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)).
You may assume nums1 and nums2 cannot be both empty.
Example 1:
nums1 = [1, 3] nums2 = [2] The median is 2.0
Example 2:
nums1 = [1, 2]g nums2 = [3, 4] The median is (2 + 3)/2 = 2.5
翻译: 求两个排序数组的中位数
最容易想到的就是新建一个数组,将前两个数组的值挨个放进去,最后找到中位数。这样也能得到答案,但是时间复杂度是
O(m+n), 达不到要求的 O(log (m+n)) 、居然也通过了。。。
package pers.leetcode;
/**
* 求两个数组的中位数
*
* @author admin
* @date 2019/3/14 9:25
*/
public class MedianSortedArrays {
public static void main(String[] args) {
int[] nums1 = {1, 3};
int[] nums2 = {2};
System.out.println("中位数 : " + findMedianSortedArrays(nums1, nums2));
}
public static double findMedianSortedArrays(int[] nums1, int[] nums2){
double median;
int lengthSum = nums1.length + nums2.length;
int[] nums3 = new int[lengthSum];
int i = 0, j = 0;
while (i < nums1.length && j < nums2.length){
if (nums1[i] <= nums2[j]){
nums3[i+j] = nums1[i++];
}else {
nums3[i+j] = nums2[j++];
}
}
if (i == nums1.length){
for (int count = j; count < nums2.length; count++){
nums3[i+count] = nums2[count];
}
}
if (j == nums2.length){
for (int count = i; count < nums1.length; count++){
nums3[j+count] = nums1[count];
}
}
if (lengthSum % 2 == 0){
double sum = nums3[lengthSum/2 - 1] + nums3[lengthSum/2];
median = sum/2;
}else {
median = nums3[lengthSum/2];
}
return median;
}
}
这里给出推荐的解法:
class Solution {
public double findMedianSortedArrays(int[] A, int[] B) {
int m = A.length;
int n = B.length;
if (m > n) { // to ensure m<=n
int[] temp = A; A = B; B = temp;
int tmp = m; m = n; n = tmp;
}
int iMin = 0, iMax = m, halfLen = (m + n + 1) / 2;
while (iMin <= iMax) {
int i = (iMin + iMax) / 2;
int j = halfLen - i;
if (i < iMax && B[j-1] > A[i]){
iMin = i + 1; // i is too small
}
else if (i > iMin && A[i-1] > B[j]) {
iMax = i - 1; // i is too big
}
else { // i is perfect
int maxLeft = 0;
if (i == 0) { maxLeft = B[j-1]; }
else if (j == 0) { maxLeft = A[i-1]; }
else { maxLeft = Math.max(A[i-1], B[j-1]); }
if ( (m + n) % 2 == 1 ) { return maxLeft; }
int minRight = 0;
if (i == m) { minRight = B[j]; }
else if (j == n) { minRight = A[i]; }
else { minRight = Math.min(B[j], A[i]); }
return (maxLeft + minRight) / 2.0;
}
}
return 0.0;
}
}