Given an array of integers, find out whether there are two distinct indices i and j in the array such that the difference between nums[i] and nums[j] is at most t and the difference between i and j is at most k.

O(n log k) time O(k) space solution

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public class Solution {
    public boolean containsNearbyAlmostDuplicate(int[] nums, int k, int t) {
        if (nums == null || nums.length == 0 || k <= 0) {
            return false;
        }
        
        TreeSet<Integer> set = new TreeSet<>();
        for (int i = 0; i < nums.length; i++) {
            int cur = nums[i];
            Integer floor = set.floor(cur + t);
            if (floor != null && floor >= cur) {
                return true;
            }
            Integer ceil = set.ceiling(cur - t);
            if (ceil != null && ceil <= cur) {
                return true;
            }
            
            set.add(cur);
            if (set.size() > k) {
                set.remove(nums[i - k]);
            }
        }
        return false;
    }
}

O(n) time using Buckets

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public class Solution {
    private long getId(long num, long bucket) {
        return num < 0 ? (num + 1)/bucket - 1 : num / bucket;
    }
    
    public boolean containsNearbyAlmostDuplicate(int[] nums, int k, int t) {
        if (nums == null || nums.length == 0 || k <= 0 || t < 0) {
            return false;
        }
        Map<Long, Long> map = new HashMap<>();
        long bucket = t + 1;
        for (int i = 0; i < nums.length; i++) {
            long id = getId(nums[i], bucket);
            if (map.containsKey(id)) {
                return true;
            }
            if (map.containsKey(id - 1) && (Math.abs(nums[i] - map.get(id - 1)) < bucket)) {
                return true;
            }
            if (map.containsKey(id + 1) && (Math.abs(nums[i] - map.get(id + 1)) < bucket)) {
                return true;
            }
            map.put(id, (long) nums[i]);
            if (map.size() > k) {
                map.remove(getId(nums[i - k], bucket));
            }
        }
        return false;
    }
}