304 - Range Sum Query 2D - Immutable

Total Accepted: 14771 Total Submissions: 66244 Difficulty: Medium

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).

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

Hide Tags Dynamic Programming
Hide Similar Problems (E) Range Sum Query - Immutable (H) Range Sum Query 2D - Mutable

public class NumMatrix {

 private int[][] dp;

 public NumMatrix(int[][] matrix) {
  // https://leetcode.com/discuss/69047/clean-and-easy-to-understand-java-solution
  if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
   return;
  }
  int m = matrix.length;
  int n = matrix[0].length;
  dp = new int[m + 1][n + 1]; // dp[0][0] = 0, dp[0][j] = 0, dp[i][0] = 0,
         // 第一行第一列初始值为0

  for (int i = 1; i <= m; i++) {
   for (int j = 1; j <= n; j++) {
    dp[i][j] = dp[i - 1][j] + dp[i][j - 1] - dp[i - 1][j - 1] + matrix[i - 1][j - 1];
   }
  }

 }

 public int sumRegion(int row1, int col1, int row2, int col2) {
  return dp[row2 + 1][col2 + 1] - dp[row1][col2 + 1] - dp[row2 + 1][col1] + dp[row1][col1];
 }

 public static void main(String[] args) {
  // TODO Auto-generated method stub
  int[][] 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 } };

  // Your NumMatrix object will be instantiated and called as such:
  NumMatrix numMatrix = new NumMatrix(matrix);
  int sum1 = numMatrix.sumRegion(1, 2, 2, 4); // 12
  int sum2 = numMatrix.sumRegion(2, 1, 4, 3); // 8
  int sum3 = numMatrix.sumRegion(0, 1, 2, 3); // 19
  System.out.printf("sum1 = %d, sum2 = %d, sum3 = %d", sum1, sum2, sum3);

 }

}