Find k closest elements to a given value
Given a sorted array arr[] and a value X, find the k closest elements to X in arr[].
Examples:
Input: K = 4, X = 35
arr[] = {12, 16, 22, 30, 35, 39, 42,
45, 48, 50, 53, 55, 56}
Output: 30 39 42 45
Note that if the element is present in array, then it should not be in output, only the other closest elements are required.
In the following solutions, it is assumed that all elements of array are distinct.
A simple solution is to do linear search for k closest elements.
1) Start from the first element and search for the crossover point (The point before which elements are smaller than or equal to X and after which elements are greater). This step takes O(n) time.
2) Once we find the crossover point, we can compare elements on both sides of crossover point to print k closest elements. This step takes O(k) time.
The time complexity of the above solution is O(n).
An Optimized Solution is to find k elements in O(Logn + k) time. The idea is to use Binary Search to find the crossover point. Once we find index of crossover point, we can print k closest elements in O(k) time.
C/C++
#include<stdio.h> /* Function to find the cross over point (the point before which elements are smaller than or equal to x and after which greater than x)*/int findCrossOver(int arr[], int low, int high, int x) { // Base cases if (arr[high] <= x) // x is greater than all return high; if (arr[low] > x) // x is smaller than all return low; // Find the middle point int mid = (low + high)/2; /* low + (high - low)/2 */ /* If x is same as middle element, then return mid */ if (arr[mid] <= x && arr[mid+1] > x) return mid; /* If x is greater than arr[mid], then either arr[mid + 1] is ceiling of x or ceiling lies in arr[mid+1...high] */ if(arr[mid] < x) return findCrossOver(arr, mid+1, high, x); return findCrossOver(arr, low, mid - 1, x); } // This function prints k closest elements to x in arr[]. // n is the number of elements in arr[] void printKclosest(int arr[], int x, int k, int n) { // Find the crossover point int l = findCrossOver(arr, 0, n-1, x); int r = l+1; // Right index to search int count = 0; // To keep track of count of elements already printed // If x is present in arr[], then reduce left index // Assumption: all elements in arr[] are distinct if (arr[l] == x) l--; // Compare elements on left and right of crossover // point to find the k closest elements while (l >= 0 && r < n && count < k) { if (x - arr[l] < arr[r] - x) printf("%d ", arr[l--]); else printf("%d ", arr[r++]); count++; } // If there are no more elements on right side, then // print left elements while (count < k && l >= 0) printf("%d ", arr[l--]), count++; // If there are no more elements on left side, then // print right elements while (count < k && r < n) printf("%d ", arr[r++]), count++; } /* Driver program to check above functions */int main() { int arr[] ={12, 16, 22, 30, 35, 39, 42, 45, 48, 50, 53, 55, 56}; int n = sizeof(arr)/sizeof(arr[0]); int x = 35, k = 4; printKclosest(arr, x, 4, n); return 0; } |
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Java
// Java program to find k closest elements to a given value class KClosest { /* Function to find the cross over point (the point before which elements are smaller than or equal to x and after which greater than x)*/ int findCrossOver(int arr[], int low, int high, int x) { // Base cases if (arr[high] <= x) // x is greater than all return high; if (arr[low] > x) // x is smaller than all return low; // Find the middle point int mid = (low + high)/2; /* low + (high - low)/2 */ /* If x is same as middle element, then return mid */ if (arr[mid] <= x && arr[mid+1] > x) return mid; /* If x is greater than arr[mid], then either arr[mid + 1] is ceiling of x or ceiling lies in arr[mid+1...high] */ if(arr[mid] < x) return findCrossOver(arr, mid+1, high, x); return findCrossOver(arr, low, mid - 1, x); } // This function prints k closest elements to x in arr[]. // n is the number of elements in arr[] void printKclosest(int arr[], int x, int k, int n) { // Find the crossover point int l = findCrossOver(arr, 0, n-1, x); int r = l+1; // Right index to search int count = 0; // To keep track of count of elements // already printed // If x is present in arr[], then reduce left index // Assumption: all elements in arr[] are distinct if (arr[l] == x) l--; // Compare elements on left and right of crossover // point to find the k closest elements while (l >= 0 && r < n && count < k) { if (x - arr[l] < arr[r] - x) System.out.print(arr[l--]+" "); else System.out.print(arr[r++]+" "); count++; } // If there are no more elements on right side, then // print left elements while (count < k && l >= 0) { System.out.print(arr[l--]+" "); count++; } // If there are no more elements on left side, then // print right elements while (count < k && r < n) { System.out.print(arr[r++]+" "); count++; } } /* Driver program to check above functions */ public static void main(String args[]) { KClosest ob = new KClosest(); int arr[] = {12, 16, 22, 30, 35, 39, 42, 45, 48, 50, 53, 55, 56 }; int n = arr.length; int x = 35, k = 4; ob.printKclosest(arr, x, 4, n); } } /* This code is contributed by Rajat Mishra */ |
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Python3
