Median of Two Sorted Arrays

There are two sorted arrays A and B of size m and n respectively. Find the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)).

• Time: O(n)
• Space: O(1)

public double findMedianSortedArrays(int A[], int B[]) {
    int a = A.length, b = B.length, n = a + b;
    if (n % 2 == 0) {
        return (findkth(A, 0, B, 0, n / 2) + findkth(A, 0, B, 0, n / 2 + 1)) / 2.0;
    } else {
        return findkth(A, 0, B, 0, n / 2 + 1);
    }
}

private int findkth(int[] A, int a, int[] B, int b, int k) {
    if (A.length - a > B.length - b) {
        return findkth(B, b, A, a, k);
    }
    if (A.length <= a) {
        return B[b + k -1];
    }
    if (k == 1) {
        return Math.min(A[a], B[b]);
    }
    int midA = Math.min(k / 2, A.length - a);
    int midB = k - midA;
    if (A[a + midA - 1] < B[b + midB - 1]) {
        return findkth(A, a + midA, B, b, k - midA);
    } else if (A[a + midA - 1] > B[b + midB - 1]) {
        return findkth(A, a, B, b + midB, k - midB);
    } else {
        return A[a + midA - 1];
    }
}