思路:题目说得很明显了,一行或一列中最多放一个车,,,给了一些可以放车的点,必然有个可以放最多个车的方案,设最多放ans个车;这样的话,有些点不放车,换成另外一个地方放车也是可以最多放ans个车的,但是有些点是必须放菜能使最后可以放ans个车,问有多少个第二种情况的点;既然问点有多少个,,,我就枚举每个点不放车时,这种时候可以放的车的最大数目max_num,如果不等于ans,必然这个点满足要求;这样一来,整个题的思路就清楚了;
所以最后用一个Hungary() + 枚举删点就好了;
PS:Hungary()的思想就是寻找增广路径(这个是图论中常用的概念,请百度资料然后熟记),可以在当前匹配M的情况下,还能利用原关系找到两个未匹配点的匹配,就说明找到了一个,则此时|M| + 1就变成新的匹配了;
知道找不到这种路径,算法就结束了;
题目链接
/***************************************** Author :Crazy_AC(JamesQi) Time :2015 File Name : *****************************************/ // #pragma comment(linker, "/STACK:1024000000,1024000000") #include <iostream> #include <algorithm> #include <iomanip> #include <sstream> #include <string> #include <stack> #include <queue> #include <deque> #include <vector> #include <map> #include <set> #include <stdio.h> #include <string.h> #include <math.h> #include <stdlib.h> #include <limits.h> using namespace std; #define MEM(a,b) memset(a,b,sizeof a) #define pk push_back template<class T> inline T Get_Max(const T&a,const T&b){return a < b?b:a;} template<class T> inline T Get_Min(const T&a,const T&b){return a < b?a:b;} typedef long long ll; typedef pair<int,int> ii; const int inf = 1 << 30; const int INF = 0x3f3f3f3f; const int MOD = 1e9 + 7; const int maxn = 105; int gg[maxn][maxn]; int link[maxn];//(x,y)的匹配关系; bool vis[maxn];//每次增广保证不会重复访问; int chess[maxn * maxn][2];//棋子的位置; inline void Init(int K){ for (int i = 1;i <= K;++i) gg[chess[i][0]][chess[i][1]] = 1; } bool Search_Path(int M,int u){ for (int i = 1;i <= M;++i){ if (!vis[i] && gg[u][i]){ vis[i] = 1; if (link[i] == 0 || Search_Path(M,link[i])){ link[i] = u; return true; } } } return false; } inline int Hungary(int N,int M){ int ret = 0; for (int i = 1;i <= N;++i){ for (int j = 1;j <= M;++j) vis[j] = 0; if (Search_Path(M,i)) ret++; } return ret; } int main() { // ios::sync_with_stdio(false); // freopen("in.txt","r",stdin); // freopen("out.txt","w",stdout); int N,M,K; int iCase = 0; while(~scanf("%d%d%d",&N,&M,&K)){ int rec = 0; for (int i = 1;i <= K;++i){ scanf("%d%d",&chess[i][0],&chess[i][1]); } MEM(gg, 0); MEM(link, 0); Init(K); int ans = Hungary(N,M); for (int i = 1;i <= K;++i){ for (int j = 0;j <= M;j++) link[j] = 0; gg[chess[i][0]][chess[i][1]] ^= 1; if (Hungary(N,M) != ans) rec++; gg[chess[i][0]][chess[i][1]] ^= 1; } // printf("ans = %d\n",ans); // printf("rec = %d\n",rec); printf("Board %d have %d important blanks for %d chessmen.\n",++iCase, rec, ans); } return 0; }