Meta Binary Search | One-Sided Binary Search
Meta binary search (also called one-sided binary search by Steven Skiena in The Algorithm Design Manual on page 134) is a modified form of binary search that incrementally constructs the index of the target value in the array. Like normal binary search, meta binary search takes O(log n) time.
Examples:
Input: [-10, -5, 4, 6, 8, 10, 11], key_to_search = 10 Output: 5 Input: [-2, 10, 100, 250, 32315], key_to_search = -2 Output: 0
The exact implementation varies, but the basic algorithm has two parts:
- Figure out how many bits are necessary to store the largest array index.
- Incrementally construct the index of the target value in the array by determining whether each bit in the index should be set to 1 or 0.
Approach:
- Store number of bits to represent the largest array index in variable lg
- Use lg to start off the search in a for loop
- If element is found return pos
- Otherwise incrementally construct index to reach the target value in the for loop
- If element found return pos otherwise -1
Below is the implementation of the above approach:
C++
// C++ implementation of above approach #include <iostream>#include <cmath>#include <vector>using namespace std; // Function to show the working of Meta binary searchint bsearch(vector<int> A, int key_to_search){ int n = (int)A.size(); // Set number of bits to represent largest array index int lg = log2(n-1)+1; //while ((1 << lg) < n - 1) //lg += 1; int pos = 0; for (int i = lg ; i >= 0; i--) { if (A[pos] == key_to_search) return pos; // Incrementally construct the // index of the target value int new_pos = pos | (1 << i); // find the element in one // direction and update position if ((new_pos < n) && (A[new_pos] <= key_to_search)) pos = new_pos; } // if element found return pos otherwise -1 return ((A[pos] == key_to_search) ? pos : -1);} // Driver codeint main(void){ vector<int> A = { -2, 10, 100, 250, 32315 }; cout << bsearch(A, 10) << endl; return 0;} // This implementation was improved by Tanin |
Java
//Java implementation of above approach import java.util.Vector;import com.google.common.math.BigIntegerMath;import java.math.*; class GFG { // Function to show the working of Meta binary search static int bsearch(Vector<Integer> A, int key_to_search) { int n = (int) A.size(); // Set number of bits to represent largest array index int lg = BigIntegerMath.log2(BigInteger.valueOf(n-1),RoundingMode.UNNECESSARY) + 1; //while ((1 << lg) < n - 1) { // lg += 1; //} int pos = 0; for (int i = lg - 1; i >= 0; i--) { if (A.get(pos) == key_to_search) { return pos; } // Incrementally construct the // index of the target value int new_pos = pos | (1 << i); // find the element in one // direction and update position if ((new_pos < n) && (A.get(new_pos) <= key_to_search)) { pos = new_pos; } } // if element found return pos otherwise -1 return ((A.get(pos) == key_to_search) ? pos : -1); } // Driver code static public void main(String[] args) { Vector<Integer> A = new Vector<Integer>(); int[] arr = {-2, 10, 100, 250, 32315}; for (int i = 0; i < arr.length; i++) { A.add(arr[i]); } System.out.println(bsearch(A, 10)); }} // This code is contributed by 29AjayKumar// This implementation was improved by Tanin |
Python 3
# Python 3 implementation of # above approach # Function to show the working# of Meta binary searchimport mathdef bsearch(A, key_to_search): n = len(A) # Set number of bits to represent lg = int(math.log2(n-1)) + 1; # largest array index #while ((1 << lg) < n - 1): #lg += 1 pos = 0 for i in range(lg - 1, -1, -1) : if (A[pos] == key_to_search): return pos # Incrementally construct the # index of the target value new_pos = pos | (1 << i) # find the element in one # direction and update position if ((new_pos < n) and (A[new_pos] <= key_to_search)): pos = new_pos # if element found return # pos otherwise -1 return (pos if(A[pos] == key_to_search) else -1) # Driver codeif __name__ == "__main__": A = [ -2, 10, 100, 250, 32315 ] print( bsearch(A, 10)) # This implementation was improved by Tanin # This code is contributed# by ChitraNayal |
C#
//C# implementation of above approach using System;using System.Collections.Generic; class GFG { // Function to show the working of Meta binary search static int bsearch(List<int> A, int key_to_search) { int n = (int) A.Count; //int lg = 0; // Set number of bits to represent largest array index int lg = (int)Math.Log(n-1, 2.0) + 1; // This is redundant and will cause error //while ((1 << lg) < n - 1) //{ // lg += 1; //} int pos = 0; for (int i = lg - 1; i >= 0; i--) { if (A[pos] == key_to_search) { return pos; } // Incrementally construct the // index of the target value int new_pos = pos | (1 << i); // find the element in one // direction and update position if ((new_pos < n) && (A[new_pos] <= key_to_search)) { pos = new_pos; } } // if element found return pos otherwise -1 return ((A[pos] == key_to_search) ? pos : -1); } // Driver code static public void Main() { List<int> A = new List<int>(); int[] arr = {-2, 10, 100, 250, 32315}; for (int i = 0; i < arr.Length; i++) { A.Add(arr[i]); } Console.WriteLine(bsearch(A, 10)); }} // This code is contributed by Rajput-Ji// This implementation was improved by Tanin |
PHP
<?php// PHP implementation of above approach // Function to show the working of // Meta binary searchfunction bsearch($A, $key_to_search, $n){ // Set number of bits to represent $lg = log($n-1, 2) + 1; // largest array index // This is redundant and will cause error for some case //while ((1 << $lg) < $n - 1) //$lg += 1; $pos = 0; for ($i = $lg - 1; $i >= 0; $i--) { if ($A[$pos] == $key_to_search) return $pos; // Incrementally construct the // index of the target value $new_pos = $pos | (1 << $i); // find the element in one // direction and update $position if (($new_pos < $n) && ($A[$new_pos] <= $key_to_search)) $pos = $new_pos; } // if element found return $pos // otherwise -1 return (($A[$pos] == $key_to_search) ? $pos : -1);} // Driver code$A = [ -2, 10, 100, 250, 32315 ];$ans = bsearch($A, 10, 5);echo $ans; // This code is contributed by AdeshSingh1// This implementation was improved by Tanin?> |
Output:
1
Reference: https://www.quora.com/What-is-meta-binary-search
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