题目:
Given an unsorted array, find the maximum difference between the successive elements in its sorted form.
Try to solve it in linear time/space.
Return 0 if the array contains less than 2 elements.
You may assume all elements in the array are non-negative integers and fit in the 32-bit signed integer range.
解答:
这题挺难理解的,但是可以举例,比如说现在有1, 3, 5, 9。那么我们可以把它分成3个bucket来装,min表示在这个bucket范围中,存在的最小数和最大数。这个bucket的长度是最小可能的最大差值。(如果哪个差值比这个还小,那么为了填补这个小差值,就必然存在另一个差值比它大,那么这个数组的最大差值就比当前bucket大。所以均分下来的bucket是最小可能的最大差值)
b0: (1, 3) min = Integer.max, max = Integer.min
b1: (4, 6) min = Integer.max, max = Integer.min
b2: (7, 9) min = Integer.max, max = Integer.min
然后我们来看这个数组里的数在哪个bucket里,用(nums(i) - min) / gap来得到,
第一个数1在b0中,所以我们更新:
b0: (1, 3) min = 1, max = 1;
第二个数3在b0中,所以我们更新:
b0: (1, 3) min = 1, max = 3;
第三个数5在b1中,所以我们更新:
b1: (4, 6) min = 5, max = 5;
.
.
依次这样下去。
因为每个bucket中的最大值-最小值就是我们最小的gap, 所以我们不用计算相邻的两个数,我们只要比较后一个bucket中的最小值和前一个bucket中的最大值相差多少,取最大相差的值就是最终的结果。注意考虑min和max两个边界值也要加进去。
public int maximumGap(int[] nums) {if (nums == null || nums.length < 2) return 0;int len = nums.length;int max = nums[0], min = nums[0];for (int i = 0; i < nums.length; i++) {max = Math.max(max, nums[i]);min = Math.min(min, nums[i]);}//Math.ceil与最小的比这个数大的蒸熟,使bucket可以包含所有数int gap = (int)Math.ceil((double)(max - min) / (len - 1));int[] BucketsMIN = new int[len - 1];int[] BucketsMAX = new int[len - 1];Arrays.fill(BucketsMIN, Integer.MAX_VALUE);Arrays.fill(BucketsMAX, Integer.MIN_VALUE);for (int num : nums) {//不考虑边界,所以把边界的min和max都拿出来,单独再考虑if (num == min || num == max) continue;int bucket = (num - min) / gap;BucketsMIN[bucket] = Math.min(BucketsMIN[bucket], num);BucketsMAX[bucket] = Math.max(BucketsMAX[bucket], num);}int result = 0;int previous = min;for (int i = 0; i < len - 1; i++) {if (BucketsMIN[i] == Integer.MAX_VALUE && BucketsMAX[i] == Integer.MIN_VALUE) {continue;}result = Math.max(result, BucketsMIN[i] - previous);previous = BucketsMAX[i];}result = Math.max(result, max - previous);return result;}