SPFA模板

SPFA算法详解与实现

原创于 2020-02-11 20:22:41 发布 · 157 阅读

CC 4.0 BY-SA版权

本文深入探讨了SPFA（Shortest Path Faster Algorithm）算法，一种改进版的Bellman-Ford算法，用于解决带负权边的最短路径问题。通过详细的代码示例，讲解了SPFA算法的实现原理与过程，包括如何处理图结构、节点遍历以及距离更新等关键步骤。适合对图论和最短路径算法感兴趣的读者。

SPFA模板

#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>
#include <queue>

using namespace std;

const int MAXN = 60000 + 10;
const int INF = 0x3f3f3f3f;

struct node{
	int from, to, dis;
}edge[MAXN];

int head[MAXN];
int nxt[MAXN];
bool vis[MAXN];
long long dist1[MAXN], dist2[MAXN];
int n, m, tot = 1;

void add(int x){
	nxt[tot] = head[x];
	head[x] = tot ++;
}

void spfa1(int s){
	memset(dist1, 0x3f3f3f3f, sizeof(dist1));
	vis[s] = true;
	dist1[s] = 0;
	queue<int> q;
	q.push(s);
	while(!q.empty()){
		int u = q.front();
		q.pop();
		vis[u] = false;
		for(int i = head[u]; i; i = nxt[i])
		{
			int v = edge[i].to;
			if(dist1[v] > dist1[u] + edge[i].dis)
			{
				dist1[v] = dist1[u] + edge[i].dis;
				if(!vis[v]){
					vis[v] = true;
					q.push(v);
				}
			}
		}
	}
}

void spfa2(int s){
	memset(dist2, 0x3f3f3f3f, sizeof(dist2));
	vis[s] = true;
	dist2[s] = 0;
	queue<int> q;
	q.push(s);
	while(!q.empty())
	{
		int u = q.front();
		q.pop();
		vis[u] = false;
		for(int i = head[u]; i; i = nxt[i])
		{
			int v = edge[i].to;
			if(dist2[v] > dist2[u] + edge[i].dis)
			{
				dist2[v] = dist2[u] + edge[i].dis;
				if(!vis[v]){
					vis[v] = 1;
					q.push(v);
				}
			}
		}	
	}
}

void init()
{
	memset(head, 0, sizeof(head));
	memset(nxt, 0, sizeof(nxt));
	memset(vis, false, sizeof(vis));
	tot = 1;
}

int main()
{
	int T;
	scanf("%d", &T);
	while(T --)
	{
		init();
		scanf("%d%d", &n, &m);
		for(int i = 1; i <= m; i ++)
		{
			scanf("%d%d%d", &edge[i].from, &edge[i].to, &edge[i].dis);
			add(edge[i].from);
		}
		spfa1(1);
		init();
		for(int i = 1; i <= m; i ++)
		{
			add(edge[i].to);
			swap(edge[i].from, edge[i].to);
		}
		spfa2(1);
		long long ans = 0;
		for(int i = 1; i <= n; i ++)
			ans += dist1[i] + dist2[i];
		printf("%lld\n", ans);
	}
	return 0;
}