# Median of Two Sorted Arrays

http://www.lintcode.com/en/problem/median-of-two-sorted-arrays/

## Question

There are two sorted arrays A and B of size m and n respectively. Find the median of the two sorted arrays.

Example

Given A=[1,2,3,4,5,6] and B=[2,3,4,5], the median is 3.5.

Given A=[1,2,3] and B=[4,5], the median is 3.

## Solution

``````class Solution {
/**
* @param A: An integer array.
* @param B: An integer array.
* @return: a double whose format is *.5 or *.0
*/
public double findMedianSortedArrays(int[] A, int[] B) {
int totalLength = A.length + B.length;
if (totalLength % 2 == 1) {
return findKth(A, 0, B, 0, totalLength / 2 + 1);
}
return (findKth(A, 0, B, 0, totalLength / 2) + findKth(A, 0, B, 0, totalLength / 2 + 1)) / 2.0;
}

public int findKth(int[] A, int A_start, int[] B, int B_start, int k) {
if (A_start >= A.length) {
return B[B_start + k - 1];
}
if (B_start >= B.length) {
return A[A_start + k - 1];
}

if (k == 1) {
return Math.min(A[A_start], B[B_start]);
}

int A_key = A_start + k / 2 - 1 < A.length
? A[A_start + k / 2 - 1]
: Integer.MAX_VALUE;
int B_key = B_start + k / 2 - 1 < B.length
? B[B_start + k / 2 - 1]
: Integer.MAX_VALUE;

if (A_key < B_key) {
return findKth(A, A_start + k / 2, B, B_start, k - k / 2);
} else {
return findKth(A, A_start, B, B_start + k / 2, k - k / 2);
}

}
}
``````