Búsqueda meta binaria | Búsqueda binaria unilateral

La metabúsqueda binaria (también llamada búsqueda binaria unilateral por Steven Skiena en El manual de diseño de algoritmos en la página 134) es una forma modificada de búsqueda binaria que construye de forma incremental el índice del valor objetivo en la array. Al igual que la búsqueda binaria normal, la búsqueda binaria meta lleva un tiempo O (log n).

Ejemplos:  

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

La implementación exacta varía, pero el algoritmo básico tiene dos partes:  

1. Calcule cuántos bits son necesarios para almacenar el índice de array más grande.
2. Construya de forma incremental el índice del valor objetivo en la array determinando si cada bit en el índice debe establecerse en 1 o 0.

Acercarse:

1. Almacene el número de bits para representar el índice de array más grande en la variable lg.
2. Use lg para comenzar la búsqueda en un bucle for.
3. Si se encuentra el elemento, devuelva pos.
4. De lo contrario, construya un índice de forma incremental para alcanzar el valor objetivo en el bucle for.
5. Si se encuentra el elemento, devuelve pos; de lo contrario, -1.

A continuación se muestra la implementación del enfoque anterior: 
 

// C++ implementation of above approach
  
#include <iostream>
#include <cmath>
#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();
    // 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 code
int main(void)
{
  
    vector<int> A = { -2, 10, 100, 250, 32315 };
    cout << bsearch(A, 10) << endl;
  
    return 0;
}
  
// This implementation was improved by Tanin

//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 implementation of 
# above approach
  
# Function to show the working
# of Meta binary search
import math
def 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 code
if __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# 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 implementation of above approach
  
// Function to show the working of 
// Meta binary search
function 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
?>

<script>
// Javascript implementation of above approach
  
// Function to show the working of Meta binary search
function bsearch(A, key_to_search)
{
    let n = A.length;
    // Set number of bits to represent largest array index
    let lg = parseInt(Math.log(n-1) / Math.log(2)) + 1; 
  
    //while ((1 << lg) < n - 1)
        //lg += 1;
  
    let pos = 0;
    for (let i = lg ; i >= 0; i--) {
        if (A[pos] == key_to_search)
            return pos;
  
        // Incrementally construct the
        // index of the target value
        let 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
  
    let A = [ -2, 10, 100, 250, 32315 ];
    document.write(bsearch(A, 10));
  
</script>

1

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