Maximum and minimum of an array using minimum number of comparisons

Write a C function to return minimum and maximum in an array. You program should make minimum number of comparisons.

First of all, how do we return multiple values from a C function? We can do it either using structures or pointers.
We have created a structure named pair (which contains min and max) to return multiple values.

c

struct pair 
{
  int min;
  int max;
};  

And the function declaration becomes: struct pair getMinMax(int arr[], int n) where arr[] is the array of size n whose minimum and maximum are needed.

METHOD 1 (Simple Linear Search)
Initialize values of min and max as minimum and maximum of the first two elements respectively. Starting from 3rd, compare each element with max and min, and change max and min accordingly (i.e., if the element is smaller than min then change min, else if the element is greater than max then change max, else ignore the element)

C++

// C++ program of above implementation 
#include<iostream>
using namespace std;
 
// Pair struct is used to return 
// two values from getMinMax()
struct Pair 
{
    int min;
    int max;
}; 
 
struct Pair getMinMax(int arr[], int n)
{
    struct Pair minmax;     
    int i;
     
    // If there is only one element 
    // then return it as min and max both
    if (n == 1)
    {
        minmax.max = arr[0];
        minmax.min = arr[0];     
        return minmax;
    } 
     
    // If there are more than one elements,
    // then initialize min and max
    if (arr[0] > arr[1]) 
    {
        minmax.max = arr[0];
        minmax.min = arr[1];
    } 
    else
    {
        minmax.max = arr[1];
        minmax.min = arr[0];
    } 
     
    for(i = 2; i < n; i++)
    {
        if (arr[i] > minmax.max)     
            minmax.max = arr[i];
             
        else if (arr[i] < minmax.min)     
            minmax.min = arr[i];
    }
    return minmax;
}
 
// Driver code
int main()
{
    int arr[] = { 1000, 11, 445, 
                  1, 330, 3000 };
    int arr_size = 6;
     
    struct Pair minmax = getMinMax(arr, arr_size);
     
    cout << "Minimum element is "
         << minmax.min << endl;
    cout << "Maximum element is "
         << minmax.max;
          
    return 0;
} 
 
// This code is contributed by nik_3112

C

/* structure is used to return two values from minMax() */
#include<stdio.h>
struct pair 
{
  int min;
  int max;
};  
 
struct pair getMinMax(int arr[], int n)
{
  struct pair minmax;     
  int i;
   
  /*If there is only one element then return it as min and max both*/
  if (n == 1)
  {
     minmax.max = arr[0];
     minmax.min = arr[0];     
     return minmax;
  }    
 
  /* If there are more than one elements, then initialize min 
      and max*/
  if (arr[0] > arr[1])  
  {
      minmax.max = arr[0];
      minmax.min = arr[1];
  }  
  else
  {
      minmax.max = arr[1];
      minmax.min = arr[0];
  }    
 
  for (i = 2; i<n; i++)
  {
    if (arr[i] >  minmax.max)      
      minmax.max = arr[i];
   
    else if (arr[i] <  minmax.min)      
      minmax.min = arr[i];
  }
   
  return minmax;
}
 
/* Driver program to test above function */
int main()
{
  int arr[] = {1000, 11, 445, 1, 330, 3000};
  int arr_size = 6;
  struct pair minmax = getMinMax (arr, arr_size);
  printf("nMinimum element is %d", minmax.min);
  printf("nMaximum element is %d", minmax.max);
  getchar();
}  

Java

// Java program of above implementation
public class GFG {
/* Class Pair is used to return two values from getMinMax() */
    static class Pair {
 
        int min;
        int max;
    }
 
    static Pair getMinMax(int arr[], int n) {
        Pair minmax = new  Pair();
        int i;
 
        /*If there is only one element then return it as min and max both*/
        if (n == 1) {
            minmax.max = arr[0];
            minmax.min = arr[0];
            return minmax;
        }
 
