luogu2331 [SCOI2005]最大子矩阵

题目大意

  这里有一个n*m的矩阵,请你选出其中k个子矩阵,使得这个k个子矩阵分值之和最大。注意:选出的k个子矩阵不能相互重叠。1≤n≤100,1≤m≤2,1≤k≤10。

思路

  

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
 
const int MAX_ROW = 110, MAX_COL = 5, MAX_K = 15, MINF = 0xcfcfcfcf;
int F[MAX_ROW][MAX_ROW][MAX_K];
int A[MAX_ROW][MAX_COL];
int Sum[MAX_ROW][MAX_COL];
int TotRow, TotCol, K;
 
void InitSum()
{
    for (int row = 1; row <= TotRow; row++)
        for (int col = 1; col <= TotCol; col++)
            Sum[row][col] = Sum[row - 1][col] + Sum[row][col - 1] - Sum[row - 1][col - 1] + A[row][col];
}
 
int GetSum(int row1, int col1, int row2, int col2)
{
    return Sum[row2][col2] - Sum[row2][col1 - 1] - Sum[row1 - 1][col2] + Sum[row1 - 1][col1 - 1];
}
 
int DP1()
{
    memset(F, 0xcf, sizeof(F));
    F[0][0][0] = 0;
    for (int i = 1; i <= TotRow; i++)
    {
        for (int k = 0; k <= K; k++)
        {
            F[i][0][k] = F[i - 1][0][k];
            if (k >= 1)
                for (int j = 1; j <= i; j++)
                    F[i][0][k] = max(F[i][0][k], F[j - 1][0][k - 1] + GetSum(j, 1, i, 1));
        }
    }
    return F[TotRow][0][K];
}
 
int DP2()
{
    memset(F, 0xcf, sizeof(F));
    F[0][0][0] = 0;
    for (int i = 0; i <= TotRow; i++)
    {
        for (int j = 0; j <= TotRow; j++)
        {
            for (int k = 0; k <= K; k++)
            {
                if (i >= 1)
                    F[i][j][k] = max(F[i][j][k], F[i - 1][j][k]);
                if (j >= 1)
                    F[i][j][k] = max(F[i][j][k], F[i][j - 1][k]);
                if (k >= 1)
                {
                    for (int i1 = 1; i1 <= i; i1++)
                        F[i][j][k] = max(F[i][j][k], F[i1 - 1][j][k - 1] + GetSum(i1, 1, i, 1));
                    for (int j1 = 1; j1 <= j; j1++)
                        F[i][j][k] = max(F[i][j][k], F[i][j1 - 1][k - 1] + GetSum(j1, 2, j, 2));
                    if (i == j)
                        for (int i1 = 1; i1 <= i; i1++)
                            F[i][j][k] = max(F[i][j][k], F[i1 - 1][i1 - 1][k - 1] + GetSum(i1, 1, j, 2));
                }
            }
        }
    }
    return F[TotRow][TotRow][K];
}
 
int main()
{
    scanf("%d%d%d", &TotRow, &TotCol, &K);
    for (int i = 1; i <= TotRow; i++)
        for (int j = 1; j <= TotCol; j++)
            scanf("%d", &A[i][j]);
    InitSum();
    if (TotCol == 1)
        printf("%d\n", DP1());
    else
        printf("%d\n", DP2());
}

  

posted @   headboy2002  阅读(182)  评论(2编辑  收藏  举报
努力加载评论中...
点击右上角即可分享
微信分享提示