HDU-2255 奔小康赚大钱

来源：互联网发布：渣优化编辑：程序博客网时间：2024/05/06 21:25

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=2255

解题思路：

二分图最优匹配的裸题，需要学习一下KM算法。。这道题也可以用网络流做，等学了网络流之后再写一下网络流的解题思路。

本题提供2个版本，一个是最朴素的KM算法，一个是优化后的KM算法（另外使用了输入外挂，成功刷入杭电前三）

代码如下：

#include<iostream>#include<cstdio>#include<cstring>#include<climits>#include<algorithm>using namespace std;#define N 310int map[N][N];bool visitx[N], visity[N];int lx[N], ly[N];int match[N];int n;bool Hungary(int u) //匈牙利算法{visitx[u] = true;for(int i = 0; i < n; ++i){if(!visity[i] && lx[u] + ly[i] == map[u][i]){visity[i] = true;if(match[i] == -1 || Hungary(match[i])){match[i] = u;return true;}}}return false;}void KM_perfect_match(){int temp;memset(lx, 0, sizeof(lx)); //初始化顶标memset(ly, 0, sizeof(ly)); //ly[i]为0for(int i = 0; i < n; ++i) //lx[i]为权值最大的边for(int j = 0; j < n; ++j)lx[i] = max(lx[i], map[i][j]);for(int i = 0; i < n; ++i) //对n个点匹配{while(1){memset(visitx, false, sizeof(visitx));memset(visity, false, sizeof(visity));if(Hungary(i)) //匹配成功break;else //匹配失败，找最小值{temp = INT_MAX;for(int j = 0; j < n; ++j) //x在交错树中if(visitx[j])for(int k = 0; k < n; ++k) //y在交错树外if(!visity[k] && temp > lx[j] + ly[k] - map[j][k])temp = lx[j] + ly[k] - map[j][k];for(int j = 0; j < n; ++j) //更新顶标{if(visitx[j])lx[j] -= temp;if(visity[j])ly[j] += temp;}}}}}int main(){int ans;while(scanf("%d", &n) != EOF){ans = 0;memset(match, -1, sizeof(match));for(int i = 0; i < n; ++i)for(int j = 0; j < n; ++j)scanf("%d", &map[i][j]);KM_perfect_match();for(int i = 0; i < n; ++i) //权值相加ans += map[match[i]][i];printf("%d\n", ans);}return 0;}

优化版本：

#include<iostream>#include<cstdio>#include<cstring>#include<climits>#include<algorithm>using namespace std;#define N 310int map[N][N];bool visitx[N], visity[N];int lx[N], ly[N];int slack[N];int match[N];int n;int Scan(){int res = 0 , ch ;while( !( ( ch = getchar() ) >= '0' && ch <= '9' ) ){if( ch == EOF )  return 1 << 30 ;}res = ch - '0' ;while( ( ch = getchar() ) >= '0' && ch <= '9' )res = res * 10 + ( ch - '0' ) ;return res ;}bool Hungary(int u) //匈牙利算法{visitx[u] = true;for(int i = 0; i < n; ++i){if(visity[i])continue;if(lx[u] + ly[i] == map[u][i]){visity[i] = true;if(match[i] == -1 || Hungary(match[i])){match[i] = u;return true;}}else //不在相等子图slack[i] = min(slack[i], lx[u] + ly[i] - map[u][i]);}return false;}void KM_perfect_match(){int temp;memset(lx, 0, sizeof(lx)); //初始化顶标memset(ly, 0, sizeof(ly)); //ly[i]为0for(int i = 0; i < n; ++i) //lx[i]为权值最大的边for(int j = 0; j < n; ++j)lx[i] = max(lx[i], map[i][j]);for(int i = 0; i < n; ++i) //对n个点匹配{for(int j = 0; j < n; ++j)slack[j] = INT_MAX;while(1){memset(visitx, false, sizeof(visitx));memset(visity, false, sizeof(visity));if(Hungary(i)) //匹配成功break;else //匹配失败，找最小值{temp = INT_MAX;for(int j = 0; j < n; ++j)if(!visity[j])if(temp > slack[j])temp = slack[j];for(int j = 0; j < n; ++j) //更新顶标{if(visitx[j])lx[j] -= temp;if(visity[j])ly[j] += temp;elseslack[j] -= temp;}}}}}int main(){int ans;while(scanf("%d", &n) != EOF){ans = 0;memset(match, -1, sizeof(match));for(int i = 0; i < n; ++i)for(int j = 0; j < n; ++j)map[i][j] = Scan();KM_perfect_match();for(int i = 0; i < n; ++i) //权值相加ans += map[match[i]][i];printf("%d\n", ans);}return 0;}