UVa 10092 The Problem With the Problem Setter ( SAP )

最新推荐文章于 2018-08-21 07:08:28 发布

原创最新推荐文章于 2018-08-21 07:08:28 发布 · 1.6k 阅读

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本文深入分析了一道使用网络流算法解决SAP（最大流问题）的编程题，阐述了如何构建图并实现算法。通过实例演示，详细解释了SAP算法的原理及在该问题中的应用过程。

这道TLE了，用的是最初的网络流算法，具体叫什么算法我就记不清了，但是像这样的数据，是超时了

这道题主要是SAP求最大流

数据不大，矩阵可以解决，后面的文章会写关于SAP的知识的学习笔记里面，会详细说一下SAP算法，这里就直接说一下这道题

这道题建图不难，就是源点和题目，容量1，题目和目录，容量1，目录和汇点，容量是目录所包含的题目数

代码如下：（这也是一道模板题）

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
using namespace std;

const int N = 1100;
int maze[N][N], pre[N], gap[N], dis[N], cur[N];

int sap ( int start, int end, int nodenum ) {
    memset( cur, 0, sizeof(cur));
    memset( gap, 0, sizeof(gap));
    memset( dis, 0, sizeof(dis));
    int u = pre[start] = start, maxflow = 0, aug = -1;
    gap[0] = nodenum;
    while ( dis[start] < nodenum ) {
        loop:
            for ( int v = cur[u]; v < nodenum; v++ ) 
                if( maze[u][v] && dis[u] == dis[v] + 1 ) {
                    if ( aug == -1 || aug > maze[u][v] ) aug = maze[u][v];
                    pre[v] = u;
                    u = cur[u] = v;
                    if ( v == end ) {
                        maxflow += aug;
                        for ( u = pre[u]; v != start; v = u, u = pre[u] ) {
                            maze[u][v] -= aug;
                            maze[v][u] += aug;
                        }
                        aug = -1;
                    }
                    goto loop;
                }
        int mindis = nodenum - 1;
        for ( int v = 0; v < nodenum; v++ ) 
            if ( maze[u][v] && mindis > dis[v] ) {
                cur[u] = v;
                mindis = dis[v];
            }
        if ( ( --gap[dis[u]]) == 0 ) break;
        gap[dis[u] = mindis+1]++;
        u = pre[u];
    }
    return maxflow;
}
int a[22][N], num[22];
int main()
{
    int nk, np;
    while ( scanf("%d%d", &nk, &np) == 2 ) {
        if( nk == 0 &&np == 0 ) break;
        memset( maze, 0, sizeof(maze));
        int sum = 0;
        for ( int i = 1; i <= nk; ++i ) {
            scanf("%d", &num[i]);
            maze[0][i] = num[i];
            sum += num[i];
        }
        for ( int i = nk+1; i <= nk+np; ++i ) maze[i][nk+np+1] = 1;
        int m, t;
        for ( int i = 1; i <= nk; ++i ) a[i][0] = 0;
        for ( int i = nk+1; i <= nk+np; i++) {
            scanf("%d", &m);
            while ( m-- ) {
                scanf("%d", &t);
                a[t][++a[t][0]] = i;
                maze[t][i] = 1;
            }
        }
        if( sap(0, nk+np+1, nk+np+2) != sum ) printf("0\n");
        else{
            printf("1\n");
            for (int i = 1; i <= nk; i++ ) {
                bool first = true;
                for ( int j = 1; j <= a[i][0]; ++j ) {
                    if( maze[i][a[i][j]] == 0 ) {
                        if( first ) first = false;
                        else printf(" ");
                        printf("%d", a[i][j] - nk );
                    }
                }
                printf("\n");
            }
        }
    }
    return 0;
}