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| 1 | +package com.cjl.leetcode; |
| 2 | + |
| 3 | +import java.util.HashMap; |
| 4 | +import java.util.HashSet; |
| 5 | +import java.util.Map; |
| 6 | +import java.util.Set; |
| 7 | + |
| 8 | +/* |
| 9 | + 4. 寻找两个正序数组的中位数 |
| 10 | + 问题描述: |
| 11 | + 给定两个大小分别为 m 和 n 的正序(从小到大)数组 nums1 和 nums2。请你找出并返回这两个正序数组的 中位数 。 |
| 12 | + 示例 1: |
| 13 | + 输入:nums1 = [1,3], nums2 = [2] |
| 14 | + 输出:2.00000 |
| 15 | + 解释:合并数组 = [1,2,3] ,中位数 2 |
| 16 | + 示例 2: |
| 17 | + 输入:nums1 = [1,2], nums2 = [3,4] |
| 18 | + 输出:2.50000 |
| 19 | + 解释:合并数组 = [1,2,3,4] ,中位数 (2 + 3) / 2 = 2.5 |
| 20 | + 示例 3: |
| 21 | + 输入:nums1 = [0,0], nums2 = [0,0] |
| 22 | + 输出:0.00000 |
| 23 | + 示例 4: |
| 24 | + 输入:nums1 = [], nums2 = [1] |
| 25 | + 输出:1.00000 |
| 26 | + 示例 5: |
| 27 | + 输入:nums1 = [2], nums2 = [] |
| 28 | + 输出:2.00000 |
| 29 | + 提示: |
| 30 | + nums1.length == m |
| 31 | + nums2.length == n |
| 32 | + 0 <= m <= 1000 |
| 33 | + 0 <= n <= 1000 |
| 34 | + 1 <= m + n <= 2000 |
| 35 | + -10^6 <= nums1[i], nums2[i] <= 10^6 |
| 36 | + 进阶: |
| 37 | + 你能设计一个时间复杂度为 O(log (m+n)) 的算法解决此问题吗? |
| 38 | + */ |
| 39 | +public class Question_4 { |
| 40 | + |
| 41 | + // 遍历求中位数法 |
| 42 | + // 时间复杂度是O(M+N),空间复杂度是O(1) |
| 43 | + public double solution1(int[] nums1, int[] nums2) { |
| 44 | + int len = nums1.length + nums2.length; |
| 45 | + int left = -1; |
| 46 | + int right = -1; |
| 47 | + int nums1Start = 0; |
| 48 | + int nums2Start = 0; |
| 49 | + for (int i = 0; i <= len/2; i++) { |
| 50 | + left = right; |
| 51 | + if(nums1Start < nums1.length && (nums2Start >= nums2.length || nums1[nums1Start] < nums2[nums2Start])){ |
| 52 | + right = nums1[nums1Start++]; |
| 53 | + }else{ |
| 54 | + right = nums2[nums2Start++]; |
| 55 | + } |
| 56 | + } |
| 57 | + if((len & 1) == 0){ |
| 58 | + return (left + right)/2.0; |
| 59 | + }else{ |
| 60 | + return right; |
| 61 | + } |
| 62 | + } |
| 63 | + |
| 64 | + // 二分查找法求中位数 |
| 65 | + // 时间复杂度是O(log(M+N)),空间复杂度是O(1) |
| 66 | + public double solution2(int[] nums1, int[] nums2){ |
| 67 | + int len1 = nums1.length; |
| 68 | + int len2 = nums2.length; |
| 69 | + int left = (len1 + len2 + 1)/2; |
| 70 | + int right = (len1 + len2 + 2)/2; |
| 71 | + return (findKth(nums1, 0, nums2, 0, left) + findKth(nums1, 0, nums2, 0, right)) / 2.0; |
| 72 | + } |
| 73 | + |
| 74 | + private int findKth(int[] nums1, int nums1Start, int[] nums2, int nums2Start, int k) { |
| 75 | + if (nums1Start >= nums1.length) { |
| 76 | + //nums1为空数组 |
| 77 | + return nums2[nums2Start + k - 1]; |
| 78 | + } |
| 79 | + if (nums2Start >= nums2.length) { |
| 80 | + //nums2为空数组 |
| 81 | + return nums1[nums1Start + k - 1]; |
| 82 | + } |
| 83 | + if (k == 1) { |
| 84 | + return Math.min(nums1[nums1Start], nums2[nums2Start]); |
| 85 | + } |
| 86 | + int midVal1 = (nums1Start + k / 2 - 1 < nums1.length) ? nums1[nums1Start + k / 2 - 1] : Integer.MAX_VALUE; |
| 87 | + int midVal2 = (nums2Start + k / 2 - 1 < nums2.length) ? nums2[nums2Start + k / 2 - 1] : Integer.MAX_VALUE; |
| 88 | + if (midVal1 < midVal2) { |
| 89 | + return findKth(nums1, nums1Start + k / 2, nums2, nums2Start, k - k / 2); |
| 90 | + } else { |
| 91 | + return findKth(nums1, nums1Start, nums2, nums2Start + k / 2, k - k / 2); |
| 92 | + } |
| 93 | + } |
| 94 | +} |
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