HDU 1688 Sightseeing

题目链接：Sightseeing

题意：求最短路和比最短路长度+1的所有路径条数。

附代码：用数组记录最短和次短路径的长度和条数，一次更新，直到没有边可以更新。

#include <stdio.h>
#include <string.h>
#include <iostream>
#include <vector>
using namespace std;
#define maxn 1010

struct Node {
    int to, val;
    Node(int to, int val) {
        this->to = to;
        this->val = val;
    }
};// 保存每个点的所有边及其权值

vector<Node> edge[maxn];

int step[maxn][2]; //bushu[i][j] 表示i点第j短路的长度
int cnt[maxn][2]; // cnt[i][j]表示i点第j短路的条数

int main() {
    int t;
    scanf("%d", &t);
    while(t--) {
        int n, m;
        scanf("%d%d", &n, &m);

        for (int i=1; i<=n; ++i) {
            edge[i].clear();
            step[i][0] = maxn*maxn;
            step[i][1] = maxn*maxn;
            cnt[i][0] = 0;
            cnt[i][1] = 0;
        }

        for (int i=0; i<m; ++i) {
            int x, y, z;
            scanf("%d%d%d", &x, &y, &z);
            edge[x].push_back(Node(y, z));
        }

        int st, ed;
        scanf("%d%d", &st, &ed);

        step[st][0] = 0; // 初始化源点
        step[st][1] = maxn*maxn;
        cnt[st][0] = 1;
        cnt[st][1] = 0;

        bool ok = false;

        while(1) {
           ok = false;
            for (int i=1; i<=n; ++i) {
               for (int k=0; k<2; ++k) {
                   if (cnt[i][k] && i != ed) {
                   for (int j=0; j<edge[i].size(); ++j) {
                        int to = edge[i][j].to;
                        int val = edge[i][j].val;

                            if (step[to][0] > step[i][k] + val) { // 更新最短路
                                step[to][1] = step[to][0];
                                cnt[to][1] = cnt[to][0];
                                step[to][0] = step[i][k] + val;
                                cnt[to][0] = cnt[i][k];
                                ok = true;
                            }
                            else if (step[to][0] == step[i][k] + val) {
                                cnt[to][0] += cnt[i][k];
                                ok = true;
                            }
                            else if (step[to][1] > step[i][k] + val) { // 更新次短路
                                step[to][1] = step[i][k] + val;
                                cnt[to][1] = cnt[i][k];
                                ok = true;
                            }
                            else if (step[to][1] == step[i][k] + val) {
                                cnt[to][1] += cnt[i][k];
                                ok = true;
                            }
                        }
                     cnt[i][k] = 0;
                   }
               }
            }
            if (ok == false) break;
        }

//        for (int i=1; i<=n; ++i) {
//            cout << i << "==" << step[i][0] << " " << cnt[i][0] << " " << step[i][1] << " " << cnt[i][1] << endl;
//        }
        int ans = cnt[ed][0];
        if (step[ed][1] == step[ed][0] + 1) {
            ans += cnt[ed][1];
        }
        printf("%d
", ans);
    }
    return 0;
}

/*
HDU 1688
*/

#include <stdio.h>
#include <string.h>
#include <iostream>
#include <vector>
#define maxn 1010
#include <queue>
using namespace std;

struct Node {
    int v, w;
    Node(int v, int w) {
        this->v = v;
        this->w = w;
    }
};

vector <Node> edge[maxn];
int st, ed;
int step[maxn][2];
int cnt[maxn][2];
int mp[maxn][maxn];

void bfs(int st) {
    queue<int> que;
    que.push(st);
    while(!que.empty()) {
        int now = que.front();
        que.pop();
       // cout << now << "-----------------
";
        for (int k=0; k<2; ++k) {
            if (cnt[now][k] && now != ed) {
                for (int j=0; j<edge[now].size(); ++j) {
                    int v = edge[now][j].v;
                    int val = edge[now][j].w;
                    if (step[v][0] > step[now][k] + val) {
                        step[v][1] = step[v][0];
                        cnt[v][1] = cnt[v][0];
                        step[v][0] = step[now][k] + val;
                        cnt[v][0] = cnt[now][k];
                        que.push(v);
                       // cout << v << "==1==" << step[v][0] << " " << cnt[v][0] << " " << step[v][1] << " " << cnt[v][1] << endl;
                    }
                    else if (step[v][0] == step[now][k] + val) {
                        cnt[v][0] += cnt[now][k];
                        que.push(v);
                       // cout << v << "==2==" << step[v][0] << " " << cnt[v][0] << " " << step[v][1] << " " << cnt[v][1] << endl;
                    }
                    else if (step[v][1] > step[now][k] + val) {
                        step[v][1] = step[now][k] + val;
                        cnt[v][1] = cnt[now][k];
                        que.push(v);
                       // cout << v << "==3==" << step[v][0] << " " << cnt[v][0] << " " << step[v][1] << " " << cnt[v][1] << endl;
                    }
                    else if (step[v][1] == step[now][k] + val) {
                        cnt[v][1] += cnt[now][k];
                        que.push(v);
                        //cout << v << "==4==" << step[v][0] << " " << cnt[v][0] << " " << step[v][1] << " " << cnt[v][1] << endl;
                    }
                }
                cnt[now][k] = 0;
            }
        }
    }
}

int main() {
    int t;
    scanf("%d", &t);
    while(t--) {
        int n, m;
        scanf("%d%d", &n, &m);
        for (int i=1; i<=n; ++i) {
            edge[i].clear();
            step[i][0] = maxn*maxn;
            step[i][1] = maxn*maxn;
            cnt[i][0] = 0;
            cnt[i][1] = 0;
        }

        for (int i=0; i<m; ++i) {
            int u, v, w;
            scanf("%d%d%d", &u, &v, &w);
            edge[u].push_back(Node(v, w));
        }

        scanf("%d%d", &st, &ed);
        step[st][0] = 0;
        cnt[st][0] = 1;

        bfs(st);
//
//        for (int i=1; i<=n; ++i) {
//            cout << i << "==" << step[i][0] << " " << cnt[i][0] << " " << step[i][1] << " " << cnt[i][1] << endl;
//        }

        int ans = cnt[ed][0];
        if (step[ed][1] == step[ed][0] + 1) {
            ans += cnt[ed][1];
        }
        printf("%d
", ans);
    }
    return 0;
}

/*
99
3 3
1 2 1
2 3 1
1 3 1
1 3

*/