4. Median of Two Sorted Arrays

题目:

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)).

链接: http://leetcode.com/problems/median-of-two-sorted-arrays/

题解：

把题目从find median转换为find k/2 th最小值。注意边界条件当k = 1时取A[0]与B[0]两数中较小者。Time Complexity O(log(m + n))，Space Complexity O(1)

public class Solution {

    public double findMedianSortedArrays(int A[], int B[]) {

        int len = A.length + B.length;

        if(len % 2 == 0)

            return (findKth(A, 0, B, 0, len / 2) + findKth(A, 0, B, 0, len / 2 + 1)) / 2.0;

        else

            return findKth(A, 0, B, 0, len / 2 + 1);        

    }

    

    private double 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);

    }

}

Reference: 

http://www.cnblogs.com/springfor/p/3861890.html

http://blog.csdn.net/yutianzuijin/article/details/11499917