4. Median of Two Sorted Arrays

题目：

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　

 

复杂度：

时间：O(n+m)、空间：O(1)

 

实现：

public class Solution {
    public double findMedianSortedArrays(int[] nums1, int[] nums2) {
        if(nums1.length == 0 && nums2.length == 0) {
            return 0;
        } else if(nums1.length == 0) {
            if(nums2.length % 2 == 0) {
                return (nums2[nums2.length / 2 - 1] + nums2[nums2.length / 2]) / (double)2;
            } else {
                return nums2[nums2.length / 2];
            }
        } else if(nums2.length == 0) {
            if(nums1.length % 2 == 0) {
                return (nums1[nums1.length / 2 - 1] + nums1[nums1.length / 2]) / (double)2;
            } else {
                return nums1[nums1.length / 2];
            }
        } else {
            // store lastest tow values
            int[] nums = new int[] { 0, 0 };
            
            // merge join
            int nums1Index = 0, nums2Index = 0, counter = 0;
            for(int i = 0; i < nums1.length + nums2.length; ++i) {
                nums[0] = nums[1];
                if(nums1Index < nums1.length && (nums2Index >= nums2.length || nums1[nums1Index] < nums2[nums2Index])) {
                    nums[1] = nums1[nums1Index];
                    nums1Index++;
                } else {
                    nums[1] = nums2[nums2Index];
                    nums2Index++;
                }
                
                if((++counter == ((nums1.length + nums2.length) / 2 + 1))) {
                     if((nums1.length + nums2.length) % 2 == 0) {
                         return (nums[0] + nums[1]) / (double)2;
                     } else {
                         return nums[1];
                     }
                }
            }
            
            return 0;
        }
    }
}

 

应用：

• SQL Server Merge Join