Folyd multi-source shortest path

Table of contents

Introduction

accomplish

code

Questions about Floyd

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Introduction

First we need to know what is the shortest path from a to b

The shortest path from a to b is the minimum distance (cost) from point a to point b

The multi-source shortest path means that we can find the shortest path between any a and b.

Then Folyd is the shortest path from multiple sources, that is, finding the shortest path between any a and b.

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accomplish

First introduce a term " relaxation "

What does relaxation mean? The shortest path of this point is updated. It can be updated by one point or by b-connected changes (dijkstra and bellman-ford and spfa)

So what is Floyd’s thinking?

1. Choose a k
2. Choose a
3. Choose a b
4. relax a->b

Oh, by the way, some friends guessed it, triple cycle! ! ! Keep it simple

By now you should know how to write code, right?

Friends who still don’t know how to do it, come with me.

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code

#include <iostream>
#include <cstring>

using namespace std;

const int N = 5e2 + 5;

int n, m;
int G[N][N]; //邻接矩阵

void Floyd() {
	for (int k = 1; k <= n; k ++)
		for (int a = 1; a <= n; a ++)
			for (int b = 1; b <= n; b ++)
				G[a][b] = min(G[a][b], G[a][k] + G[k][b]);
}

int main() {
	cin >> n >> m;
	memset(G, 0x3f, sizeof G);
	for (int i = 1; i <= m; i ++) {
		int a, b, c;
		cin >> a >> b >> c;
		G[a][b] = c; // a到b 距离为c
	}

	for (int i = 1; i <= n; i ++)
		G[i][i] = 0;//自己到自己为0

	Floyd();

//	for (int i = 1; i <= n; i ++) {
//		for (int j = 1; j <= n; j ++)
//			cout << G[i][j] << ' ';
//		cout << '\n';
//	}
	int a, b;
	cin >> a >> b;
	cout << G[a][b];
	return 0;
}

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Questions about Floyd

Ippondori 1342

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