Issue #133 is completed by a Dijkstra's algorithm implemented with queue.PriorityQueue data-structure

Author: Hamid Gasmi

3-graph-algorithms/2_paths_in_graphs/dijkstra_priorityQueue.py

@@ -0,0 +1,66 @@
+import sys
+import queue
+from collections import namedtuple
+
+Edge = namedtuple('Edge', ['vertex', 'weight'])
+
+class Graph:
+    def __init__(self, n, edges):
+        self.adjacency_list = [[] for _ in range(n)]
+        self.build_adjacency_list(n, edges)
+
+    def build_adjacency_list(self, n, edges):
+        for ((s, d), w) in edges:
+            self.adjacency_list[s - 1].append(Edge(d - 1, w))
+
+    # Implementation: Binary Heap
+    # ... The number of flight ~ the number of cities => |V| ~ |E| => Sparse Graph => Binary Heap is more efficient
+    # ... T(n) = O((|V| + |E|) log |V|)
+    def dijkstra(self, s, t):
+        
+        # w <= 10^3 and |V| <= 10^4
+        # Shortest Path Cost <= 10^3 * 10^4 + 1
+        distances = [10**7 + 1] * len(self.adjacency_list)
+        distances[s] = 0
+        
+        parents = [None] * len(self.adjacency_list)
+        parents[s] = -1
+
+        q = queue.PriorityQueue()
+        for v in range(0, len(self.adjacency_list)):
+            if v == s:
+                continue
+            q.put([distances[v], v])
+        q.put([distances[s], s])
+
+        while not q.empty():
+            v_min_weight = q.get()
+            v = v_min_weight[1]
+
+            if v == t:
+                return distances[t]
+            
+            for a_tuple in self.adjacency_list[v]:
+                a_candidate_distance = distances[v] + a_tuple.weight
+                if distances[a_tuple.vertex] > a_candidate_distance:
+                    distances[a_tuple.vertex] = a_candidate_distance
+                    parents[a_tuple.vertex] = v
+                    q.put([distances[a_tuple.vertex], a_tuple.vertex])
+
+        return distances[t]
+
+def distance(n, edges, s, t):
+
+    aFlightNetwork = Graph(n, edges)
+    distance = aFlightNetwork.dijkstra(s, t) 
+    return -1 if distance == 10**7 + 1 else distance
+
+if __name__ == '__main__':
+    input = sys.stdin.read()
+    data = list(map(int, input.split()))
+    n, m = data[0:2]
+    data = data[2:]
+    edges = list(zip(zip(data[0:(3 * m):3], data[1:(3 * m):3]), data[2:(3 * m):3]))
+    data = data[3 * m:]
+    s, t = data[0] - 1, data[1] - 1
+    print(distance(n, edges, s, t))

3-graph-algorithms/2_paths_in_graphs/dijkstra_tests/01

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+4 4
+1 2 1
+4 1 2
+2 3 2
+1 3 5
+1 3

3-graph-algorithms/2_paths_in_graphs/dijkstra_tests/01e

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+3

3-graph-algorithms/2_paths_in_graphs/dijkstra_tests/01r

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+3

3-graph-algorithms/2_paths_in_graphs/dijkstra_tests/02

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+5 9
+1 2 4
+1 3 2
+2 3 2
+3 2 1
+2 4 2
+3 5 4
+5 4 1
+2 5 3
+3 4 4
+1 5

3-graph-algorithms/2_paths_in_graphs/dijkstra_tests/02e

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+6

3-graph-algorithms/2_paths_in_graphs/dijkstra_tests/02r

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+6

3-graph-algorithms/2_paths_in_graphs/dijkstra_tests/03

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+3 3
+1 2 7
+1 3 5
+2 3 2
+3 2

3-graph-algorithms/2_paths_in_graphs/dijkstra_tests/03e

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+-1

3-graph-algorithms/2_paths_in_graphs/dijkstra_tests/03r

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+-1