004 Median of Two Sorted Arrays ⭐

最新推荐文章于 2025-12-03 23:35:37 发布

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本文介绍了一个复杂度为O(log(m+n))的算法，用于找出两个已排序数组的中位数。通过巧妙地使用二分法，该算法有效地解决了问题，并提供了详细的实现步骤。

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)).

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(object):
    def findMedianSortedArrays(self, A, B):
        """
        :type nums1: List[int]
        :type nums2: List[int]
        :rtype: float
        """
        m,n=len(A),len(B)
        if m>n:
            A,B,m,n=B,A,n,m
        imin=0
        imax=m
        halflen=(m+n+1)/2
        while imin<=imax:
            i=(imin+imax)/2
            j=halflen-i
            if i<m and B[j-1]>A[i]:
                imin=i+1
            elif i>0 and A[i-1]>B[j]:
                imax=i-1
            else:
                if i==0:
                    lmax=B[j-1]
                elif j==0:
                    lmax=A[i-1]
                else:
                    lmax=max(A[i-1],B[j-1])
                if (m+n)%2==1:
                    return lmax
                if i == m: 
                    rmin = B[j]
            	elif j == n: 
                    rmin = A[i]
            	else: 
                    rmin = min(A[i], B[j])
                return (lmax + rmin)/2.0

这题挺难，看了答案，这个二分法的思路挺精巧