LeetCode – Range Sum Query 2D – Immutable (Java)

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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).

Analysis

Since the assumption is that there are many calls to sumRegion method, we should use some extra space to store the intermediate results.

The solution is similar to other sum related problems such as . The basic idea is demonstrated in the following example:

Here we define an array sum[][] which stores the sum value from (0,0) to the current cell.

Java Solution

public class NumMatrix {
    int [][] sum;
 
    public NumMatrix(int[][] matrix) {
        if(matrix==null || matrix.length==0||matrix[0].length==0)
            return;
 
        int m = matrix.length;
        int n = matrix[0].length;
        sum = new int[m][n];
 
        for(int i=0; i<m; i++){
            int sumRow=0;
            for(int j=0; j<n; j++){
                if(i==0){
                    sumRow += matrix[i][j];
                    sum[i][j]=sumRow;
                }else{
                    sumRow += matrix[i][j];
                    sum[i][j]=sumRow+sum[i-1][j];
                }
 
            }
        }
    }
 
    public int sumRegion(int row1, int col1, int row2, int col2) {
        if(this.sum==null) 
            return 0;
 
        int topRightX = row1;
        int topRightY = col2;
 
        int bottomLeftX=row2;
        int bottomLeftY= col1;
 
        int result=0;
 
        if(row1==0 && col1==0){
            result = sum[row2][col2];
        }else if(row1==0){
            result = sum[row2][col2]
                    -sum[bottomLeftX][bottomLeftY-1];
 
        }else if(col1==0){
            result = sum[row2][col2]
                    -sum[topRightX-1][topRightY];
        }else{
            result = sum[row2][col2]
                    -sum[topRightX-1][topRightY]
                    -sum[bottomLeftX][bottomLeftY-1]
                    +sum[row1-1][col1-1];
        }
 
        return result;
    }
}

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