4. Median of Two Sorted Arrays

Posted 2020-10-09 暗影侠客

4. Median of Two Sorted Arrays

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

 1 /**
 2  * @param {number[]} nums1
 3  * @param {number[]} nums2
 4  * @return {number}
 5  */
 6 
 7 
 8 var findMedianSortedArrays = function(nums1, nums2) {
 9 
10   //题目要求时间复杂度在log(n)的范围，而且是给定有序数组，
11   //可以转化为找第K大的数，思想就是二分查找。   
12   function findkth(a,m,b,n,k){
13       
14       //保证a的查找范围 小于 b的
15     if(m > n){
16         return findkth(b,n,a,m,k);
17     }
18      
19   //因为m<n 所以n>0
20     if(m == 0){
21           return b[k-1]; 
22     }
23      
24 
25     if(k == 1){
26         return Math.min(a[0],b[0]);
27     }
28         
29     var pa = Math.min(k>>1,m),pb = k - pa;
30       
31     if(a[pa - 1] < b[pb -1]){
32         return findkth(a.slice(pa),m-pa,b,n,k-pa); 
33     }else if(a[pa -1] > b[pb -1]){
34         //console.log(a,m,b.slice(pb),n-pb,k-pb);
35         return findkth(a,m,b.slice(pb),n-pb,k-pb); 
36     }else{
37         return a[pa-1];
38     }
39         
40   }
41     
42     var n = nums1.length;
43     var m = nums2.length; 
44     var total = n + m;         
45     var k = total>>1;   
46     
47     //奇数的话
48     if(total & 0x1){         
49         return findkth(nums1,n,nums2,m,k+1);     
50     }else{    
51         return (findkth(nums1,n,nums2,m,k) + findkth(nums1,n,nums2,m,k+1))/2;
52     }
53 };