Dijkstra模板

最新推荐文章于 2025-06-11 17:00:14 发布

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最新推荐文章于 2025-06-11 17:00:14 发布

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原文链接：http://www.cnblogs.com/Tokisaki-Kurumi-/p/8855725.html

本文详细介绍了Dijkstra算法的两种实现方式：原始版本和优先队列优化版本。通过具体代码展示了如何寻找图中两点间的最短路径，适用于了解和学习Dijkstra算法原理及其应用。

Dijkstra

struct node
{
	long long x,d;
	node();
	node(long long xx,long long dd){
		x = xx;
		d = dd;
	}
};

vector<node> edge[maxn];

void dijkstra(long long x)
{
	long long i,j;
	for(i=0;i<n;i++) vis[i] = 0,dis[i] = INF;
	dis[x] = 0;

	for(i=0;i<n;i++){
		long long minn = INF;
		long long u = 0;
		for(j=0;j<n;j++){
			if(!vis[j] && minn > dis[j]){
				minn = dis[j];
				u = j;
//                cout<<"A "<<minn<<" "<<u<<endl;
			}
		}
        vis[u] = 1;
		for(j=0;j<edge[u].size();j++){
            long long v = edge[u][j].x;
			if(!vis[v] && (minn + edge[u][j].d) < dis[v])
				dis[v] = minn + edge[u][j].d;
		}
	}
}

优先队列优化

const int MAXN = 50010;
const ll INF = ((ll)1<<62);
struct node{
    int x;
    ll d;
    node(){}
    node(int a,ll b){x = a;d = b;}
    bool operator < (const node & a) const
    {
        if(d == a.d) return x < a.x;
        else return d > a.d;
    }
};

vector<node> edge[MAXN];    //记得清边
ll dis[MAXN];
int N;  //N从1到N

void Dijkstra(int s)
{
    for(int i = 1; i <= N; i++) dis[i] = INF;
    dis[s] = 0;
    priority_queue<node> q;
    q.push(node(s,dis[s]));
    while(!q.empty()){
        node x = q.top();
        q.pop();
        for(int i = 0;i < edge[x.x].size(); i++){
            node y = edge[x.x][i];
            if(dis[y.x] > x.d + y.d){
                dis[y.x] = x.d + y.d;
                q.push(node(y.x,dis[y.x]));
            }
        }
    }
}