Java/src/main/java/com/thealgorithms/searches/BinarySearch2dArray.java

package com.thealgorithms.searches;

/*
To apply this method, the provided array must be strictly sorted. In this method, two pointers, one
at 0th row & the other at the last row are taken & the searching is done on the basis of the middle
element of the middle column. If that element is equal to target, its coordinates are returned, else
if it is smaller than the target, the rows above that element are ignored (because the elements
above it will also be smaller than the target), else that element is greater than the target, then
the rows below it are ignored.
 */
public class BinarySearch2dArray {

    static int[] BinarySearch(int[][] arr, int target) {
        int rowCount = arr.length, colCount = arr[0].length;

        if (rowCount == 1) {
            return binarySearch(arr, target, 0, 0, colCount);
        }

        int startRow = 0, endRow = rowCount - 1, midCol = colCount / 2;

        while (startRow < endRow - 1) {
            int midRow = startRow + (endRow - startRow) / 2; // getting the index of middle row

            if (arr[midRow][midCol] == target) {
                return new int[] {midRow, midCol};
            } else if (arr[midRow][midCol] < target)
                startRow = midRow;
            else
                endRow = midRow;
        }
        /*
            if the above search fails to find the target element, these conditions will be used to
           find the target element, which further uses the binary search algorithm in the places
           which were left unexplored.
             */
        if (arr[startRow][midCol] == target)
            return new int[] {
                startRow,
                midCol,
            };

        if (arr[endRow][midCol] == target) return new int[] {endRow, midCol};

        if (target <= arr[startRow][midCol - 1])
            return binarySearch(arr, target, startRow, 0, midCol - 1);

        if (target >= arr[startRow][midCol + 1] && target <= arr[startRow][colCount - 1])
            return binarySearch(arr, target, startRow, midCol + 1, colCount - 1);

        if (target <= arr[endRow][midCol - 1])
            return binarySearch(arr, target, endRow, 0, midCol - 1);
        else
            return binarySearch(arr, target, endRow, midCol + 1, colCount - 1);
    }

    static int[] binarySearch(int[][] arr, int target, int row, int colStart, int colEnd) {
        while (colStart <= colEnd) {
            int midIndex = colStart + (colEnd - colStart) / 2;

            if (arr[row][midIndex] == target)
                return new int[] {
                    row,
                    midIndex,
                };
            else if (arr[row][midIndex] < target)
                colStart = midIndex + 1;
            else
                colEnd = midIndex - 1;
        }

        return new int[] {-1, -1};
    }
}