【leetcode】Median of Two Sorted Arrays

题目简述：

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)).

解题思路：

这本身是个很简单的题目，但是题目要求他的复杂度为O(log(m+n))，就很有难度了。不过首先我们还是可以明确我们要用分治法。关键是怎么分治呢？我们有如下的思路（核心思想是求第k小）：

class Solution:
    def findk(self, A, m, B, n, k):
        if m > n:
            return self.findk(B, n, A, m, k)
        if m == 0:
            return B[k-1]
        if k == 1:
            return min(A[0],B[0])
        pa = min(k / 2, m)
        pb = k - pa
        if A[pa - 1] < B[pb - 1]: 
            return self.findk(A[pa:], m - pa, B, n, k - pa)
        elif A[pa - 1] > B[pb - 1]:
            return self.findk(A, m, B[pb:], n - pb, k - pb)
        else:
            return A[pa - 1]

    # @return a float
    def findMedianSortedArrays(self, A, B):
        la = len(A)
        lb = len(B)
        l = la + lb
        if l % 2 == 0:
            return (self.findk(A, la, B, lb, l/2+1) + self.findk(A, la, B, lb, l/2))/2.0
        else:
            return self.findk(A, la, B, lb, l/2+1)

很容易证明这个想法的复杂度正是O(log(m+n))