UVa 10755 - Garbage Heap 三维最大子矩阵问题转化为1维..

A上C(20,2)卡上下界...B上C(20,2)卡上下界...在C的方向上做一维的最大连续字串问题...这样把3维的最大子矩阵问题就转化为1维的了...

预处理...sum[ x ] [ y ] [ z ] 代表在z这个二维平面上...(1,1)和(x,y)分别为对角坐标的矩阵的所有数之和....

Program:

//http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1696
#include<iostream>
#include<stdio.h>
#include<string.h>
#include<cmath>
#include<map>
#include<algorithm>
#define ll long long
#define oo 2000000000
using namespace std;    
int A,B,C;
ll sum[22][22][22];
ll getsum(int As,int Ae,int Bs,int Be,int C)
{
      return sum[Ae][Be][C]-sum[As-1][Be][C]-sum[Ae][Bs-1][C]+sum[As-1][Bs-1][C];
}
int main()
{    
      int T,t,i,j,k,As,Ae,Bs,Be,Cs,Ce;
      ll m,ans;
      cin>>T;
      for (t=1;t<=T;t++)
      {
            cin>>A>>B>>C;
            memset(sum,0,sizeof(sum));
            for (i=1;i<=A;i++)
              for (j=1;j<=B;j++)
                for (k=1;k<=C;k++)
                {
                     cin>>sum[i][j][k];
                     sum[i][j][k]+=sum[i-1][j][k]+sum[i][j-1][k]-sum[i-1][j-1][k]; 
                }
            ans=-oo;
            ans*=10000;
            for (As=1;As<=A;As++)
              for (Ae=As;Ae<=A;Ae++)
                for (Bs=1;Bs<=B;Bs++)
                  for (Be=Bs;Be<=B;Be++)
                  {
                         Cs=Ce=1;
                         m=0;
                         while (Ce<=C)
                         {
                               m+=getsum(As,Ae,Bs,Be,Ce);
                               if (m>ans) ans=m;
                               while (m<0 && Cs<=Ce)
                               {
                                     m-=getsum(As,Ae,Bs,Be,Cs);
                                     Cs++;
                                     if (Cs<=Ce && m>ans) ans=m; //保证至少一个矩阵
                               }
                               Ce++;
                         }
                  }
            if (t!=1) cout<<endl;
            cout<<ans<<endl;
      }
      return 0;
}
/*
1
2 3 3
21 -39 4 -39 4 -44 1 -32 -25 -35 2 17 6 10 2 -12 -22 35 

ans 55

1
1 2 2
-38 40 21 -34 

ans 40
*/