93 lines
2.8 KiB
Markdown
93 lines
2.8 KiB
Markdown
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---
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title: Exponential Search
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---
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## Exponential Search
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Exponential Search also known as finger search, searchs for an element in a sorted array by jumping `2^i` elements every iteration where i represents the
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value of loop control variable, and then verifying if the search element is present between last jump and the current jump
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# Complexity Worst Case
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O(log(N))
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Often confused because of the name, the algorithm is named so not because of the time complexity.
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The name arises as a result of the algorithm jumping elements with steps equal to exponents of 2
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# Works
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1. Jump the array `2^i` elements at a time searching for the condition `Array[2^(i-1)] < valueWanted < Array[2^i]`. If `2^i` is greater than the lenght of array, then set the upper bound to the length of the array.
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2. Do a binary search between `Array[2^(i-1)]` and `Array[2^i]`
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# Code
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```
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// C++ program to find an element x in a
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// sorted array using Exponential search.
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#include <bits/stdc++.h>
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using namespace std;
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int binarySearch(int arr[], int, int, int);
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// Returns position of first ocurrence of
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// x in array
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int exponentialSearch(int arr[], int n, int x)
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{
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// If x is present at firt location itself
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if (arr[0] == x)
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return 0;
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// Find range for binary search by
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// repeated doubling
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int i = 1;
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while (i < n && arr[i] <= x)
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i = i*2;
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// Call binary search for the found range.
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return binarySearch(arr, i/2, min(i, n), x);
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}
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// A recursive binary search function. It returns
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// location of x in given array arr[l..r] is
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// present, otherwise -1
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int binarySearch(int arr[], int l, int r, int x)
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{
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if (r >= l)
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{
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int mid = l + (r - l)/2;
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// If the element is present at the middle
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// itself
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if (arr[mid] == x)
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return mid;
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// If element is smaller than mid, then it
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// can only be present n left subarray
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if (arr[mid] > x)
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return binarySearch(arr, l, mid-1, x);
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// Else the element can only be present
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// in right subarray
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return binarySearch(arr, mid+1, r, x);
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}
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// We reach here when element is not present
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// in array
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return -1;
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}
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int main(void)
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{
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int arr[] = {2, 3, 4, 10, 40};
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int n = sizeof(arr)/ sizeof(arr[0]);
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int x = 10;
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int result = exponentialSearch(arr, n, x);
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(result == -1)? printf("Element is not present in array")
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: printf("Element is present at index %d", result);
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return 0;
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}
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```
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# More Information
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- <a href='https://en.wikipedia.org/wiki/Exponential_search' target='_blank' rel='nofollow'>Wikipedia</a>
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- <a href='https://www.geeksforgeeks.org/exponential-search/' target='_blank' rel='nofollow'>GeeksForGeeks</a>
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# Credits
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[C++ Implementation](https://www.wikitechy.com/technology/exponential-search/)
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