How to find sum of elements above secondary diagonal in matrix?

Question

I tried searching for the solution to this problem for a while now and couldn't find anything. How do I sum the elements above the secondary diagonal in a matrix (just with loops, nothing fancy) in Java?

This is what I tried:

public static void Page106Ex3$H(int[][] mat) {
    int sum = 0;

    for (int i = 1; i < mat.length; i++) {
        for (int j = i-1; j >= 0; j--) {
            sum += mat[i][j];
        }
    }

    System.out.println("Sum: " + sum);
}

You should not use `$` in an identifier in Java. While `$` is legal, its use is reserved for the Java tools chain itself and 3rd-party tools. If you use `$` in your code, you are liable to write code that accidentally collides with ... generated code. — Stephen C, Dec 31 '21 at 07:39

score 3 · Answer 1 · 2021-12-31T08:19:51.007

For square matrix of any order you can use this code,

This code has answer for both primary and secondary diagonals and are separated by comments in the code

private static void calcDiagonalSumMatrix(int[][] mat) {
        int sum = 0, leftDiagonal = 0, rightDiagonal = mat[0].length - 1;

        //This loop is for primary diagonal
        for (int[] ints : mat) {
            sum += ints[leftDiagonal++];
        }
        
        //This loop is for secondary diagonal
        for(int [] intArray: mat) {
            sum += intArray[rightDiagonal--];
        }

        //This loop is what you have to use
        for(int x = 0; x < matrix.length; x++) {
            rightDiagonal--;
            for(int y = rightDiagonal; y >=0; y--) {
                sum += mat[x][y];
        }
    }

        System.out.println(sum);
    }

Explanation :

Three integers variables are declared one to calculate sum then the leftDiagonal is to calculate the index of top left to bottom right diagonal and the rightDiagonal is used as index of top right to bottom left diagonal.
Then using the enhanced for loops or foreach loops, calculate the sum of the leftDiagonal and that same of right diagonal.
In each for loop for left diagonal the loop first picks the first set of array then the leftDiagonal variable which acts as the index will start from 0 and increase by one for each loops and the same goes for the rightDiagonal except the right diagonal starts from the order - 1 which is the index of the top right element.
Then the third loop actually has two loop, the outer loop will be taking the int array elements then the innermost loop will loop through the elements that the first loop took and adds up the elements from each int[] set excluding the secondary diagonal elements.

score 1 · Answer 2 · edited Dec 31 '21 at 07:51

The secondary diagonal element in row i is present at (mat.length-i-1). In a row all the elements before the element present at secondary diagonal comes above the secondary diagonal we need to add them.

The below solution is considering indexing start from 0.

public static void Page106Ex3$H(int[][] mat) {
    int sum = 0;
    int n = mat.length;
    for (int i = 0; i < n; i++) {
         int j = n - i - 2; // index of element just before the 
                            // secondary diagonal element in row i
         while(j >= 0){
            sum += mat[i][j];
            j--;
         }
    }
    System.out.println("Sum: " + sum);

}

score 1 · Accepted Answer · answered Dec 31 '21 at 07:45

If the elements on the secondary are not included, the number of columns in the nested loop should be decremented with indexes starting from 0.

public static int sumOver2ndDiagonal(int[][] arr) {
    int sum = 0;
    for (int i = 0, n = arr.length - 1; i < n; i++) {
        for (int j = 0, m = arr[i].length - 1 - i; j < m; j++) {
            sum += arr[i][j];
        }
    }
    return sum;
}

Test:

System.out.println(sumOver2ndDiagonal(
    new int[][]{
        { 1,  2,  3,  4},
        { 5,  6,  7,  8},
        { 9, 10, 11, 12},
        {13, 14, 15, 16}
    }
));
// 1 + 2 + 3 + 5 + 6 + 9
// -> 26

How to find sum of elements above secondary diagonal in matrix?

3 Answers3