最短路径（Dijkstra，Floyd）

1. Dijkstra算法

代码（优先队列+邻接表优化）HDU-2544

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 106;
const int INF = 0x3f3f3f3f;

typedef pair<int, int> p;
vector<p> v[N];
int dis[N];

int n, m;
void dijk(int u)
{
    memset(dis, INF, sizeof(dis));
    dis[u] = 0;
    priority_queue<p, vector<p>, greater<p> > q;
    q.push(make_pair(0, u));
    while(!q.empty()){
        p t = q.top();
        q.pop();
        if(dis[t.second] != t.first)
            continue;
        for (int i = 0; i < v[t.second].size(); i++){
            if(dis[v[t.second][i].first]>t.first+v[t.second][i].second)
            {
                dis[v[t.second][i].first]=t.first+v[t.second][i].second;
                q.push(make_pair(dis[v[t.second][i].first],v[t.second][i].first));
            }
        }
    }
    cout << dis[n] << endl;
}

int main()
{
    while(cin >> n >> m){
        if(n == 0 && m == 0)
            break;
        for (int i = 1; i <= n; i++){
            v[i].clear();
        }
            int x, y, w;
        while(m--){
            scanf("%d%d%d", &x, &y, &w);
            v[x].push_back(make_pair(y, w));
            v[y].push_back(make_pair(x, w));
        }
        dijk(1);
    }
    return 0;
}

上面写法不是人看的。。。。。

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int INF = 0x3f3f3f3f;
const int N = 1e4 + 10;

int n, m, x, y, val;
int to[N], ne[N], w[N], h[N], idx;
int dis[N];

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

struct node{
    int u, di;
    node(int u, int di):u(u), di(di){}
    friend bool operator < (const node& a, const node& b) {
        return a.di > b.di;
    }
};

void dijk(){
    memset(dis, INF, sizeof(dis)), dis[1] = 0;      // 初始化
    priority_queue<node> q;                         // 优先小的 di
    q.push((node(1, 0)));                           // 放入 1 号点
    while(!q.empty()){              
        node cnt = q.top();                                 
        q.pop();
        if(dis[cnt.u] != cnt.di)
            continue;
        for(int i = h[cnt.u]; ~i; i = ne[i]){       // 更新和 u 相邻的所有边
            if(dis[to[i]] > cnt.di + w[i]){         // 
                dis[to[i]] = cnt.di + w[i];
                q.push(node(to[i], dis[to[i]]));
            }
        }
    }
    printf("%d\n", dis[n]);
}

int main(){
    while(scanf("%d%d", &n, &m)){
        if(n == 0 && m == 0)
            break;
        memset(h, -1, sizeof(h)), idx = 0;
        while(m--){
            scanf("%d%d%d", &x, &y, &val);
            add(x, y, val);
            add(y, x, val);
        }
        dijk();
    }
    return 0;
}

图的顶点小的情况下，用邻接表存：

int t, v, e, s, k, c;
int dd[M][M];
int kk[N];

struct node{
    int u, di;
    node(int u, int di):u(u), di(di){}
    friend bool operator < (const node& a, const node& b) {
        return a.di > b.di;
    }
};

int dis[N];

int dijk(int rt){
    memset(dis, INF, sizeof(dis)), dis[rt] = 0;      // 初始化
    priority_queue<node> q;                         // 优先小的 di
    q.push((node(rt, 0)));                           // 放入 1 号点
    while(!q.empty()){              
        node cnt = q.top();                                 
        q.pop();
        if(dis[cnt.u] != cnt.di)
            continue;
        for(int i = 1; i <= v; i++){
            if(dis[i] > cnt.di + dd[cnt.u][i]){
                dis[i] = cnt.di + dd[cnt.u][i];
                q.push(node(i, dis[i]));
            }
        }
    }
    int res = 0;
    for(int i = 1; i <= v; i++){
        res = max(res, dis[i]);
    }
    return res;
}


int main(){
    scanf("%d", &t);
    while(t--){
        memset(dd, INF, sizeof(dd));
        scanf("%d%d%d%d%d", &v, &e, &s, &k, &c);
        for(int i = 0; i < k; i++){
            scanf("%d", &kk[i]);
        }
        for(int i = 0, x, y, z; i < e; i++){
            scanf("%d%d%d", &x, &y, &z);
            dd[x][y] = dd[y][x] = min(dd[x][y], z);
        }
        int slen = dijk(s);
        for (int i = 1; i < k; i++){
            dd[kk[i - 1]][kk[i]] = dd[kk[i]][kk[i - 1]] = 0;
        }
        int ans = dijk(kk[0]);
        if(slen > ans * c){
            printf("%d\n", ans);
        }else{
            printf("%d\n", slen);
        }
    }
    return 0;
}