        /* If there are more than one elements, then initialize min 
    and max*/
        if (arr[0] > arr[1]) {
            minmax.max = arr[0];
            minmax.min = arr[1];
        } else {
            minmax.max = arr[1];
            minmax.min = arr[0];
        }
 
        for (i = 2; i < n; i++) {
            if (arr[i] > minmax.max) {
                minmax.max = arr[i];
            } else if (arr[i] < minmax.min) {
                minmax.min = arr[i];
            }
        }
 
        return minmax;
    }
 
    /* Driver program to test above function */
    public static void main(String args[]) {
        int arr[] = {1000, 11, 445, 1, 330, 3000};
        int arr_size = 6;
        Pair minmax = getMinMax(arr, arr_size);
        System.out.printf("\nMinimum element is %d", minmax.min);
        System.out.printf("\nMaximum element is %d", minmax.max);
 
    }
 
}

Python3

# Python program of above implementation
 
# structure is used to return two values from minMax()
 
class pair:
    def __init__(self):
        self.min = 0
        self.max = 0
 
def getMinMax(arr: list, n: int) -> pair:
    minmax = pair()
 
    # If there is only one element then return it as min and max both
    if n == 1:
        minmax.max = arr[0]
        minmax.min = arr[0]
        return minmax
 
    # If there are more than one elements, then initialize min
    # and max
    if arr[0] > arr[1]:
        minmax.max = arr[0]
        minmax.min = arr[1]
    else:
        minmax.max = arr[1]
        minmax.min = arr[0]
 
    for i in range(2, n):
        if arr[i] > minmax.max:
            minmax.max = arr[i]
        elif arr[i] < minmax.min:
            minmax.min = arr[i]
 
    return minmax
 
# Driver Code
if __name__ == "__main__":
    arr = [1000, 11, 445, 1, 330, 3000]
    arr_size = 6
    minmax = getMinMax(arr, arr_size)
    print("Minimum element is", minmax.min)
    print("Maximum element is", minmax.max)
 
# This code is contributed by
# sanjeev2552

C#

// C# program of above implementation
using System;
 
class GFG 
{
    /* Class Pair is used to return 
    two values from getMinMax() */
    class Pair 
    {
        public int min;
        public int max;
    }
 
    static Pair getMinMax(int []arr, int n)
    {
        Pair minmax = new Pair();
        int i;
 
        /* If there is only one element 
        then return it as min and max both*/
        if (n == 1)
        {
            minmax.max = arr[0];
            minmax.min = arr[0];
            return minmax;
        }
 
        /* If there are more than one elements,
        then initialize min and max*/
        if (arr[0] > arr[1])
        {
            minmax.max = arr[0];
            minmax.min = arr[1];
        } 
        else
        {
            minmax.max = arr[1];
            minmax.min = arr[0];
        }
 
        for (i = 2; i < n; i++)
        {
            if (arr[i] > minmax.max) 
            {
                minmax.max = arr[i];
            } 
            else if (arr[i] < minmax.min)
            {
                minmax.min = arr[i];
            }
        }
        return minmax;
    }
 
    // Driver Code
    public static void Main(String []args) 
    {
        int []arr = {1000, 11, 445, 1, 330, 3000};
        int arr_size = 6;
        Pair minmax = getMinMax(arr, arr_size);
        Console.Write("Minimum element is {0}",
                                   minmax.min);
        Console.Write("\nMaximum element is {0}", 
                                     minmax.max);
    }
}
 
// This code is contributed by PrinciRaj1992

Output:

Minimum element is 1
Maximum element is 3000

Time Complexity: O(n)

In this method, total number of comparisons is 1 + 2(n-2) in worst case and 1 + n – 2 in best case.
In the above implementation, worst case occurs when elements are sorted in descending order and best case occurs when elements are sorted in ascending order.

METHOD 2 (Tournament Method)
Divide the array into two parts and compare the maximums and minimums of the two parts to get the maximum and the minimum of the whole array.

