[BZOJ 3144] [Hnoi2013] 切糕 【最小割】

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>

using namespace std;

const int MaxN = 40, MaxNode = 65000 + 15, INF = 999999999, Dx[5] = {0, 0, 1, -1}, Dy[5] = {1, -1, 0, 0};

int P, Q, R, D, S, T, Tot, MaxFlow;
int Idx[MaxN][MaxN][MaxN], V[MaxN][MaxN][MaxN], Num[MaxNode], d[MaxNode];
 
struct Edge
{
    int v, w;
    Edge *Next, *Other;
} E[MaxNode * 6], *Pi = E, *Point[MaxNode], *Last[MaxNode];
  
inline void AddEdge(int x, int y, int z)
{
    Edge *Q = ++Pi; ++Pi;
    Pi -> v = y; Pi -> w = z;
    Pi -> Next = Point[x]; Point[x] = Pi; Pi -> Other = Q;
    Q -> v = x; Q -> w = 0;
    Q -> Next = Point[y]; Point[y] = Q; Q -> Other = Pi;
}
  
inline int gmin(int a, int b) {return a < b ? a : b;}
  
int DFS(int Now, int Flow)
{
    if (Now == T) return Flow;
    int ret = 0;
    for (Edge *j = Last[Now]; j; j = j -> Next)
        if (j -> w && d[Now] == d[j -> v] + 1)
        {
            Last[Now] = j;
            int p = DFS(j -> v, gmin(j -> w, Flow - ret));
            ret += p; j -> w -= p; j -> Other -> w += p;
            if (ret == Flow) return ret;
        }
    if (d[S] >= Tot) return ret;
    if (--Num[d[Now]] == 0) d[S] = Tot;
    ++Num[++d[Now]];
    Last[Now] = Point[Now];
    return ret;
}
 
inline bool Inside(int x, int y)
{
    if (x < 1 || x > P) return false;
    if (y < 1 || y > Q) return false;
    return true;
}

int main()
{
	scanf("%d%d%d%d", &P, &Q, &R, &D);
	for (int i = 1; i <= R; ++i) 
		for (int j = 1; j <= P; ++j)
			for (int k = 1; k <= Q; ++k)
				scanf("%d", &V[j][k][i]);
	for (int i = 1; i <= P; ++i)
		for (int j = 1; j <= Q; ++j)
			for (int k = 1; k <= R; ++k)
				Idx[i][j][k] = (k - 1) * (P * Q) + (i - 1) * Q + j;
	Tot = Idx[P][Q][R]; S = ++Tot; T = ++Tot;
	for (int i = 1; i <= P; ++i)
		for (int j = 1; j <= Q; ++j)
		{
			Idx[i][j][1] = S;
			Idx[i][j][R + 1] = T;
			for (int k = 1; k <= R; ++k)
			{
				AddEdge(Idx[i][j][k], Idx[i][j][k + 1], V[i][j][k]);
				if (k > D + 1)
				{
					int x, y;
					for (int f = 0; f < 4; ++f)
					{
						x = i + Dx[f]; y = j + Dy[f];
						if (!Inside(x, y)) continue;
						AddEdge(Idx[i][j][k], Idx[x][y][k - D], INF);
					}
				}
			}
		}
	MaxFlow = 0;
    memset(d, 0, sizeof(d));
    memset(Num, 0, sizeof(Num)); Num[0] = Tot;
    for (int i = 1; i <= Tot; ++i) Last[i] = Point[i];
    while (d[S] < Tot) MaxFlow += DFS(S, INF);
    printf("%d\n", MaxFlow);
	return 0;
}