0004-Median-of-Two-Sorted-Arrays.py

'''
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:

nums1 = [1, 3]
nums2 = [2]

The median is 2.0

Example 2:

nums1 = [1, 2]
nums2 = [3, 4]

The median is (2 + 3)/2 = 2.5
'''
class Solution:
    def findMedianSortedArrays(self, nums1: List[int], nums2: List[int]) -> float:
        m, n = len(nums1), len(nums2)
        if m > n:
            nums1, nums2, m, n = nums2, nums1, n, m
        if not n:
            return
        
        imin, imax, half_len = 0, m, (m + n + 1) // 2
        while imin <= imax:
            i = (imin + imax) // 2
            j = half_len - i
            if i < m and nums2[j - 1] > nums1[i]:
                imin = i + 1
            elif i > 0 and nums1[i - 1] > nums2[j]:
                imax = i - 1
            else:
                if not i:
                    max_left = nums2[j - 1]
                elif not j:
                    max_left = nums1[i - 1]
                else:
                    max_left = max(nums1[i - 1], nums2[j - 1])
                    
                if (m + n) % 2 == 1:
                    return max_left
                
                if i == m:
                    min_right = nums2[j]
                elif j == n:
                    min_right = nums1[i]
                else:
                    min_right = min(nums1[i], nums2[j])
                    
                return (max_left + min_right) / 2.0