# Find closest value for every element in array

Given an array of integers, find the closest element for every element.

Examples:

Input : arr[] = {10, 5, 11, 6, 20, 12}

Output : 6, -1, 10, 5, 12, 11Input : arr[] = {10, 5, 11, 10, 20, 12}

Output : 5 -1 10 5 12 11

A **simple solution** is to run two nested loops. We pick an outer element one by one. For every picked element, we traverse remaining array and find closest element. Time complexity of this solution is O(n*n)

An **efficient solution **is to use Self Balancing BST (Implemented as set in C++ and TreeSet in Java). In a Self Balancing BST, we can do both insert and closest greater operations in O(Log n) time.

`// Java program to demonstrate insertions in TreeSet` `import` `java.util.*;` ` ` `class` `TreeSetDemo {` ` ` `public` `static` `void` `closestGreater(` `int` `[] arr)` ` ` `{` ` ` `if` `(arr.length == -` `1` `) {` ` ` `System.out.print(-` `1` `+ ` `" "` `);` ` ` `return` `;` ` ` `}` ` ` ` ` `// Insert all array elements into a TreeMap.` ` ` `// A TreeMap value indicates whether an element` ` ` `// appears once or more.` ` ` `TreeMap<Integer, Boolean> tm = ` ` ` `new` `TreeMap<Integer, Boolean>();` ` ` `for` `(` `int` `i = ` `0` `; i < arr.length; i++) {` ` ` ` ` `// A value "True" means that the key` ` ` `// appears more than once.` ` ` `if` `(tm.containsKey(arr[i]))` ` ` `tm.put(arr[i], ` `true` `);` ` ` `else` ` ` `tm.put(arr[i], ` `false` `);` ` ` `}` ` ` ` ` `// Find smallest greater element for every` ` ` `// array element` ` ` `for` `(` `int` `i = ` `0` `; i < arr.length; i++) {` ` ` ` ` `// If there are multiple occurrences` ` ` `if` `(tm.get(arr[i]) == ` `true` `)` ` ` `{` ` ` `System.out.print(arr[i] + ` `" "` `);` ` ` `continue` `;` ` ` `}` ` ` ` ` `// If element appears only once` ` ` `Integer greater = tm.higherKey(arr[i]);` ` ` `Integer lower = tm.lowerKey(arr[i]);` ` ` `if` `(greater == ` `null` `)` ` ` `System.out.print(lower + ` `" "` `);` ` ` `else` `if` `(lower == ` `null` `)` ` ` `System.out.print(greater + ` `" "` `);` ` ` `else` `{` ` ` `int` `d1 = greater - arr[i];` ` ` `int` `d2 = arr[i] - lower;` ` ` `if` `(d1 > d2)` ` ` `System.out.print(lower + ` `" "` `);` ` ` `else` ` ` `System.out.print(greater + ` `" "` `);` ` ` `}` ` ` `}` ` ` `}` ` ` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `[] arr = { ` `10` `, ` `5` `, ` `11` `, ` `6` `, ` `20` `, ` `12` `, ` `10` `};` ` ` `closestGreater(arr);` ` ` `}` `}` |

**Output:**

10 6 12 5 12 11 10

**Exercise :** Another efficient solution is to use sorting that also works in O(n Log n) time. Write complete algorithm and code for sorting based solution.

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