HDU 3416 Marriage Match IV（ISAP+最短路）题解

题意：从A走到B，有最短路，问这样不重复的最短路有几条

思路：先来讲选有效边，我们从start和end各跑一次最短路，得到dis1和dis2数组，如果dis1[u] + dis2[v] + cost[u][v] == dis1[end]，那么uv这条边是最短路的一条边。然后我们选完边，把边加入ISAP，然后跑一边就行了...还没学过SAP只会敲模板....

错误思路：刚开始想的是先求出最短路，然后用费用流spfa去跑，边容量1，如果跑出一条路径费用等于最短路，那么路径+1，继续跑，但是超时了，看了半天是spfa跑费用流太慢的关系...等我学会网络流其他算法再来看这种emmm

代码：

#include<cstdio>
#include<set>
#include<cmath>
#include<stack>
#include<vector>
#include<queue>
#include<cstring>
#include<string>
#include<sstream>
#include<iostream>
#include<algorithm>
#define ll long long
using namespace std;
const int maxn = 1000+5;
const int INF = 0x3f3f3f3f;

//网络流ISAP
struct Node{
    int to,next,cap,flow;
}edge[200005];
int tot;
int head[maxn];
int gap[maxn],dep[maxn],pre[maxn],cur[maxn];
void init(){
    tot = 0;
    memset(head,-1,sizeof(head));
}
void addEdge(int u,int v,int w,int rw = 0){
    edge[tot].to = v;
    edge[tot].cap = w;
    edge[tot].flow = 0;
    edge[tot].next = head[u];
    head[u] = tot++;

    edge[tot].to = u;
    edge[tot].cap = rw;
    edge[tot].flow = 0;
    edge[tot].next = head[v];
    head[v] = tot++;
}
int sap(int start,int end,int N){
    memset(gap,0,sizeof(gap));
    memset(dep,0,sizeof(dep));
    memcpy(cur,head,sizeof(head));
    int u = start;
    pre[u] = -1;
    gap[u] = N;
    int ans = 0;
    while(dep[start] < N){
        if(u == end){
            int Min = INF;
            for(int i = pre[u];i != -1;i = pre[edge[i^1].to]){
                if(Min > edge[i].cap - edge[i].flow){
                    Min = edge[i].cap - edge[i].flow;
                }
            }
            for(int i = pre[u];i != -1;i = pre[edge[i^1].to]){
                edge[i].flow += Min;
                edge[i^1].flow -= Min;
            }
            u = start;
            ans += Min;
            continue;
        }
        bool flag = false;
        int v;
        for(int i = cur[u];i != -1;i = edge[i].next){
            v = edge[i].to;
            if(edge[i].cap- edge[i].flow && dep[v] + 1 == dep[u]){
                flag = true;
                cur[u] = pre[v] = i;
                break;
            }
        }
        if(flag){
            u = v;
            continue;
        }
        int Min = N;
        for(int i = head[u];i != -1;i = edge[i].next){
            if(edge[i].cap - edge[i].flow && dep[edge[i].to] < Min){
                Min = dep[edge[i].to];
                cur[u] = i;
            }
        }
        gap[dep[u]]--;
        if(!gap[dep[u]]) return ans;
        dep[u] = Min + 1;
        gap[dep[u]]++;
        if(u != start) u = edge[pre[u]^1].to;
    }
    return ans;
}

struct road{
    int v,cost,next;
}e[200005];
int head2[maxn],tol,MinPath;
void addRoad(int u,int v,int w){
    e[tol].v = v;
    e[tol].cost = w;
    e[tol].next = head2[u];
    head2[u] = tol++;
}
bool vis1[maxn];
int cnt[maxn],dist[maxn];
bool SPFA(int st,int n){
    memset(vis1,false,sizeof(vis1));
    for(int i = 0;i <= n;i++) dist[i] = INF;
    vis1[st] = true;
    dist[st] = 0;
    queue<int> q;
    while(!q.empty()) q.pop();
    q.push(st);
    memset(cnt,0,sizeof(cnt));
    cnt[st] = 1;
    while(!q.empty()){
        int u = q.front();
        q.pop();
        vis1[u] = false;
        for(int i = head2[u];i != -1;i = e[i].next){
            int v = e[i].v;
            if(dist[v] > dist[u] + e[i].cost){
                dist[v] = dist[u] + e[i].cost;
                if(!vis1[v]){
                    vis1[v] = true;
                    q.push(v);
                    if(++cnt[v] > n) return false;
                }
            }
        }
    }
    return true;
}
int dis1[maxn];
int u[100005],v[100005],w[100005];
int main(){
    int n,m,T;
    scanf("%d",&T);
    while(T--){
        init();
        scanf("%d%d",&n,&m);
        for(int i = 0;i < m;i++){
            scanf("%d%d%d",&u[i],&v[i],&w[i]);
        }
        int st,en;
        scanf("%d%d",&st,&en);
        tol = 0;
        memset(head2,-1,sizeof(head2));
        for(int i = 0;i < m;i++){
            addRoad(u[i],v[i],w[i]);
        }
        SPFA(st,n);
        MinPath = dist[en];
        memcpy(dis1,dist,sizeof(dist));
        tol = 0;
        memset(head2,-1,sizeof(head2));
        for(int i = 0;i < m;i++){
            addRoad(v[i],u[i],w[i]);
        }
        SPFA(en,n);
        for(int i = 0;i < m;i++){
            if(dis1[u[i]] + dist[v[i]] + w[i] == MinPath)
                addEdge(u[i],v[i],1);
        }
        int flow = sap(st,en,n);
        printf("%d
",flow);
    }
    return 0;
}