给定一个数组，求如果排序之后，相邻两数的最大差值，要求时 间复杂度O(N)，且要求不能用非基于比较的排序

Posted 2021-10-21 lihuazhu

思路：

　　桶排序

　　N个数，设置 N+ 1 个桶，，一定有一个空桶，，为的是保证最大差值一定是不是出现在同一个桶中；

　　只要比较 非空桶 的最小值，与前一个 非空桶的最大值，求 最大的差值，

 

  1 package my_basic;
  2 
  3 import java.text.Bidi;
  4 import java.util.Arrays;
  5 
  6 public class MaxGap {
  7 
  8     /*给定一个数组，求如果排序之后，相邻两数的最大差值，要求时 间复杂度O(N)，且要求不能用非基于比较的排序*/
  9     
 10     public static int maxGap(int[] arr) {
 11         if (arr == null || arr.length < 2) {
 12             return 0;
 13         }
 14         //获取最小值 最大值
 15         int len = arr.length;
 16         int min = Integer.MAX_VALUE;
 17         int max = Integer.MIN_VALUE;
 18         for (int i = 0; i < arr.length; i++) {
 19             min = Math.min(min, arr[i]);
 20             max = Math.max(max, arr[i]);
 21         }
 22         if (min == max) {
 23             return 0;
 24         }
 25         //放到桶里
 26         boolean[] hasNum = new boolean[len + 1];
 27         int[] mins = new int[len + 1];
 28         int[] maxs = new int[len + 1];
 29         
 30         int bid = 0;
 31 //        for (int i = 0; i < arr.length; i++) {
 32 //            bid = bucket(arr[i], len, min, max);
 33 //            hasNum[bid] = true;
 34 //            mins[bid] = Math.min(mins[bid], arr[i]);
 35 //            maxs[bid] = Math.max(maxs[bid], arr[i]);        
 36 //        }
 37         for (int i = 0; i < len; i++) {
 38             bid = bucket(arr[i], len, min, max);
 39             mins[bid] = hasNum[bid] ? Math.min(mins[bid], arr[i]) : arr[i];
 40             maxs[bid] = hasNum[bid] ? Math.max(maxs[bid], arr[i]) : arr[i];
 41             hasNum[bid] = true;
 42         }
 43         
 44         //找最大间距
 45         int res =0;
 46         int m = maxs[0];
 47         for(int i=1 ;i <= len;i++) {
 48             if (hasNum[i]) {
 49                 res = (mins[i] - m)>res ? (mins[i] - m) : res;
 50                 m = maxs[i];
 51             }
 52         }
 53         return res;
 54 
 55     }
 56     
 57     //放到几号桶里
 58     public static int bucket(long num, long len, long min, long max) {
 59         return (int) ((num - min) * len / (max - min));
 60     }
 61     
 62     //对数器
 63     public static int[] generateRandomArray(int maxSize, int maxValue) {
 64         int[] arr = new int[(int) ((maxSize + 1) * Math.random())];
 65         for (int i = 0; i < arr.length; i++) {
 66             arr[i] = (int) ((maxValue + 1) * Math.random()) - (int) (maxValue * Math.random());
 67         }
 68         return arr;
 69     }
 70     public static int comparetor(int[] arr) {
 71         if (arr==null || arr.length < 2) {
 72             return 0;
 73         }
 74         Arrays.sort(arr);
 75 //        printArray(arr);
 76         int res=0;
 77         for (int i = 1; i < arr.length; i++) {
 78             res = (arr[i] - arr[i-1]) > res? (arr[i] - arr[i-1]) :res;
 79         }
 80         return res;
 81     }
 82     
 83     public static void printArray(int[] arr) {
 84         for (int i = 0; i < arr.length; i++) {
 85             System.out.print(arr[i]+" ");
 86         }
 87         System.out.println();
 88     }
 89     public static int[] copyArray(int[] arr) {
 90         if (arr == null) {
 91             return null;
 92         }
 93         int[] res = new int[arr.length];
 94         for (int i = 0; i < arr.length; i++) {
 95             res[i] = arr[i];
 96         }
 97         return res;
 98     }
 99 
100     public static void main(String[] args) {
101         int maxSize =10;
102         int maxValue = 50;
103         boolean succeed = true;
104         int[] arr1 = generateRandomArray(maxSize, maxValue);
105         printArray(arr1);        
106         int res = maxGap(arr1);
107         
108         int[] arr2 = copyArray(arr1);
109         int res2 = comparetor(arr2);
110         if (res != res2) {
111             printArray(arr1);
112             printArray(arr2);
113             System.out.println(res);
114             System.out.println(res2);
115             
116         }else {
117             System.out.println("nice!");
118         }
119         
120     }
121 
122     
123 
124 }