# Function to find the cross over point # (the point before which elements are # smaller than or equal to x and after # which greater than x) def findCrossOver(arr, low, high, x) : # Base cases if (arr[high] <= x) : # x is greater than all return high if (arr[low] > x) : # x is smaller than all return low # Find the middle point mid = (low + high) // 2 # low + (high - low)// 2 # If x is same as middle element, # then return mid if (arr[mid] <= x and arr[mid + 1] > x) : return mid # If x is greater than arr[mid], then # either arr[mid + 1] is ceiling of x # or ceiling lies in arr[mid+1...high] if(arr[mid] < x) : return findCrossOver(arr, mid + 1, high, x) return findCrossOver(arr, low, mid - 1, x) # This function prints k closest elements to x # in arr[]. n is the number of elements in arr[] def printKclosest(arr, x, k, n) : # Find the crossover point l = findCrossOver(arr, 0, n - 1, x) r = l + 1 # Right index to search count = 0 # To keep track of count of # elements already printed # If x is present in arr[], then reduce # left index. Assumption: all elements # in arr[] are distinct if (arr[l] == x) : l -= 1 # Compare elements on left and right of crossover # point to find the k closest elements while (l >= 0 and r < n and count < k) : if (x - arr[l] < arr[r] - x) : print(arr[l], end = " ") l -= 1 else : print(arr[r], end = " ") r += 1 count += 1 # If there are no more elements on right # side, then print left elements while (count < k and l >= 0) : print(arr[l], end = " ") l -= 1 count += 1 # If there are no more elements on left # side, then print right elements while (count < k and r < n) : print(arr[r], end = " ") r += 1 count += 1 # Driver Code if __name__ == "__main__" : arr =[12, 16, 22, 30, 35, 39, 42, 45, 48, 50, 53, 55, 56] n = len(arr) x = 35 k = 4 printKclosest(arr, x, 4, n) # This code is contributed by Ryuga |
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C#
// C# program to find k closest elements to // a given value using System; class GFG { /* Function to find the cross over point (the point before which elements are smaller than or equal to x and after which greater than x)*/ static int findCrossOver(int []arr, int low, int high, int x) { // Base cases // x is greater than all if (arr[high] <= x) return high; // x is smaller than all if (arr[low] > x) return low; // Find the middle point /* low + (high - low)/2 */ int mid = (low + high)/2; /* If x is same as middle element, then return mid */ if (arr[mid] <= x && arr[mid+1] > x) return mid; /* If x is greater than arr[mid], then either arr[mid + 1] is ceiling of x or ceiling lies in arr[mid+1...high] */ if(arr[mid] < x) return findCrossOver(arr, mid+1, high, x); return findCrossOver(arr, low, mid - 1, x); } // This function prints k closest elements // to x in arr[]. n is the number of // elements in arr[] static void printKclosest(int []arr, int x, int k, int n) { // Find the crossover point int l = findCrossOver(arr, 0, n-1, x); // Right index to search int r = l + 1; // To keep track of count of elements int count = 0; // If x is present in arr[], then reduce // left index Assumption: all elements in // arr[] are distinct if (arr[l] == x) l--; // Compare elements on left and right of // crossover point to find the k closest // elements while (l >= 0 && r < n && count < k) { if (x - arr[l] < arr[r] - x) Console.Write(arr[l--]+" "); else Console.Write(arr[r++]+" "); count++; } // If there are no more elements on right // side, then print left elements while (count < k && l >= 0) { Console.Write(arr[l--]+" "); count++; } // If there are no more elements on left // side, then print right elements while (count < k && r < n) { Console.Write(arr[r++] + " "); count++; } } /* Driver program to check above functions */ public static void Main() { int []arr = {12, 16, 22, 30, 35, 39, 42, 45, 48, 50, 53, 55, 56}; int n = arr.Length; int x = 35; printKclosest(arr, x, 4, n); } } // This code is contributed by nitin mittal. |
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PHP
<?php // PHP Program to Find k closest // elements to a given value /* Function to find the cross over point (the point before which elements are smaller than or equal to x and after which greater than x) */function findCrossOver($arr, $low, $high, $x) { // Base cases // x is greater than all if ($arr[$high] <= $x) return $high; // x is smaller than all if ($arr[$low] > $x) return $low; // Find the middle point /* low + (high - low)/2 */ $mid = ($low + $high)/2; /* If x is same as middle element, then return mid */ if ($arr[$mid] <= $x and $arr[$mid + 1] > $x) return $mid; /* If x is greater than arr[mid], then either arr[mid + 1] is ceiling of x or ceiling lies in arr[mid+1...high] */ if($arr[$mid] < $x) return findCrossOver($arr, $mid + 1, $high, $x); return findCrossOver($arr, $low, $mid - 1, $x); } // This function prints k // closest elements to x in arr[]. // n is the number of elements // in arr[] function printKclosest($arr, $x, $k, $n) { // Find the crossover point $l = findCrossOver($arr, 0, $n - 1, $x); // Right index to search $r = $l + 1; // To keep track of count of // elements already printed $count = 0; // If x is present in arr[], // then reduce left index // Assumption: all elements // in arr[] are distinct if ($arr[$l] == $x) $l--; // Compare elements on left // and right of crossover // point to find the k // closest elements while ($l >= 0 and $r < $n and $count < $k) { if ($x - $arr[$l] < $arr[$r] - $x) echo $arr[$l--]," "; else echo $arr[$r++]," "; $count++; } // If there are no more // elements on right side, // then print left elements while ($count < $k and $l >= 0) echo $arr[$l--]," "; $count++; // If there are no more // elements on left side, // then print right elements while ($count < $k and $r < $n) echo $arr[$r++]; $count++; } // Driver Code $arr =array(12, 16, 22, 30, 35, 39, 42, 45, 48, 50, 53, 55, 56); $n = count($arr); $x = 35; $k = 4; printKclosest($arr, $x, 4, $n); // This code is contributed by anuj_67. ?> |
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Output:
39 30 42 45
The time complexity of this method is O(Logn + k).
Exercise: Extend the optimized solution to work for duplicates also, i.e., to work for arrays where elements don’t have to be distinct.
This article is contributed by Rahul Jain. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
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