标题效果:鉴于加权值矩阵,带走一个地方的权利值之后,与其相邻的格儿童权利值变0。问多少可以取出到右值。
思维:Amber论文题目。不难建设,图着色。颜色从S连边,还有一种颜色向T连边。再把相邻的格子连边。之后跑最小割,用总权值减去最大流就是答案。
CODE:
#include <queue>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define MAX 400
#define MAXP 40000
#define MAXE 500010
#define INF 0x3f3f3f3f
#define S 0
#define T 39999
using namespace std;
const int dx[] = {0,1,0,-1,0};
const int dy[] = {0,0,1,0,-1}; int m,n,cnt;
int src[MAX][MAX],num[MAX][MAX]; int head[MAXP],total = 1;
int next[MAXE],aim[MAXE],flow[MAXE]; int deep[MAXP]; inline void Add(int x,int y,int f)
{
next[++total] = head[x];
aim[total] = y;
flow[total] = f;
head[x] = total;
} bool BFS()
{
static queue<int> q;
while(!q.empty()) q.pop();
memset(deep,0,sizeof(deep));
deep[S] = 1;
q.push(S);
while(!q.empty()) {
int x = q.front(); q.pop();
for(int i = head[x]; i; i = next[i])
if(flow[i] && !deep[aim[i]]) {
deep[aim[i]] = deep[x] + 1;
q.push(aim[i]);
if(aim[i] == T) return true;
}
}
return false;
} int Dinic(int x,int f)
{
if(x == T) return f;
int temp = f;
for(int i = head[x]; i; i = next[i])
if(flow[i] && deep[aim[i]] == deep[x] + 1 && temp) {
int away = Dinic(aim[i],min(temp,flow[i]));
if(!away) deep[aim[i]] = 0;
flow[i] -= away;
flow[i^1] += away;
temp -= away;
}
return f - temp;
} int main()
{
cin >> m >> n;
int sum = 0;
for(int i = 1; i <= m; ++i)
for(int j = 1; j <= n; ++j) {
scanf("%d",&src[i][j]);
sum += src[i][j];
num[i][j] = ++cnt;
if((i + j)&1)
Add(S,num[i][j],src[i][j]),Add(num[i][j],S,0);
else
Add(num[i][j],T,src[i][j]),Add(T,num[i][j],0);
}
for(int i = 1; i <= m; ++i)
for(int j = 1; j <= n; ++j) {
if(((i + j)&1) == 0) continue;
for(int k = 1; k <= 4; ++k) {
int fx = i + dx[k];
int fy = j + dy[k];
if(!fx || !fy || fx > m || fy > n) continue;
Add(num[i][j],num[fx][fy],INF);
Add(num[fx][fy],num[i][j],0);
}
}
int max_flow = 0;
while(BFS())
max_flow += Dinic(S,INF);
cout << sum - max_flow << endl;
return 0;
}
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