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:

  1. Figure out how many bits are necessary to store the largest array index.
  2. 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:

  1. Store number of bits to represent the largest array index in variable lg
  2. Use lg to start off the search in a for loop
  3. If element is found return pos
  4. Otherwise incrementally construct index to reach the target value in the for loop
  5. If element found return pos otherwise -1

Below is the implementation of the above approach:

C++

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// C++ implementation of above approach
#include <iostream>
#include <vector>
using namespace std;
  
// Function to show the working of Meta binary search
int bsearch(vector<int> A, int key_to_search)
{
    int n = (int)A.size();
    int lg = 0;
  
    // Set number of bits to represent largest array index
    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
int main(void)
{
  
    vector<int> A = { -2, 10, 100, 250, 32315 };
    cout << bsearch(A, 10) << endl;
  
    return 0;
}

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Java

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//Java implementation of above approach 
import java.util.Vector;
  
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();
        int lg = 0;
  
        // Set number of bits to represent largest array index 
        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

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Python 3

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# Python 3 implementation of 
# above approach
  
# Function to show the working
# of Meta binary search
def bsearch(A, key_to_search):
  
    n = len(A)
    lg = 0
  
    # Set number of bits to represent
    # 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 code
if __name__ == "__main__":
  
    A = [ -2, 10, 100, 250, 32315 ]
    print( bsearch(A, 10))
  
# This code is contributed
# by ChitraNayal

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C#

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//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 
        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

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PHP

= 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 ?>

Output:

1

Reference: https://www.quora.com/What-is-meta-binary-search



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