Given a sorted array of n uniformly distributed values arr[], write a function to search for a particular element x in the array.
Linear Search finds the element in O(n) time, Jump Search takes O(√ n) time and Binary Search take O(Log n) time.
The Interpolation Search is an improvement over Binary Search for instances, where the values in a sorted array are uniformly distributed. Binary Search always goes to the middle element to check. On the other hand, interpolation search may go to different locations according to the value of the key being searched. For example, if the value of the key is closer to the last element, interpolation search is likely to start search toward the end side.
To find the position to be searched, it uses following formula.
// The idea of formula is to return higher value of pos // when element to be searched is closer to arr[hi]. And // smaller value when closer to arr[lo] pos = lo + [ (x-arr[lo])*(hi-lo) / (arr[hi]-arr[Lo]) ] arr[] ==> Array where elements need to be searched x ==> Element to be searched lo ==> Starting index in arr[] hi ==> Ending index in arr[]
Algorithm
Rest of the Interpolation algorithm is the same except the above partition logic.
Step1: In a loop, calculate the value of “pos” using the probe position formula.
Step2: If it is a match, return the index of the item, and exit.
Step3: If the item is less than arr[pos], calculate the probe position of the left sub-array. Otherwise calculate the same in the right sub-array.
Step4: Repeat until a match is found or the sub-array reduces to zero.
Below is the implementation of algorithm.
C++
// C++ program to implement interpolation search #include<bits/stdc++.h> using namespace std; // If x is present in arr[0..n-1], then returns // index of it, else returns -1. int interpolationSearch(int arr[], int n, int x) { // Find indexes of two corners int lo = 0, hi = (n - 1); // Since array is sorted, an element present // in array must be in range defined by corner while (lo <= hi && x >= arr[lo] && x <= arr[hi]) { if (lo == hi) { if (arr[lo] == x) return lo; return -1; } // Probing the position with keeping // uniform distribution in mind. int pos = lo + (((double)(hi - lo) / (arr[hi] - arr[lo])) * (x - arr[lo])); // Condition of target found if (arr[pos] == x) return pos; // If x is larger, x is in upper part if (arr[pos] < x) lo = pos + 1; // If x is smaller, x is in the lower part else hi = pos - 1; } return -1; } // Driver Code int main() { // Array of items on which search will // be conducted. int arr[] = {10, 12, 13, 16, 18, 19, 20, 21, 22, 23, 24, 33, 35, 42, 47}; int n = sizeof(arr)/sizeof(arr[0]); int x = 18; // Element to be searched int index = interpolationSearch(arr, n, x); // If element was found if (index != -1) cout << "Element found at index " << index; else cout << "Element not found."; return 0; } // This code is contributed by Mukul Singh. |
C
// C program to implement interpolation search #include<stdio.h> // If x is present in arr[0..n-1], then returns // index of it, else returns -1. int interpolationSearch(int arr[], int n, int x) { // Find indexes of two corners int lo = 0, hi = (n - 1); // Since array is sorted, an element present // in array must be in range defined by corner while (lo <= hi && x >= arr[lo] && x <= arr[hi]) { if (lo == hi){ if (arr[lo] == x) return lo; return -1; } // Probing the position with keeping // uniform distribution in mind. int pos = lo + (((double)(hi-lo) / (arr[hi]-arr[lo]))*(x - arr[lo])); // Condition of target found if (arr[pos] == x) return pos; // If x is larger, x is in upper part if (arr[pos] < x) lo = pos + 1; // If x is smaller, x is in the lower part else hi = pos - 1; } return -1; } // Driver Code int main() { // Array of items on which search will // be conducted. int arr[] = {10, 12, 13, 16, 18, 19, 20, 21, 22, 23, 24, 33, 35, 42, 47}; int n = sizeof(arr)/sizeof(arr[0]); int x = 18; // Element to be searched int index = interpolationSearch(arr, n, x); // If element was found if (index != -1) printf("Element found at index %d", index); else printf("Element not found."); return 0; } |
Java
