05 August 2008
矩阵的区域和，新的矩阵的每个元素都满足一定条件 - 二维前缀和， 为了方便计算，前缀和的矩阵dp的行列均比mat多1，那么dp[i][j]就是（0 <= 行 <= i， 0 <= 列 <= j)范围内的和，可通过动态规划求出；
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class Solution {
public int[][] matrixBlockSum(int[][] mat, int K) {
int row = mat.length;
int col = mat[0].length;
int[][] result = new int[row][col];
int[][] dp = new int[row + 1][col + 1];
for (int i = 1; i <= row; i++) {
for (int j = 1; j <= col; j++) {
dp[i][j] = mat[i - 1][j - 1] + dp[i][j - 1] + dp[i - 1][j] - dp[i - 1][j - 1];
}
}
for (int i = 1; i <= row; i++) {
for (int j = 1; j <= col; j++) {
int x0 = Math.max(i - K - 1, 0);
int x1 = Math.min(i + K, row);
int y0 = Math.max(j - K - 1, 0);
int y1 = Math.min(j + K, col);
result[i - 1][j - 1] = dp[x1][y1] - dp[x1][y0] - dp[x0][y1] + dp[x0][y0];
}
}
return result;
}
}