304. Range Sum Query 2D - Immutable

Problem:

right corner (row2, col2).

The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and (row2, col2) = (4, 3), which contains sum = 8.

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:

1. You may assume that the matrix does not change.
2. There are many calls to sumRegion function.
3. You may assume that row1 ≤ row2 and col1 ≤ col2.

Analysis:

和mutable那道思路一样的。只是在算sum的时候用到了dp.

Solution:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

class NumMatrix { int[][] dp; public NumMatrix(int[][] matrix) { if (matrix.length == 0 || matrix[0].length == 0) return; int m = matrix.length, n = matrix[0].length; dp = new int[m + 1][n + 1]; for (int r = 0; r < m; r++) for (int c = 0; c < n; c++) { dp[r + 1][c + 1] = dp[r][c + 1] + dp[r + 1][c] + matrix[r][c] - dp[r][c]; } } public int sumRegion(int row1, int col1, int row2, int col2) { return dp[row2 + 1][col2 + 1] - dp[row2 + 1][col1] - dp[row1][col2 + 1] + dp[row1][col1]; } } /** * Your NumMatrix object will be instantiated and called as such: * NumMatrix obj = new NumMatrix(matrix); * int param_1 = obj.sumRegion(row1,col1,row2,col2); */