Find largest element from array without using conditional operator

Given an array of n-elements, we have to find the largest element among them without using any conditional operator like greater than or less than.

Examples:

Input : arr[] = {5, 7, 2, 9}
Output : Largest element = 9

Input : arr[] = {15, 0, 2, 15}
Output : Largest element = 15

First Approach (Use of Hashing) : To find the largest element from the array we may use the concept the of hashing where we should maintain a hash table of all element and then after processing all array element we should find the largest element in hash by simply traversing the hash table from end.



But there are some drawbacks of this approach like in case of very large elements maintaining a hash table is either not possible or not feasible.

Better Approach (Use of Bitwise AND) : Recently we have learn how to find the largest AND value pair from a given array. Also, we know that if we take bitwise AND of any number with INT_MAX (whose all bits are set bits) then the result will be that number itself. Now, using this property we will try to find the largest element from the array without any use conditional operator like greater than or less than.

For finding the largest element we will first insert an extra element i.e. INT_MAX in array, and after that we will try to find the maximum AND value of any pair from the array. This obtained maximum value will contain AND value of INT_MAX and largest element of original array and is our required result.

Below is the implementation of above approach :

C++

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// C++ Program to find largest element from array
#include <bits/stdc++.h>
using namespace std;
  
// Utility function to check number of 
// elements having set msb as of pattern
int checkBit(int pattern, vector<int> arr, int n)
{
    int count = 0;
    for (int i = 0; i < n; i++)
        if ((pattern & arr[i]) == pattern)
            count++;
    return count;
}
  
// Function for finding maximum and value pair
int largest(int arr[], int n)
{
    // Create a vector of given array
    vector<int> v(arr, arr + n);
  
    // Insert INT_MAX and update n
    v.push_back(INT_MAX);
    n++;
  
    int res = 0;
  
    // Iterate over total of 30bits from
    // msb to lsb
    for (int bit = 31; bit >= 0; bit--) 
    {
  
        // Find the count of element having set msb
        int count = checkBit(res | (1 << bit), v, n);
  
        // if count | 1 != 1 set particular 
        // bit in result
        if ((count | 1) != 1)
            res |= (1 << bit);
    }
  
    return res;
}
  
// Driver Code
int main()
{
    int arr[] = { 4, 8, 6, 2 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << "Largest element = " << largest(arr, n);
    return 0;
}

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Java

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// Java Program to find largest element from array
import java.util.Vector;
import java.util.Arrays;
  
class GfG 
{
  
// Utility function to check number of 
// elements having set msb as of pattern
static int checkBit(int pattern, Vector<Integer> arr, int n)
{
    int count = 0;
    for (int i = 0; i < n; i++)
        if ((pattern & arr.get(i)) == pattern)
            count++;
    return count;
}
  
// Function for finding maximum and value pair
static int largest(int arr[], int n)
{
    // Create a vector of given array
    Vector<Integer> v = new Vector<>();
    for(Integer a:arr)
        v.add(a);
  
    // Insert INT_MAX and update n
    v.add(Integer.MAX_VALUE);
    n++;
  
    int res = 0;
  
    // Iterate over total of 30bits from
    // msb to lsb
    for (int bit = 31; bit >= 0; bit--) 
    {
  
        // Find the count of element having set msb
        int count = checkBit(res | (1 << bit), v, n);
  
        // if count | 1 != 1 set particular 
        // bit in result
        if ((count | 1) != 1)
            res |= (1 << bit);
    }
  
    return res;
}
  
// Driver Code
public static void main(String[] args) 
{
    int arr[] = { 4, 8, 6, 2 };
    int n = arr.length;
    System.out.println("Largest element = "
                            largest(arr, n));
}
}
  
/* This code contributed by PrinciRaj1992 */

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Python3

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# Python3 Program to find largest 
# element from array
import math as mt
  
# Utility function to check number of 
# elements having set msb as of pattern
def checkBit(pattern, arr, n):
    count = 0
    for i in range(n):
        if ((pattern & arr[i]) == pattern):
            count += 1
    return count
  
# Function for finding maximum 
# and value pair
def largest(arr, n):
  
    # Create a vector of given array
    v = arr
  
    # Insert max value of Int and update n
    v.append(2**31 - 1)
    n = n + 1
  
    res = 0
  
    # Iterate over total of 30bits
    # from msb to lsb
    for bit in range(31, -1, -1):
  
        # Find the count of element 
        # having set msb
        count = checkBit(res | (1 << bit), v, n)
  
        # if count | 1 != 1 set particular
        # bit in result
        if ((count | 1) != 1):
            res |= (1 << bit)
      
    return res
  
# Driver Code
arr = [4, 8, 6, 2
n = len(arr)
print("Largest element =", largest(arr, n))
  
# This code is contributed by
# Mohit kumar 29

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C#

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// C# Program to find largest element from array
using System;    
using System.Collections.Generic;    
  
class GfG 
{
   
// Utility function to check number of 
// elements having set msb as of pattern
static int checkBit(int pattern, List<int> arr, int n)
{
    int count = 0;
    for (int i = 0; i < n; i++)
        if ((pattern & arr[i]) == pattern)
            count++;
    return count;
}
   
// Function for finding maximum and value pair
static int largest(int []arr, int n)
{
    // Create a vector of given array
    List<int> v = new List<int>();
    foreach(int a in arr)
        v.Add(a);
   
    // Insert INT_MAX and update n
    v.Add(int.MaxValue);
    n++;
   
    int res = 0;
   
    // Iterate over total of 30bits from
    // msb to lsb
    for (int bit = 31; bit >= 0; bit--) 
    {
   
        // Find the count of element having set msb
        int count = checkBit(res | (1 << bit), v, n);
   
        // if count | 1 != 1 set particular 
        // bit in result
        if ((count | 1) != 1)
            res |= (1 << bit);
    }
   
    return res;
}
   
// Driver Code
public static void Main(String[] args) 
{
    int []arr = { 4, 8, 6, 2 };
    int n = arr.Length;
    Console.WriteLine("Largest element = "
                            largest(arr, n));
}
}
  
// This code contributed by Rajput-Ji

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PHP

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<?php
// php Program to find largest
// element from array
  
// Utility function to check 
// number of elements having
// set msb as of pattern
function checkBit($pattern,$arr,$n)
{
    $count = 0;
    for ($i = 0; $i < $n; $i++)
        if (($pattern & $arr[$i]) == $pattern)
            $count++;
    return $count;
}
  
// Function for finding 
// maximum and value pair
function largest($arr, $n)
{
    $res = 0;
  
    // Iterate over total of 
    // 30bits from msb to lsb
    for ($bit = 31; $bit >= 0; $bit--)
    {
  
        // Find the count of element 
        // having set msb
        $count = checkBit($res | (1 << $bit),$arr, $n);
  
        // if count | 1 != 1 set 
        // particular bit in result
        if ($count | 1 != 1)
            $res |= (1 << $bit);
    }
  
    return $res;
}
  
    // Driver code
    $arr = array( 4, 8, 6, 2 );
    $n = sizeof($arr) / sizeof($arr[0]);
    echo "Largest element = ". largest($arr, $n);
  
// This code is contributed by mits  
?>

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Output:

Largest element = 8


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