Leetcode 4 Median of Two Sorted Arrays - 思维决定一切 - 博客频道 - CSDN.NET



方案1:假设两个数组总共有n个元素,那么显然我们有用O(n)时间和O(n)空间的方法:用merge sort的思路排序,排序好的数组取出下标为k-1的元素就是我们需要的答案。 这个方法比较容易想到,但是有没有更好的方法呢? 但是,当k很接近于n的时候,这个方法还是很费时间的。当然,我们可以判断一下,如果k比n/2大的话,我们可以从最大的元素开始找。但是如果我们要找所有元素的中位数呢?时间还是O(n/2)=O(n)的。有没有更好的方案呢? 我们可以考虑从k入手。如果我们每次都能够剔除一个一定在第k大元素之前的元素,那么我们需要进行k次。但是如果每次我们都剔除一半呢?所以用这种类似于二分的思想,我们可以这样考虑: Assume that the number of elements in A and B are both larger than k/2, and if we compare the k/2-th smallest element in A(i.e. A[k/2-1]) and the k-th smallest element in B(i.e. B[k/2 - 1]), there are three results: (Becasue k can be odd or even number,

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