# Find k closest numbers in an unsorted array

Given an unsorted array and two numbers x and k, find k closest values to x.

Examples:

```Input : arr[] = {10, 2, 14, 4, 7, 6}, x = 5, k = 3
Output : 4 6 7
Three closest values of x are 4, 6 and 7.

Input : arr[] = {-10, -50, 20, 17, 80}, x = 20, k = 2
Output : 17, 20
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

A simple solution is to sort the array. Then apply the method discussed to k closest values in a sorted array.

Time Complexity : O(n Log n)

A better solution is to use Heap Data Structure
1) Make a max heap of differences with first k elements.
2) For every element starting from (k+1)-th element, do following.
…..a) Find difference of current element with x.
…..b) If difference is more than root of heap, ignore current element.
…..c) Else insert the current element to the heap after removing the root.
3) Finally the heap has k closest elements.

## C++

 `// C++ program to find k closest elements ` `#include ` `using` `namespace` `std; ` ` `  `void` `printKclosest(``int` `arr[], ``int` `n, ``int` `x, ` `                   ``int` `k) ` `{ ` `    ``// Make a max heap of difference with ` `    ``// first k elements. ` `    ``priority_queue > pq; ` `    ``for` `(``int` `i = 0; i < k; i++) ` `        ``pq.push({ ``abs``(arr[i] - x), i }); ` ` `  `    ``// Now process remaining elements. ` `    ``for` `(``int` `i = k; i < n; i++) { ` ` `  `        ``int` `diff = ``abs``(arr[i] - x); ` ` `  `        ``// If difference with current ` `        ``// element is more than root, ` `        ``// then ignore it. ` `        ``if` `(diff > pq.top().first) ` `            ``continue``; ` ` `  `        ``// Else remove root and insert ` `        ``pq.pop(); ` `        ``pq.push({ diff, i }); ` `    ``} ` ` `  `    ``// Print contents of heap. ` `    ``while` `(pq.empty() == ``false``) { ` `        ``cout << arr[pq.top().second] << ``" "``; ` `        ``pq.pop(); ` `    ``} ` `} ` ` `  `// Driver program to test above functions ` `int` `main() ` `{ ` `    ``int` `arr[] = { -10, -50, 20, 17, 80 }; ` `    ``int` `x = 20, k = 2; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` `    ``printKclosest(arr, n, x, k); ` `    ``return` `0; ` `} `

## Python3

 `# Python3 program to find k closest elements  ` `import` `math ` `import` `sys ` `from` `queue ``import` `PriorityQueue ` `def` `printKclosest(arr,n,x,k): ` ` `  `    ``# Make a max heap of difference with  ` `    ``# first k elements.  ` `    ``pq ``=` `PriorityQueue() ` `    ``for` `i ``in` `range``(k): ` `        ``pq.put((``-``abs``(arr[i]``-``x),i)) ` ` `  `    ``# Now process remaining elements ` `    ``for` `i ``in` `range``(k,n): ` `        ``diff ``=` `abs``(arr[i]``-``x) ` `        ``p,pi ``=` `pq.get() ` `        ``curr ``=` `-``p ` ` `  `        ``# If difference with current  ` `        ``# element is more than root,  ` `        ``# then put it back.  ` `        ``if` `diff>curr: ` `            ``pq.put((``-``curr,pi)) ` `            ``continue` `        ``else``: ` ` `  `            ``# Else remove root and insert ` `            ``pq.put((``-``diff,i)) ` `             `  `    ``# Print contents of heap. ` `    ``while``(``not` `pq.empty()): ` `        ``p,q ``=` `pq.get() ` `        ``print``(``"{} "``.``format``(arr[q]),end ``=` `"") ` ` `  `# Driver program to test above functions  ` `if` `__name__``=``=``'__main__'``: ` `    ``arr ``=` `[``-``10``,``-``50``,``20``,``17``,``80``] ` `    ``x,k ``=` `20``,``2` `    ``n ``=` `len``(arr) ` `    ``printKclosest(arr, n, x, k) ` ` `  `# This code is contributed by Vikash Kumar 37 `

Output:

```17 20
```

Time Complexity : O(n Log k)

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