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 83 | #include <cstdio> #include <cstring> #include <algorithm> using namespace std; #define Update(x, y) x = max(x, y) const int MAX_ROW = 110, MAX_COL = 5, MAX_K = 15, MAX_STATE = 5, MINF = 0xcfcfcfcf; int F[MAX_ROW][MAX_STATE][MAX_K]; int A[MAX_ROW][MAX_COL]; int TotRow, TotCol, K; 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++) { Update(F[i][0][k], F[i - 1][0][k]), Update(F[i][0][k], F[i - 1][1][k]); if (k >= 1) Update(F[i][1][k], A[i][1] + F[i - 1][0][k - 1]), Update(F[i][1][k], A[i][1] + F[i - 1][1][k - 1]); Update(F[i][1][k], A[i][1] + F[i - 1][1][k]); } } return max(F[TotRow][0][K], F[TotRow][1][K]); } int DP2() { memset (F, 0xcf, sizeof (F)); F[0][0][0] = 0; for ( int i = 1; i <= TotRow; i++) for ( int k = 0; k <= K; k++) { for ( int j = 0; j <= 4; j++) Update(F[i][0][k], F[i - 1][j][k]); if (k >= 1) for ( int j = 0; j <= 4; j++) Update(F[i][1][k], A[i][1] + F[i - 1][j][k - 1]); Update(F[i][1][k], A[i][1] + F[i - 1][1][k]); Update(F[i][1][k], A[i][1] + F[i - 1][3][k]); if (k >= 1) for ( int j = 0; j <= 4; j++) Update(F[i][2][k], A[i][2] + F[i - 1][j][k - 1]); Update(F[i][2][k], A[i][2] + F[i - 1][2][k]); Update(F[i][2][k], A[i][2] + F[i - 1][3][k]); if (k >= 2) for ( int j = 0; j <= 4; j++) Update(F[i][3][k], A[i][1] + A[i][2] + F[i - 1][j][k - 2]); if (k >= 1) Update(F[i][3][k], A[i][1] + A[i][2] + F[i - 1][1][k - 1]), Update(F[i][3][k], A[i][1] + A[i][2] + F[i - 1][2][k - 1]); Update(F[i][3][k], A[i][1] + A[i][2] + F[i - 1][3][k]); if (k >= 1) for ( int j = 0; j <= 4; j++) Update(F[i][4][k], A[i][1] + A[i][2] + F[i - 1][j][k - 1]); Update(F[i][4][k], A[i][1] + A[i][2] + F[i - 1][4][k]); } int ans = MINF; for ( int i = 0; i <= 4; i++) Update(ans, F[TotRow][i][K]); return ans; } 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]); if (TotCol == 1) printf ( "%d\n" , DP1()); else printf ( "%d\n" , DP2()); } |
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()); } |
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