题面链接

https://www.acwing.com/problem/content/description/852/

思路

和朴素版的Dijkstra类似，只不过我们对边的存储进行堆优化，优先将短的边先更新（基于贪心策略）

代码

#include<bits/stdc++.h>
using namespace std;
//----------------自定义部分----------------
#define ll long long
#define mod 1000000007
#define endl "\n"
#define PII pair<int,int>
#define INF 0x3f3f3f3f

int dx[4]={0,-1,0,1},dy[4]={-1,0,1,0};

ll ksm(ll a,ll b) {
	ll ans = 1;
	for(;b;b>>=1LL) {
		if(b & 1) ans = ans * a % mod;
		a = a * a % mod;
	}
	return ans;
}

ll lowbit(ll x){return -x & x;}

const int N = 2e6+10;
//----------------自定义部分----------------
int n,m,q;

vector<PII> E[N];
int dis[N];
bool vis[N];

void slove(){
	memset(dis,INF,sizeof dis);
	dis[1] = 0;
	priority_queue<PII,vector<PII>,greater<PII> >que;
	que.push({0,1});
	while(!que.empty()){
		PII t = que.top();
		que.pop();
		int p = t.second;
		if(vis[p]) continue;
		vis[p] = true;
		for(int i = 0,l = E[p].size(); i < l; ++i){
			int j = E[p][i].first,k = E[p][i].second;
			if(dis[j] > dis[p] + k){
				dis[j] = dis[p] + k;
				que.push({dis[j],j});
			}
		}	
	}
	if(dis[n] == INF)
		cout<<-1<<endl;
	else cout<<dis[n]<<endl;
}

int main()
{
	std::ios::sync_with_stdio(false);
	std::cin.tie(nullptr);
	std::cout.tie(nullptr);
	
	cin>>n>>m;
	
	int u,v,w;
	for(int i = 0;i < m; ++i) {
		cin>>u>>v>>w;
		E[u].push_back({v,w});
	}
	slove();
	
	return 0;
}