164 Maximum Gap 最大间距
给定一个无序的数组,找出数组在排序后相邻的元素之间最大的差值。
尽量尝试在线性时间和空间复杂度情况下解决此问题。
若数组元素个数少于2,则返回0。
假定所有的元素都是非负整数且范围在32位有符号整数范围内。
详见:https://leetcode.com/problems/maximum-gap/description/
Java实现:题目要求是要线性的时间和空间,那么只能用桶排序。同一个桶里的数差值不会有不同桶间的差值大,所以找桶内最大和下一个非空桶的桶内最小进行比较即可。
class Solution {
public int maximumGap(int[] nums) {
int n=nums.length;
if (nums == null || n < 2){
return 0;
}
// 计算数组中的最大值和最小值
int min = nums[0];
int max = nums[0];
for (int num:nums) {
min = min>num?num:min;
max = max<num?num:max;
}
// the minimum possibale gap, ceiling of the integer division
int gap = (int)Math.ceil((double)(max - min)/(n - 1));
int[] bucketsMIN = new int[n - 1]; // 记录桶中的最小值
int[] bucketsMAX = new int[n - 1]; // 记录桶中最大值
Arrays.fill(bucketsMIN, Integer.MAX_VALUE);
Arrays.fill(bucketsMAX, Integer.MIN_VALUE);
// put numbers into buckets
for (int num:nums) {
if (num == min || num == max){
continue;
}
int idx = (num - min) / gap; // index of the right position in the buckets
bucketsMIN[idx] = Math.min(num, bucketsMIN[idx]);
bucketsMAX[idx] = Math.max(num, bucketsMAX[idx]);
}
// scan the buckets for the max gap
int maxGap = Integer.MIN_VALUE;
int previous = min;
for (int i = 0; i < n - 1; i++) {
if (bucketsMIN[i] == Integer.MAX_VALUE && bucketsMAX[i] == Integer.MIN_VALUE){
// 跳过空桶
continue;
}
// min value minus the previous value is the current gap
maxGap = Math.max(maxGap, bucketsMIN[i] - previous);
// update previous bucket value
previous = bucketsMAX[i];
}
maxGap = Math.max(maxGap, max - previous); // 更新最大间隔
return maxGap;
}
}
参考:https://www.cnblogs.com/grandyang/p/4234970.html
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