Pair MaxMin(array, array_size)
   if array_size = 1
      return element as both max and min
   else if arry_size = 2
      one comparison to determine max and min
      return that pair
   else    /* array_size  > 2 */
      recur for max and min of left half
      recur for max and min of right half
      one comparison determines true max of the two candidates
      one comparison determines true min of the two candidates
      return the pair of max and min

Implementation

C++

// C++ program of above implementation 
#include<iostream>
using namespace std;
 
// structure is used to return 
// two values from minMax() 
struct Pair 
{
    int min;
    int max;
}; 
 
struct Pair getMinMax(int arr[], int low,
                                 int high)
{
    struct Pair minmax, mml, mmr;     
    int mid;
     
    // If there is only on element 
    if (low == high)
    {
        minmax.max = arr[low];
        minmax.min = arr[low];     
        return minmax;
    } 
     
    // If there are two elements 
    if (high == low + 1)
    { 
        if (arr[low] > arr[high]) 
        {
            minmax.max = arr[low];
            minmax.min = arr[high];
        } 
        else
        {
            minmax.max = arr[high];
            minmax.min = arr[low];
        } 
        return minmax;
    }
     
    // If there are more than 2 elements 
    mid = (low + high) / 2; 
    mml = getMinMax(arr, low, mid);
    mmr = getMinMax(arr, mid + 1, high); 
     
    // Compare minimums of two parts
    if (mml.min < mmr.min)
        minmax.min = mml.min;
    else
        minmax.min = mmr.min;     
     
    // Compare maximums of two parts
    if (mml.max > mmr.max)
        minmax.max = mml.max;
    else
        minmax.max = mmr.max;     
     
    return minmax;
}
 
// Driver code
int main()
{
    int arr[] = { 1000, 11, 445,
                  1, 330, 3000 };
    int arr_size = 6;
     
    struct Pair minmax = getMinMax(arr, 0, 
                             arr_size - 1);
                              
    cout << "Minimum element is "
         << minmax.min << endl;
    cout << "Maximum element is "
         << minmax.max;
          
    return 0;
}
 
// This code is contributed by nik_3112

C

/* structure is used to return two values from minMax() */
#include<stdio.h>
struct pair 
{
  int min;
  int max;
};  
 
struct pair getMinMax(int arr[], int low, int high)
{
  struct pair minmax, mml, mmr;       
  int mid;
   
  /* If there is only on element */
  if (low == high)
  {
     minmax.max = arr[low];
     minmax.min = arr[low];     
     return minmax;
  }    
   
  /* If there are two elements */
  if (high == low + 1)
  {  
     if (arr[low] > arr[high])  
     {
        minmax.max = arr[low];
        minmax.min = arr[high];
     }  
     else
     {
        minmax.max = arr[high];
        minmax.min = arr[low];
     }  
     return minmax;
  }
   
  /* If there are more than 2 elements */
  mid = (low + high)/2;  
  mml = getMinMax(arr, low, mid);
  mmr = getMinMax(arr, mid+1, high);  
   
  /* compare minimums of two parts*/
  if (mml.min < mmr.min)
    minmax.min = mml.min;
  else
    minmax.min = mmr.min;     
 
  /* compare maximums of two parts*/
  if (mml.max > mmr.max)
    minmax.max = mml.max;
  else
    minmax.max = mmr.max;     
  
  return minmax;
}
 
/* Driver program to test above function */
int main()
{
  int arr[] = {1000, 11, 445, 1, 330, 3000};
  int arr_size = 6;
  struct pair minmax = getMinMax(arr, 0, arr_size-1);
  printf("nMinimum element is %d", minmax.min);
  printf("nMaximum element is %d", minmax.max);
  getchar();
}

Java

// Java program of above implementation
public class GFG {
/* Class Pair is used to return two values from getMinMax() */
    static class Pair {
 
        int min;
        int max;
    }
 
    static Pair getMinMax(int arr[], int low, int high) {
        Pair minmax = new Pair();
        Pair mml = new Pair();
        Pair mmr = new Pair();
        int mid;
 
        /* If there is only on element */
        if (low == high) {
            minmax.max = arr[low];
            minmax.min = arr[low];
            return minmax;
        }
 
