Problem of the Day

Tuesday, January 20, 2026

Problem:

Consider the following definitions, with integer values stored in a two-dimensional array.

int[][] arr2d = {{ 0,  1,  2,  3},
                 { 4,  5,  6,  7},
                 { 8,  9, 10, 11}};
int height = arr2d.length;
int width = arr2d[0].length;

It's possible to represent these same row-column values in a single-dimensional array.

int[] arr1d = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11};
int n = /* code not shown */;

where a value at index n corresponds with a given value at the position row, col. Which of the following calculations can replace /* code not shown */ to calculate the index n whose value correctly corresponds with that from the two-dimensional array at position row, col?

n = row * height + col
n = col * height + row
n = col * width + row
n = row * width + col

Show solution:

The correct answer is d. The value 6 for example, at row 1 and column 2, would have its index n calculated as n = row * width + col, or n = 1 * 4 + 2, which is 7, the index of that value in the one-dimensional array.