Bzoj2007: [Noi2010]海拔

题面

传送门

Sol

显然是求这样一个东西

绿色的线为分割线，左上海拔为\(0\)，右下为\(1\)
分隔线经过的边就是贡献的答案
那么这就是平面图最小割，转成对偶图求最短路就好了

\(SPFA\)真心慢，以后还是跑\(Dijstra\)

# include <bits/stdc++.h>
# define RG register
# define IL inline
# define Fill(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long ll;
const int _(1e6 + 5);
typedef int Arr[_];

IL int Input(){
    RG int x = 0, z = 1; RG char c = getchar();
    for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1;
    for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48);
    return x * z;
}

int n, cnt, S, T, id[505][505], num;
Arr dis, vis, first;
struct Edge{
	int to, next, w;
} edge[_  << 1];
queue <int> Q;

IL void Add(RG int u, RG int v, RG int w){
    edge[cnt] = (Edge){v, first[u], w}, first[u] = cnt++;
}

IL int SPFA(){
    Fill(dis, 127); dis[S] = 0;
    vis[S] = 1; Q.push(S);
    while(!Q.empty()){
        RG int u = Q.front(); Q.pop();
        for(RG int e = first[u]; e != -1; e = edge[e].next){
			RG int w = edge[e].w, v = edge[e].to;
            if(dis[u] + w < dis[v]){
                dis[v] = dis[u] + w;
                if(!vis[v]) vis[v] = 1, Q.push(v); 
            }
		}
        vis[u] = 0;
    }
    return dis[T];
}

int main(RG int argc, RG char* argv[]){
    Fill(first, -1), n = Input();
    for(RG int i = 1; i <= n; ++i)
        for(RG int j = 1; j <= n; ++j)
            id[i][j] = ++num;
    T = num + 1; RG int r = n + 1;
	for(RG int i = 1; i <= r; ++i)
		for(RG int j = 1; j <= n; ++j){
			RG int v = Input();
			if(i == 1) Add(id[i][j], T, v);
			else if(i == r) Add(S, id[i - 1][j], v);
			else Add(id[i][j], id[i - 1][j], v);
		}
	for(RG int i = 1; i <= n; ++i)
		for(RG int j = 1; j <= r; ++j){
			RG int v = Input();
			if(j == 1) Add(S, id[i][j], v);
			else if(j == r) Add(id[i][j - 1], T, v);
			else Add(id[i][j - 1], id[i][j], v);
		}
	for(RG int i = 1; i <= r; ++i)
		for(RG int j = 1; j <= n; ++j){
			RG int v = Input();
			if(i == 1) Add(T, id[i][j], v);
			else if(i == r) Add(id[i - 1][j], S, v);
			else Add(id[i - 1][j], id[i][j], v);
		}
	for(RG int i = 1; i <= n; ++i)
		for(RG int j = 1; j <= r; ++j){
			RG int v = Input();
			if(j == 1) Add(id[i][j], S, v);
			else if(j == r) Add(T, id[i][j - 1], v);
			else Add(id[i][j], id[i][j - 1], v);
		}
    printf("%d\n", SPFA());
    return 0;
}