Searching in an array where adjacent differ by at most k
Last Updated : 29 Mar, 2024
A step array is an array of integers where each element has a difference of at most k with its neighbor. Given a key x, we need to find the index value of x if multiple-element exist to return the first occurrence of the key.
Examples:
Input : arr[] = {4, 5, 6, 7, 6} k = 1 x = 6 Output : 2 The first index of 6 is 2. Input : arr[] = {20, 40, 50, 70, 70, 60} k = 20 x = 60 Output : 5 The index of 60 is 5
This problem is mainly an extension of Search an element in an array where difference between adjacent elements is 1.
A Simple Approach is to traverse the given array one by one and compare every element with the given element 'x'. If matches, then return index.
The above solution can be Optimized using the fact that the difference between all adjacent elements is at most k. The idea is to start comparing from the leftmost element and find the difference between the current array element and x. Let this difference be 'diff'. From the given property of the array, we always know that x must be at least 'diff/k' away, so instead of searching one by one, we jump 'diff/k'.
Below is the implementation of the above idea.
C++ // C++ program to search an element in an array // where difference between adjacent elements is atmost k #include<bits/stdc++.h> using namespace std; // x is the element to be searched in arr[0..n-1] // such that all elements differ by at-most k. int search(int arr[], int n, int x, int k) { // Traverse the given array starting from // leftmost element int i = 0; while (i < n) { // If x is found at index i if (arr[i] == x) return i; // Jump the difference between current // array element and x divided by k // We use max here to make sure that i // moves at-least one step ahead. i = i + max(1, abs(arr[i]-x)/k); } cout << "number is not present!"; return -1; } // Driver program to test above function int main() { int arr[] = {2, 4, 5, 7, 7, 6}; int x = 6; int k = 2; int n = sizeof(arr)/sizeof(arr[0]); cout << "Element " << x << " is present at index " << search(arr, n, x, k); return 0; } // Java program to search an element in // an array where difference between adjacent elements is atmost k import java.io.*; class GFG { // x is the element to be searched // in arr[0..n-1] such that all // elements differ by at-most k. static int search(int arr[], int n, int x, int k) { // Traverse the given array starting // from leftmost element int i = 0; while (i < n) { // If x is found at index i if (arr[i] == x) return i; // Jump the difference between // current array element and x // divided by k We use max here // to make sure that i moves // at-least one step ahead. i = i + Math.max(1, Math.abs(arr[i] - x) / k); } System.out.println("number is " + "not present!"); return -1; } // Driver program to test above function public static void main(String[] args) { int arr[] = { 2, 4, 5, 7, 7, 6 }; int x = 6; int k = 2; int n = arr.length; System.out.println("Element " + x + " is present at index " + search(arr, n, x, k)); } } // This code is contributed by vt_m # Python 3 program to search an element in an array # where difference between adjacent elements is atmost k # x is the element to be searched in arr[0..n-1] # such that all elements differ by at-most k. def search(arr, n, x, k): # Traverse the given array starting from # leftmost element i = 0 while (i < n): # If x is found at index i if (arr[i] == x): return i # Jump the difference between current # array element and x divided by k # We use max here to make sure that i # moves at-least one step ahead. i = i + max(1, int(abs(arr[i] - x) / k)) print("number is not present!") return -1 # Driver program to test above function arr = [2, 4, 5, 7, 7, 6] x = 6 k = 2 n = len(arr) print("Element", x, "is present at index",search(arr, n, x, k)) # This code is contributed # by Smitha Dinesh Semwal // C# program to search an element in // an array where difference between //adjacent elements is atmost k class GFG { // x is the element to be searched // in arr[0..n-1] such that all // elements differ by at-most k. static int search(int []arr, int n, int x, int k) { // Traverse the given array starting // from leftmost element int i = 0; while (i < n) { // If x is found at index i if (arr[i] == x) return i; // Jump the difference between // current array element and x // divided by k We use max here // to make sure that i moves // at-least one step ahead. i = i + Math.Max(1, Math.Abs(arr[i] - x) / k); } Console.Write("number is " + "not present!"); return -1; } // Driver Code public static void Main() { int []arr = { 2, 4, 5, 7, 7, 6 }; int x = 6; int k = 2; int n = arr.Length; Console.Write("Element " + x + " is present at index " + search(arr, n, x, k)); } } // This code is contributed by Nitin Mittal. <?php // PHP program to search an // element in an array //where difference between //adjacent elements is atmost k // x is the element to be // searched in arr[0..n-1] // such that all elements // differ by at-most k. function search($arr, $n, $x, $k) { // Traverse the given array // starting from leftmost element $i = 0; while ($i < $n) { // If x is found at index i if ($arr[$i] == $x) return $i; // Jump the difference between current // array element and x divided by k // We use max here to make sure that i // moves at-least one step ahead. $i = $i + max(1, abs($arr[$i] - $x) / $k); } echo "number is not present!"; return -1; } // Driver Code { $arr = array(2, 4, 5, 7, 7, 6); $x = 6; $k = 2; $n = sizeof($arr)/sizeof($arr[0]); echo "Element $x is present". "at index ", search($arr, $n, $x, $k); return 0; } // This code is contributed by nitin mittal. ?> <script> // Javascript program to search an element in an array // where difference between adjacent elements is atmost k // x is the element to be searched in arr[0..n-1] // such that all elements differ by at-most k. function search(arr, n, x, k) { // Traverse the given array starting from // leftmost element var i = 0; while (i < n) { // If x is found at index i if (arr[i] == x) return i; // Jump the difference between current // array element and x divided by k // We use max here to make sure that i // moves at-least one step ahead. i = i + Math.max(1, Math.abs(arr[i]-x)/k); } document.write( "number is not present!"); return -1; } // Driver program to test above function var arr = [2, 4, 5, 7, 7, 6]; var x = 6; var k = 2; var n = arr.length; document.write( "Element " + x + " is present at index " + search(arr, n, x, k)); </script> Output: Element 6 is present at index 5
Time Complexity: O(n)
Auxiliary Space: O(1)
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