Median of Two Sorted Arrays

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)).

題意：尋找兩個有序數組的中位數，要求複雜度爲O(log (m+n)).
思路：問題本質其實就是求兩個有序數組的第Kth的數，那麼我們可以這樣考慮，分別求出a,b兩個數組中第k/2th的數，這兩個數有三種情況

          當a[k/2]<b[k/2]時，那麼原kth數肯定不在a[k/2]之前的數內，然後拋棄a[k/2]之前的所有數，再在剩餘的數裏求k-(k/2)th數，其餘兩種情況同理，遞歸二分，所以複雜度降到對數級別

double find_kth(int a[],int m,int b[],int n,int k){
    if(m>n)
      return find_kth(b,n,a,m,k);
    if(m==0)
      return b[k-1];
    if(k==1)
      return min(a[0],b[0]);
    int pa=min(k/2,m),pb=k-pa;
    if(a[pa-1]<b[pb-1])
      return find_kth(a+pa,m-pa,b,n,k-pa);
    else if(a[pa-1]>b[pb-1])
           return find_kth(a,m,b+pb,n-pb,k-pb);
         else
           return a[pa-1];
}


class Solution {
public:
    double findMedianSortedArrays(int A[], int m, int B[], int n) {
        int sum=m+n;
        if(sum%2){
            return find_kth(A,m,B,n,sum/2+1);
        }
        else
            return (find_kth(A,m,B,n,sum/2)+find_kth(A,m,B,n,sum/2+1))/2;
    }
};