hdu 5889 Barricade最小割

Posted 2022-10-30 mfcheer

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=5889

解法：求最短路图上的最小割，先在图上源点和终点分别求一遍最短路。再在最短路图上求最小割。
最小割==最大流定理

代码：

#include <stdio.h>
#include <math.h>
#include <algorithm>
#include <iostream>
#include <string.h>

using namespace std;

const int MAXN = 10100;//点数的最大值
const int MAXM = 400010;//边数的最大值
const int INF = 0x3f3f3f3f;
struct Edge

    int to, next, cap, flow;
edge[MAXM];//注意是MAXM
int tol;
int head[MAXN];
int gap[MAXN], dep[MAXN], pre[MAXN], cur[MAXN];

void init()

    tol = 0;
    memset(head, -1, sizeof(head));

//加边，单向图三个参数，双向图四个参数
void addedge(int u, int v, int w, int rw = 0)

    edge[tol].to = v; edge[tol].cap = w; edge[tol].next = head[u];
    edge[tol].flow = 0; head[u] = tol++;
    edge[tol].to = u; edge[tol].cap = rw; edge[tol].next = head[v];
    edge[tol].flow = 0; head[v] = tol++;


//输入参数：起点、终点、点的总数
//点的编号没有影响，只要输入点的总数

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[0] = 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;


int n, m;
int diss[MAXN][MAXN];
bool vis[MAXN];
int d[MAXN];
int d2[MAXN];

void dijkstra(int s)

    for (int i = 1;i <= n;i++)
    
        vis[i] = 0;
        if (diss[s][i] == 1)
            d[i] = 1;
        else
            d[i] = INF;
    
    d[s] = 0;

    while (1)
    
        int min = INF, v = -1;
        for (int i = 1;i <= n;i++)
            if (!vis[i] && d[i]<min)
            
                v = i;
                min = d[i];
            
        if (v == -1)
            break;
        vis[v] = 1;
        for (int i = 1;i <= n;i++)
            if (diss[v][i] == 1)
                if (!vis[i] && d[i] > d[v] + 1)
                    d[i] = 1 + d[v];
    


void dijkstra2(int s)

    for (int i = 1;i <= n;i++)
    
        vis[i] = 0;
        if (diss[s][i] == 1)
            d2[i] = 1;
        else
            d2[i] = INF;
    
    d2[s] = 0;

    while (1)
    
        int min = INF, v = -1;
        for (int i = 1;i <= n;i++)
            if (!vis[i] && d2[i]<min)
            
                v = i;
                min = d2[i];
            
        if (v == -1)
            break;
        vis[v] = 1;
        for (int i = 1;i <= n;i++)
            if (diss[v][i] == 1)
                if (!vis[i] && d2[i] > d2[v] + 1)
                    d2[i] = 1 + d2[v];
    


struct Node

    int u, v, w;
node[MAXM];

int main()

    int T;
    scanf("%d", &T);
    while (T--)
    
        scanf("%d %d", &n, &m);

        int u, v, w;

        memset(diss, 0, sizeof(diss));
        for (int i = 0;i < m;i++)
        
            scanf("%d%d%d", &u, &v, &w);

            node[i].u = u;
            node[i].v = v;
            node[i].w = w;

            diss[u][v] = diss[v][u] = 1;
        

        memset(d, -1, sizeof(d));
        memset(d2, -1, sizeof(d2));
        dijkstra(1);
        dijkstra2(n);

        init();
        for (int i = 0;i < m;i++)
        
            u = node[i].u;
            v = node[i].v;
            w = node[i].w;

            if (d[u] + d2[v] + 1 == d[n] && d[u] !=-1 && d2[v] != -1)
                addedge(u, v, w, 0);
            if ( d[v] + d2[u] + 1 == d[n] && d[v] != -1 && d2[u] != -1)
                addedge(v, u, w, 0);
        
        int ans = sap(1, n, n);
        printf("%d\\n", ans);
    
    return 0;