+    print("shortest distance to last node", find_shortest_distance(wmat, 0, 7))