Binary Search in 2D Array

Question

I wonder, can binary search be applied on a 2D array?

• What would the conditions on the array be? Sorted on 2D??

Answer 1

Just pretend it's a 1D array and calculate the correct row and column as you divide and conquer:

/**
* @param grid {[[number]]} A 2D NxM grid of numbers
* @param targetValue {number} The target value to search
* @return {[number]} A list containing the row and column. For example, [0,5] means row 0 column 5 
*/
function search (grid, targetValue) {
    let rows = grid.length;
    let cols = grid[0].length;

    let leftBound = 0;
    let rightBound = rows * cols - 1;

    while (true) {
        let currentIndex = parseInt((leftBound + rightBound) / 2);
        let currentRow = parseInt(currentIndex / cols);
        let currentColumn = currentIndex % cols;
        let currentValue = grid[currentRow][currentColumn];

        if (currentValue === targetValue) {
            return [currentRow, currentColumn];
        }
        else if (rightBound <= leftBound) {
            return [-1, -1];
        }
        else if (currentValue < targetValue) {
            leftBound = currentIndex + 1;
        }
        else {
            rightBound = currentIndex - 1;
        }
    }

}

search([[11,12,15,23],[25,28,31,32],[35,45,47,47],[50,51,55,56],[65,65,78,88]], 45);