【LOJ】#2205. 「HNOI2014」画框

题解

我原来根本不会KM

更新每个节点增加的最小值的时候，要忽略那个方访问过的右节点！！！

然后就和最小乘积生成树一样了

代码

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <queue>
#include <cmath>
#define enter putchar('\n')
#define space putchar(' ')
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define pii pair<int,int>
#define eps 1e-7
#define MAXN 100005
//#define ivorysi
using namespace std;
typedef long long int64;
typedef double db;
typedef vector<int> poly;

template<class T>
void read(T &res) {
	res = 0;char c = getchar();T f = 1;
	while(c < '0' || c > '9') {
		if(c == '-') f = -1;
		c = getchar();
	}
	while(c >= '0' && c <= '9') {
		res = res * 10 + c - '0';
		c = getchar();
	}
	res *= f;
}
template<class T>
void out(T x) {
	if(x < 0) {putchar('-');x = -x;}
	if(x >= 10) {
		out(x / 10);
	}
	putchar('0' + x % 10);
}
int T;
int N,ans;
int A[75][75],B[75][75],C[75][75];
bool vis_l[75],vis_r[75];
int slack[75],matk[75],ex_l[75],ex_r[75];
bool match(int u) {
	vis_l[u] = 1;
	for(int v = 1 ; v <= N ; ++v) {
		if(vis_r[v]) continue;
		int gap = C[u][v] - (ex_l[u] + ex_r[v]);
		if(gap == 0) {
			vis_r[v] = 1;
			if(matk[v] == -1 || match(matk[v])) {
				matk[v] = u;
				return 1;
			}
		}
		else slack[v] = min(slack[v],gap);
	}
	return 0;
}
pii KM() {
	for(int i = 1 ; i <= N ; ++i) matk[i] = -1;
	for(int i = 1 ; i <= N ; ++i) {
		ex_l[i] = 1000000000;ex_r[i] = 0;
		for(int j = 1 ; j <= N ; ++j) {
			if(C[i][j] < ex_l[i]) ex_l[i] = C[i][j];
		}
	}
	for(int i = 1 ; i <= N ; ++i) {
		for(int j = 1 ; j <= N ; ++j) slack[j] = 1000000000;
		while(1) {
			memset(vis_l,0,sizeof(vis_l));
			memset(vis_r,0,sizeof(vis_r));
			if(match(i)) break;
			int d = 1000000000;
			for(int j = 1 ; j <= N ; ++j) if(!vis_r[j]) d = min(d,slack[j]);
			for(int j = 1 ; j <= N ; ++j) {
				if(vis_l[j]) ex_l[j] += d;
				if(vis_r[j]) ex_r[j] -= d;
				else slack[j] -= d;
			}
		}
	}
	int rA = 0,rB = 0;
	for(int i = 1 ; i <= N  ; ++i) {
		rA += A[matk[i]][i];
		rB += B[matk[i]][i];
	}
	return mp(rA,rB);
}
void Init() {
	read(N);
	for(int i = 1 ; i <= N ; ++i) {
		for(int j = 1 ; j <= N ; ++j) {
			read(A[i][j]);
		}
	}
	for(int i = 1 ; i <= N ; ++i) {
		for(int j = 1 ; j <= N ; ++j) {
			read(B[i][j]);
		}
	}
}
void Calc(pii S,pii T) {
	for(int i = 1 ; i <= N ; ++i) {
		for(int j = 1 ; j <= N ; ++j) {
			C[i][j] = (S.se - T.se) * A[i][j] + (T.fi - S.fi) * B[i][j];
		}
	}
	pii M = KM();
	ans = min(ans,M.fi * M.se);
	if((T.fi - M.fi) * (S.se - M.se) - (S.fi - M.fi) * (T.se - M.se) <= 0) return;
	Calc(S,M);Calc(M,T);
}
void Solve() {
	ans = 0x7fffffff;
	memcpy(C,A,sizeof(C));
	pii S = KM();
	ans = min(ans,S.fi * S.se);
	memcpy(C,B,sizeof(C));
	pii T = KM();
	ans = min(ans,T.fi * T.se);
	if(S != T) Calc(S,T);
	out(ans);enter;
}
int main() {
#ifdef ivorysi
	freopen("f1.in","r",stdin);
#endif
	read(T);
	while(T--) {
		Init();
		Solve();
	}
	return 0;
}