Range Sum Query 2D - Immutable
題意：
Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2).
Example:
Given matrix = [
[3, 0, 1, 4, 2],
[5, 6, 3, 2, 1],
[1, 2, 0, 1, 5],
[4, 1, 0, 1, 7],
[1, 0, 3, 0, 5]
]
- sumRegion(2, 1, 4, 3) -> 8
- sumRegion(1, 1, 2, 2) -> 11
- sumRegion(1, 2, 2, 4) -> 12
Note: You may assume that the matrix does not change. There are many calls to sumRegion function.
解題思路：
建立一個sum 的二維陣列
sum[i][j] 表示從matrix[0][0] - matrix[i][j] 的submatrix元素總和，接著只需要利用subarray sum的方式
sum[i] - sum[j] 表示sum[i到j]的元素總和
public class NumMatrix {
int[][] sum;
public NumMatrix(int[][] matrix) {
if (matrix == null || matrix.length == 0) {
return;
}
int rows = matrix.length;
int cols = matrix[0].length;
sum = new int[rows + 1][cols + 1];
for (int i = 1; i <= rows; i++) {
for (int j = 1; j <= cols; j++) {
sum[i][j] = sum[i - 1][j] + sum[i][j - 1] + matrix[i - 1][j - 1] - sum[i - 1][j - 1];
}
}
}
public int sumRegion(int row1, int col1, int row2, int col2) {
return sum[row2 + 1][col2 + 1] - sum[row1][col2 + 1] - sum[row2 + 1][col1] + sum[row1][col1];
}
}
// Your NumMatrix object will be instantiated and called as such:
// NumMatrix numMatrix = new NumMatrix(matrix);
// numMatrix.sumRegion(0, 1, 2, 3);
// numMatrix.sumRegion(1, 2, 3, 4);