304.Range Sum Query 2D - Immutable

304.Range Sum Query 2D - Immutable

• 題目描述：Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (*row*1, *col*1) and lower right corner (*row*2, *col*2).

• 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

• 題目描述：給定矩陣，輸入一個範圍，找出矩陣範圍內元素的和

• 代碼：

  class NumMatrix {
  
     private int[][] dp;
  
        public NumMatrix(int[][] matrix) {
            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];
            for(int i=1;i<=m;i++) {
                for(int j=1;j<=n;j++) {
                    dp[i][j] = matrix[i - 1][j - 1] + dp[i - 1][j] + dp[i][j - 1] - dp[i - 1][j - 1];
                }
            }
        }
  
        public int sumRegion(int row1, int col1, int row2, int col2) {
            int iMin = Math.min(row1, row2);
            int iMax = Math.max(row1, row2);
  
            int jMin = Math.min(col1, col2);
            int jMax = Math.max(col1, col2);
  
            return dp[iMax + 1][jMax + 1] - dp[iMax + 1][jMin] - dp[iMin][jMax + 1] + dp[iMin][jMin];
        }
  }
  
  /**
  * Your NumMatrix object will be instantiated and called as such:
  * NumMatrix obj = new NumMatrix(matrix);
  * int param_1 = obj.sumRegion(row1,col1,row2,col2);
  */