4. Median of Two Sorted Arrays

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

/**
 * @param {number[]} nums1
 * @param {number[]} nums2
 * @return {number}
 */


var findMedianSortedArrays = function(nums1, nums2) {

  //题目要求时间复杂度在log(n)的范围，而且是给定有序数组，
  //可以转化为找第K大的数，思想就是二分查找。   
  function findkth(a,m,b,n,k){
      
      //保证a的查找范围 小于 b的
    if(m > n){
        return findkth(b,n,a,m,k);
    }
     
  //因为m<n 所以n>0
    if(m == 0){
          return b[k-1]; 
    }
     

    if(k == 1){
        return Math.min(a[0],b[0]);
    }
        
    var pa = Math.min(k>>1,m),pb = k - pa;
      
    if(a[pa - 1] < b[pb -1]){
        return findkth(a.slice(pa),m-pa,b,n,k-pa); 
    }else if(a[pa -1] > b[pb -1]){
        //console.log(a,m,b.slice(pb),n-pb,k-pb);
        return findkth(a,m,b.slice(pb),n-pb,k-pb); 
    }else{
        return a[pa-1];
    }
        
  }
    
    var n = nums1.length;
    var m = nums2.length; 
    var total = n + m;         
    var k = total>>1;   
    
    //奇数的话
    if(total & 0x1){         
        return findkth(nums1,n,nums2,m,k+1);     
    }else{    
        return (findkth(nums1,n,nums2,m,k) + findkth(nums1,n,nums2,m,k+1))/2;
    }
};