AcWing 850. Dijkstra求最短路 II(堆优化版,适用于稀疏图)

AcWing 850. Dijkstra求最短路 II

使用堆找到不在s中,距离最近的点,降低时间复杂度,时间复杂度为mlogn

#include <bits/stdc++.h>

using namespace std;

typedef pair<int, int> PII;
#define x first
#define y second
//堆里存一对编号，先存最小值，再存结点
const int N = 150010;

int n, m;
//稀疏图用邻接表
int h[N], e[N], ne[N], w[N], idx;
int dis[N];
bool st[N];

void add(int a, int b, int c){
	e[idx] = b, w[idx] = c, ne[idx] = h[a], h[a] = idx++;
}

int dijkstra(){
	memset(dis, 0x3f, sizeof dis);
	dis[1] = 0;
	
    priority_queue<PII, vector<PII>, greater<PII>> heap;
    heap.push({0, 1});
    
    while(heap.size()){
        auto t = heap.top(); heap.pop();
        int index = t.y, distance = t.x;
        if(st[index]) continue;
        st[index] = true;
        for(int i = h[index]; i != -1; i = ne[i]){
            int j = e[i];
            if(dis[j] > distance + w[i]){
                dis[j] = distance + w[i];
                heap.push({dis[j], j});
            }
        }
    }
	
	//不连通
	if(dis[n] == 0x3f3f3f3f) return -1;
	return dis[n];

}
int main(){
	scanf("%d%d", &n, &m);
	memset(h, -1, sizeof h);
	

	while(m--){
		int a, b, c;
		scanf("%d%d%d", &a, &b, &c);
		add(a, b, c);
	}
	
	cout << dijkstra() << endl;
		
	return 0;

}