leetcode4. Median of Two Sorted

There are two sorted arrays nums1 and nums2 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)).
You may assume nums1 and nums2 cannot be both empty.

Example 1:
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nums1 = [1, 3]
nums2 = [2]
The median is 2.0

Example 2:
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nums1 = [1, 2]
nums2 = [3, 4]
The median is (2 + 3)/2 = 2.5

Note:
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假设中位数左边有k个数，探析每个数组前k/2的数，剔除较小的那组k/2（所谓剔除便是更新start），接着递归
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递归运算使问题思路简化：
1. 某个数组为空
2. k=1的情况
3. k不为1的情况：更新start

class Solution:
    def findMedianSortedArrays(self, nums1, nums2):
        """
        :type nums1: List[int]
        :type nums2: List[int]
        :rtype: float
        """
        def getKth(nums1,start1,end1,nums2,start2,end2,k):
            len1 = end1 - start1 + 1
            len2 = end2 - start2 + 1
            if len1 > len2: return getKth(nums2, start2, end2, nums1, start1, end1, k)  
            #让 len1 的长度小于 len2，这样就能保证如果有数组空了，一定是 len1
            if len1 == 0: return nums2[start2 + k - 1]
            if k == 1: return min(nums1[start1], nums2[start2])
            i = start1 + min(len1, k // 2) - 1
            j = start2 + min(len2, k // 2) - 1
            if nums1[i] > nums2[j]: return getKth(nums1, start1, end1, nums2, j + 1, end2, k - (j - start2 + 1))
            else: return getKth(nums1, i + 1, end1, nums2, start2, end2, k - (i - start1 + 1))


        n = len(nums1)
        m = len(nums2)
        left = (n + m + 1) // 2
        right = (n + m + 2) // 2
        return (getKth(nums1, 0, n - 1, nums2, 0, m - 1, left) + getKth(nums1, 0, n - 1, nums2, 0, m - 1, right)) / 2 
        #将偶数和奇数的情况合并，如果是奇数，会求两次同样的 k

参考文章：
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http://windliang.cc/2018/07/18/leetCode-4-Median-of-Two-Sorted-Arrays/