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{"ops":[{"insert":"Implement the following algorithm for the single source shortest path problem in a directed weighted graph. You must use a min-priority queue to implement Q in the pseudocode. For priority queue, you are allowed to use the priority queue provided by the STL library or your own implementation. You must take input from the user.\nfunction dijkstra(G)"},{"attributes":{"code-block":true},"insert":"\n"},{"insert":"    for each v \u2208 V"},{"attributes":{"code-block":true},"insert":"\n"},{"insert":"        d[V] = infinite"},{"attributes":{"code-block":true},"insert":"\n"},{"insert":"      d[s] = 0;S = \u2205;Q =V;"},{"attributes":{"code-block":true},"insert":"\n"},{"insert":"     "},{"attributes":{"code-block":true},"insert":"\n"},{"insert":"    while Q IS NOT EMPTY"},{"attributes":{"code-block":true},"insert":"\n"},{"insert":"        U = ExtractMIN (Q);"},{"attributes":{"code-block":true},"insert":"\n"},{"insert":"        S = S \u222a {u};"},{"attributes":{"code-block":true},"insert":"\n"},{"insert":"        for each V \u2208 u->ADJ[]"},{"attributes":{"code-block":true},"insert":"\n"},{"insert":"          if (d[v] > d[u]+w(u,v))"},{"attributes":{"code-block":true},"insert":"\n"},{"insert":"              d[v] = d[u]+w(u,v);"},{"attributes":{"code-block":true},"insert":"\n"},{"insert":"               p[v] = u;"},{"attributes":{"code-block":true},"insert":"\n"},{"insert":"    "},{"attributes":{"code-block":true},"insert":"\n"},{"attributes":{"bold":true},"insert":"Sample Input:"},{"insert":"\n"},{"attributes":{"bold":true},"insert":"V E "},{"insert":"\n"},{"attributes":{"bold":true},"insert":"u v weight(u,v) "},{"insert":"\n"},{"attributes":{"bold":true},"insert":"\u2026 Src node"},{"insert":"\n4 5\n0 1 10 \n0 2 6 \n0 3 5\n1 3 15 \n2 3 4 \n1\n"},{"attributes":{"bold":true},"insert":"Sample Output"},{"insert":"\nno path from 1 to 0 \nsp from 1 to 1: 1, length: 0 \nno path from 1 to 2 \nsp from 1 to 3: 1-->3, length: 15\n\n\n\n"}]}

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