洛谷 P3371【模板】单源最短路径（弱化版）

题面

既然是模板， 那就直接贴代码？

两种思路

1.迪杰斯特拉

#include <cstdio>
#include <cstring>
#include <iostream>
using namespace std;
const int N = 500007;
int head[N], cnt, n, m, s;
long long dis[N];
bool vis[N];
struct node {
    int next, to;
    long long w;
}e[N];
void add(int x, int y, long long z) {
    e[++cnt].next = head[x];
    e[cnt].to = y;
    e[cnt].w = z;
    head[x] = cnt;
} 
void dijkstra(int s) {
    for(int i = 1; i <= n; i++) dis[i] = 2147483647; 
    dis[s] = 0;
    for(int i = 1; i <= n; i++) {
        int k = 1, maxn = 2147483647;
        for(int j = 1; j <= n; j++)
            if(!vis[j] && dis[j] <= maxn)
                k = j, maxn = dis[j];
        vis[k] = 1;
        for(int j = head[k]; j; j = e[j].next) 
            if(dis[e[j].to] > dis[k] + e[j].w)
                dis[e[j].to] = dis[k] + e[j].w;
    }
}
int main () {
    scanf("%d%d%d", &n, &m, &s);
    for(int i = 1; i <= m; i++) {
        int x, y;
        long long z;
        scanf("%d%d%lld", &x, &y, &z);
        add(x, y, z);
    }
    dijkstra(s);
    for(int i = 1; i <= n; i++)
        printf("%lld ", dis[i]);
    return 0;
}

2.spfa

#include <iostream>
#include <cstdio>
#include <queue>
#define N 500005
#define inf 2147483647
using namespace std;
int n, m, s, cnt;
int dis[N], vis[N], head[N];
struct node {
    int next, to, w;
}tr[N];
void add (int x, int y, int z) {
    tr[++cnt].to = y;
    tr[cnt].next = head[x];
    tr[cnt].w = z;
    head[x] = cnt;
}
void spfa () {
    queue<int> q;
    for (int i = 1; i <= n; i++) 
        dis[i] = inf;
    vis[s] = 1;
    q.push(s);
    dis[s] = 0;
    while (!q.empty()) {
        int he = q.front();
        q.pop();
        vis[he] = 0;
        for (int i = head[he]; i ;i = tr[i].next) {
            if (dis[tr[i].to] > dis[he] + tr[i].w) {
                dis[tr[i].to] = dis[he] + tr[i].w;
                if (!vis[tr[i].to]) {
                    vis[tr[i].to] = 1;
                    q.push(tr[i].to);
                }
            }
        }
    }
}
int main () {
    scanf ("%d%d%d", &n, &m, &s);
    for (int i = 1; i <= m; i++) {
        int a, b, c;
        scanf ("%d%d%d", &a, &b, &c);
        add (a, b, c);
    }
    spfa ();
    for (int i = 1; i <= n; i++) 
        if (s == i) printf ("0 ");
        else printf ("%d ", dis[i]);
    return 0;
}

 add：2019.8.15

增加堆优化后的迪杰斯特拉算法；

用来切标准版

#include <queue>
#include <cstdio>
#include <cstring>
#include <iostream>
using namespace std;
const int N = 1010001;
int n, m, s, cnt, head[N], dis[N];
bool vis[N];
struct node{
    int next, to, w;
}e[N];
int read() {
    int s = 0, w = 1;
    char ch = getchar();
    while(!isdigit(ch)){if(ch == '-') w = -1;ch = getchar();}
    while(isdigit(ch)){s = s * 10 + ch - '0';ch = getchar();}
    return s * w;
}
void add(int x, int y, int z) {
    e[++cnt].next = head[x];
    e[cnt].to = y;
    e[cnt].w = z;
    head[x] = cnt;
}
struct Node {
    int u, v;
    bool operator<(const Node &b) const {
        return u > b.u;
    }
};
void dijikstra(int s) {
    priority_queue <Node> q;
    memset(dis, 0x3f3f3f3f, sizeof(dis));
    dis[s] = 0;
    Node o;
    o.u = 0;
    o.v = s;
    q.push(o);
    while(!q.empty()) {
        int u = q.top().v;
        int d = q.top().u;
        q.pop();
        if(d != dis[u])continue;
        for(int i = head[u]; i; i = e[i].next) {
            int v = e[i].to;
            int w = e[i].w;
            if(dis[v] > dis[u] + w) {
                dis[v] = dis[u] + w;
                Node p;
                p.u = dis[v], p.v = v;
                q.push(p);
            }
        }
    }
}
int main () {
    n = read();
    m = read();
    s = read();
    while(m--) {
        int x, y, z;
        x = read();
        y = read();
        z = read();
        add (x, y, z);
    }
    dijikstra(s);
    for(int i = 1; i <= n; i++)
        printf("%d ", dis[i]);
    return 0; 
}