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Shortest path in a weighted graph(if many then lexicographically smallest)
By fluffy_x, history, 6 years ago, In English

How to find the shortest path in a weighted graph(**if many then lexicographically smallest**) using Dijkstra? — I am getting WA on 2 test cases - Problem link :Your text to link here... - Although this can be solved using BFS, but I want to know do when the graph is weighted?

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6 years ago, # |
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Let's assume X = 1. Using Dijkstra, calculate the distance Dv from node 1 to node v. For every node u, store Pu, the minimum v over all edges (v, u) such that Dv + w(v, u) = Du. It is easy to find this path now:

std::vector<int> find_path(int v) {
	std::vector<int> ans;
	for(ans.push_back(v); v != 1; ans.push_back(v = p[v]));
	std::reverse(ans.begin(), ans.end());
        return ans;
}
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    6 years ago, # ^ |
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    Got it!

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    4 years ago, # ^ |
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    Your solution is wrong. Consider this graph:

    6 6 1 2 1 1 4 1 4 3 1 3 6 1 5 6 1 2 5 1

    According to you shortest + lexographically shortest path will be 1 -> 4 -> 3 -> 6 while it should be 1 -> 2 -> 5 -> 6;

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