hdu 5889 Barricade【最小割】

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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MAXMint 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;}
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