Recursive Binary Search

Instead of a loop, the range narrows with each recursive call. The base case is an empty range: nothing left to check.

public static int binarySearch(int[] data, int target, int low, int high) {
    if (low > high) {
        return -1;
    }
    int mid = (low + high) / 2;
    if (data[mid] == target) {
        return mid;
    } else if (data[mid] < target) {
        return binarySearch(data, target, mid + 1, high);
    } else {
        return binarySearch(data, target, low, mid - 1);
    }
}

Recursive Merge Sort

Merge sort splits the array in half, recursively sorts each half, then merges the two already-sorted halves back into one sorted array.

public static int[] mergeSort(int[] data) {
    if (data.length <= 1) {
        return data;
    }
    int mid = data.length / 2;
    // split into left (0..mid-1) and right (mid..end)
    int[] sortedLeft = mergeSort(left);
    int[] sortedRight = mergeSort(right);
    return merge(sortedLeft, sortedRight);
}