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Median of Two Sorted Arrays

题目描述:

  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)).

  找两个有序数组的中位数,这并不难。可是题目把时间复杂度降到O(log(m+n)),难度就上去了。

我尝试解答,想到了把问题转换为求两个有序数组的第k小的数,奈何能力有限,最终铩羽而归。

下面贴出一个Accepted Code:

double findKth(int a[], int m, int b[], int n, int k){    //always assume that m is equal or smaller than n    if (m > n)        return findKth(b, n, a, m, k);    if (m == 0)        return b[k - 1];    if (k == 1)        return min(a[0], b[0]);    //divide k into two parts    int pa = min(k / 2, m), pb = k - pa;    if (a[pa - 1] < b[pb - 1])        return findKth(a + pa, m - pa, b, n, k - pa);    else if (a[pa - 1] > b[pb - 1])        return findKth(a, m, b + pb, n - pb, k - pb);    else        return a[pa - 1];}double findMedianSortedArrays(int A[], int m, int B[], int n){    int total = m + n;    if (total % 2 == 1)        return findKth(A, m, B, n, total / 2 + 1);    else        return (findKth(A, m, B, n, total / 2)        + findKth(A, m, B, n, total / 2 + 1)) / 2;}

如果想了解思路来源,可参考原文链接:http://blog.csdn.net/yutianzuijin/article/details/11499917
ps:

  oj论坛上有人给出了复杂度更低的算法,但是思路没有上述方法清晰。

Median of Two Sorted Arrays