// Java program to implement interpolation search class Test { // Array of items on which search will // be conducted. static int arr[] = new int[]{10, 12, 13, 16, 18, 19, 20, 21, 22, 23, 24, 33, 35, 42, 47}; // If x is present in arr[0..n-1], then returns // index of it, else returns -1. static int interpolationSearch(int x) { // Find indexes of two corners int lo = 0, hi = (arr.length - 1); // Since array is sorted, an element present // in array must be in range defined by corner while (lo <= hi && x >= arr[lo] && x <= arr[hi]) { if (lo == hi) { if (arr[lo] == x) return lo; return -1; } // Probing the position with keeping // uniform distribution in mind. int pos = lo + (((hi-lo) / (arr[hi]-arr[lo]))*(x - arr[lo])); // Condition of target found if (arr[pos] == x) return pos; // If x is larger, x is in upper part if (arr[pos] < x) lo = pos + 1; // If x is smaller, x is in the lower part else hi = pos - 1; } return -1; } // Driver method public static void main(String[] args) { int x = 18; // Element to be searched int index = interpolationSearch(x); // If element was found if (index != -1) System.out.println("Element found at index " + index); else System.out.println("Element not found."); } } |
Python
# Python program to implement interpolation search # If x is present in arr[0..n-1], then returns # index of it, else returns -1 def interpolationSearch(arr, n, x): # Find indexs of two corners lo = 0 hi = (n - 1) # Since array is sorted, an element present # in array must be in range defined by corner while lo <= hi and x >= arr[lo] and x <= arr[hi]: if lo == hi: if arr[lo] == x: return lo; return -1; # Probing the position with keeping # uniform distribution in mind. pos = lo + int(((float(hi - lo) / ( arr[hi] - arr[lo])) * ( x - arr[lo]))) # Condition of target found if arr[pos] == x: return pos # If x is larger, x is in upper part if arr[pos] < x: lo = pos + 1; # If x is smaller, x is in lower part else: hi = pos - 1; return -1 # Driver Code # Array of items oin which search will be conducted arr = [10, 12, 13, 16, 18, 19, 20, 21, 22, 23, 24, 33, 35, 42, 47] n = len(arr) x = 18 # Element to be searched index = interpolationSearch(arr, n, x) if index != -1: print "Element found at index",index else: print "Element not found" # This code is contributed by Harshit Agrawal |
C#
// C# program to implement // interpolation search using System; class GFG { // Array of items on which // search will be conducted. static int []arr = new int[]{10, 12, 13, 16, 18, 19, 20, 21, 22, 23, 24, 33, 35, 42, 47}; // If x is present in // arr[0..n-1], then // returns index of it, // else returns -1. static int interpolationSearch(int x) { // Find indexes of // two corners int lo = 0, hi = (arr.Length - 1); // Since array is sorted, // an element present in // array must be in range // defined by corner while (lo <= hi && x >= arr[lo] && x <= arr[hi]) { if (lo == hi) { if (arr[lo] == x) return lo; return -1; } // Probing the position // with keeping uniform // distribution in mind. int pos = lo + (((hi - lo) / (arr[hi] - arr[lo])) * (x - arr[lo])); // Condition of // target found if (arr[pos] == x) return pos; // If x is larger, x // is in upper part if (arr[pos] < x) lo = pos + 1; // If x is smaller, x // is in the lower part else hi = pos - 1; } return -1; } // Driver Code public static void Main() { int x = 18; // Element to be searched int index = interpolationSearch(x); // If element was found if (index != -1) Console.WriteLine("Element found " + "at index " + index); else Console.WriteLine("Element not found."); } } // This code is contributed by anuj_67. |
PHP
<?php // PHP program to implement interpolation search // If x is present in arr[0..n-1], then returns // index of it, else returns -1. function interpolationSearch($arr, $x, $n) { // Find indexes of two corners $l = 0; $h = $n - 1; // Since array is sorted, an element present // in array must be in range defined by corner while ($l <= $h and $x >= $arr[$l] and $x <= $arr[$h]) { if ($l == $h) { if ($arr[$l] == $x) return $l; return -1; } // Probing the position with keeping // uniform distribution in mind. $m = intval($l + (($x - $arr[$l]) * ($h - $l) / ($arr[$h] - $arr[$l]))); // Condition of target found if ($arr[$m] == $x) { return $m; } // If x is larger, x is in upper part elseif ($arr[$m] < $x) { $l = $m + 1; } // If x is smaller, x is in the lower part else { $h = $m - 1; } } return -1; } // Driver Code // Array of items on which search // will be conducted. $arr = array(10, 12, 13, 16, 18, 19, 20, 21, 22, 23, 24, 33, 35, 42, 47); $n = count($arr); $x = 18; // Element to be searched $index = interpolationSearch($arr, $x, $n); // If element was found if ($index != -1) echo "Element found at index " . $index; else echo "Element not found."; // This code is contributed by Deepika Pathak ?> |
Output:
Element found at index 4
Time Complexity: If elements are uniformly distributed, then O (log log n)). In worst case it can take upto O(n).
Auxiliary Space: O(1)
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