220. Contains Duplicate III

题目：

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.

链接： http://leetcode.com/problems/contains-duplicate-iii/

题解：

一开始的想法是用类似Contains Duplicate II的方法，不过好像不好写。于是研究了一下Discuss，发现有大概三种解法。

1. Sort the array， keep original index
2. TreeMap
3. Bucket sliding window.

最后暂时只做了第一种方法。排序以后再查找，这里需要自己定义一个数据结构，implements Comparable，并且还有一个inRangeTWith method来比较两个节点的原index是否在t范围内。  二刷一定要补上第二和第三种。

Time Complexity - O(n²) ， Space Complexity - O(n)

public class Solution {
    public boolean containsNearbyAlmostDuplicate(int[] nums, int k, int t) {
        if(nums == null || nums.length < 2 || t < 0 || k < 0)
            return false;

        ValueWithIndex[] arr = new ValueWithIndex[nums.length];
        for(int i = 0; i < nums.length; i++)
            arr[i] = new ValueWithIndex(nums[i], i);

        Arrays.sort(arr);

        for(int i = 0; i < arr.length; i++) {
            for(int j = i + 1; (j < arr.length) && (arr[j].inRangeTWith(arr[i], t)); j++) {
                if(Math.abs(arr[i].index - arr[j].index) <= k)
                    return true;
            }
        }
        return false;
    }

    private class ValueWithIndex implements Comparable<ValueWithIndex> {
        public int value;
        public int index; 

        public ValueWithIndex(int val, int i) {
            this.value = val;
            this.index = i;
        }

        public int compareTo(ValueWithIndex v2) {
            if(value < 0 && v2.value >= 0)
                return -1;
            if(value >= 0 && v2.value < 0)
                return 1;
            return value - v2.value;
        }

        public boolean inRangeTWith(ValueWithIndex v2, int t) { // value always >= v2.value
            if(value == v2.value)
                return true;
            if(value >= 0 && v2.value >= 0)
                return value - v2.value <= t;
            else if(value < 0 && v2.value < 0)
                return value <= v2.value + t;
            else
                return value - t <= v2.value;
        }
    }
}

二刷:

Java:

使用类似Contains Duplicates II的方法。 Time Complexity - O(n ^ 2) TLE, Space Complexity - O(n)

public class Solution {
    public boolean containsNearbyAlmostDuplicate(int[] nums, int k, int t) {
        if (nums == null || nums.length < 2) return false;
        Set<Integer> set = new HashSet<>();

        for (int i = 0; i < nums.length; i++) {
            for (int num : set) {
                if (Math.abs(num - nums[i]) <= t) return true;
            }
            set.add(nums[i]);
            if (i >= k - 1) set.remove(i - k + 1);
        }
        return false;
    }
}

新建数据结构先排序再查找。

1. 这里我们先构建一个Node class包含val和index
2. 根据数组，用nums[i]和i作为pair创建Node数组
3. 对Node数组使用nums[i]进行排序
4. 使用sliding window进行比较，这个部分比较的复杂度其实是O(n)

要注意我们的Node class继承了Comparable<Node> interface， 注意写compareTo() 和 inRangeTWith() 这两个方法时的一些边界条件地处理。

Time Complexity - O(nlogn) ， Space Complexity - O(n)

public class Solution {
    public boolean containsNearbyAlmostDuplicate(int[] nums, int k, int t) {
        if (nums == null || nums.length < 2 || t < 0 || k < 0) return false;
        int len = nums.length;
        Node[] nodes = new Node[len];
        for (int i = 0; i < len; i++) nodes[i] = new Node(nums[i], i);
        Arrays.sort(nodes);

        for (int i = 0; i < len; i++) {
            for (int j = i + 1; (j < len) && (nodes[j].inRangeTWith(nodes[i], t)); j++) {
                if (Math.abs(nodes[i].index - nodes[j].index) <= k) return true;
            }
        }
        return false;
    }

    private class Node implements Comparable<Node> {
        public int val;
        public int index; 

        public Node(int val, int i) {
            this.val = val;
            this.index = i;
        }

        public int compareTo(Node n2) {
            if (val < 0 && n2.val >= 0) return -1;
            if (val >= 0 && n2.val < 0) return 1;
            return val - n2.val;
        }

        public boolean inRangeTWith(Node n2, int t) { // value always >= v2.value
            if(val == n2.val) return true;
            if((val >= 0 && n2.val >= 0) || (val < 0 && n2.val < 0)) {
                return val - n2.val <= t;
            } else {
                return val <= n2.val - t;
            }

        }
    }
}

Reference:

https://leetcode.com/discuss/65056/java-python-one-pass-solution-o-n-time-o-n-space-using-buckets

https://leetcode.com/discuss/47974/java-treeset-implementation-nlogk

https://leetcode.com/discuss/52545/java-solution-without-dictionary-sort-nums-record-positions

https://leetcode.com/discuss/39216/ac-short-java-solution-using-treeset-and-subset-function

https://leetcode.com/discuss/38206/ac-o-n-solution-in-java-using-buckets-with-explanation

https://leetcode.com/discuss/38177/java-o-n-lg-k-solution

https://leetcode.com/discuss/38148/my-o-n-accepted-java-solution-using-hashmap

https://leetcode.com/discuss/38146/java-solution-with-treeset