        /* If there are two elements */
        if (high == low + 1) {
            if (arr[low] > arr[high]) {
                minmax.max = arr[low];
                minmax.min = arr[high];
            } else {
                minmax.max = arr[high];
                minmax.min = arr[low];
            }
            return minmax;
        }
 
        /* If there are more than 2 elements */
        mid = (low + high) / 2;
        mml = getMinMax(arr, low, mid);
        mmr = getMinMax(arr, mid + 1, high);
 
        /* compare minimums of two parts*/
        if (mml.min < mmr.min) {
            minmax.min = mml.min;
        } else {
            minmax.min = mmr.min;
        }
 
        /* compare maximums of two parts*/
        if (mml.max > mmr.max) {
            minmax.max = mml.max;
        } else {
            minmax.max = mmr.max;
        }
 
        return minmax;
    }
 
    /* Driver program to test above function */
    public static void main(String args[]) {
        int arr[] = {1000, 11, 445, 1, 330, 3000};
        int arr_size = 6;
        Pair minmax = getMinMax(arr, 0, arr_size - 1);
        System.out.printf("\nMinimum element is %d", minmax.min);
        System.out.printf("\nMaximum element is %d", minmax.max);
 
    }
}

Python3

# Python program of above implementation
def getMinMax(low, high, arr):
    arr_max = arr[low]
    arr_min = arr[low]
     
    # If there is only one element 
    if low == high:
        arr_max = arr[low]
        arr_min = arr[low]
        return (arr_max, arr_min)
         
    # If there is only two element
    elif high == low + 1:
        if arr[low] > arr[high]:
            arr_max = arr[low]
            arr_min = arr[high]
        else:
            arr_max = arr[high]
            arr_min = arr[low]
        return (arr_max, arr_min)
    else:
         
        # If there are more than 2 elements
        mid = int((low + high) / 2)
        arr_max1, arr_min1 = getMinMax(low, mid, arr)
        arr_max2, arr_min2 = getMinMax(mid + 1, high, arr)
 
    return (max(arr_max1, arr_max2), min(arr_min1, arr_min2))
 
# Driver code
arr = [1000, 11, 445, 1, 330, 3000]
high = len(arr) - 1
low = 0
arr_max, arr_min = getMinMax(low, high, arr)
print('Minimum element is ', arr_min)
print('nMaximum element is ', arr_max)
 
# This code is contributed by DeepakChhitarka

C#

// C# implementation of the approach
using System;
                     
public class GFG {
/* Class Pair is used to return two values from getMinMax() */
    public class Pair {
  
        public int min;
        public int max;
    }
  
    static Pair getMinMax(int []arr, int low, int high) {
        Pair minmax = new Pair();
        Pair mml = new Pair();
        Pair mmr = new Pair();
        int mid;
  
        /* If there is only on element */
        if (low == high) {
            minmax.max = arr[low];
            minmax.min = arr[low];
            return minmax;
        }
  
        /* If there are two elements */
        if (high == low + 1) {
            if (arr[low] > arr[high]) {
                minmax.max = arr[low];
                minmax.min = arr[high];
            } else {
                minmax.max = arr[high];
                minmax.min = arr[low];
            }
            return minmax;
        }
  
        /* If there are more than 2 elements */
        mid = (low + high) / 2;
        mml = getMinMax(arr, low, mid);
        mmr = getMinMax(arr, mid + 1, high);
  
        /* compare minimums of two parts*/
        if (mml.min < mmr.min) {
            minmax.min = mml.min;
        } else {
            minmax.min = mmr.min;
        }
  
        /* compare maximums of two parts*/
        if (mml.max > mmr.max) {
            minmax.max = mml.max;
        } else {
            minmax.max = mmr.max;
        }
  
        return minmax;
    }
  
    /* Driver program to test above function */
    public static void Main(String []args) {
        int []arr = {1000, 11, 445, 1, 330, 3000};
        int arr_size = 6;
        Pair minmax = getMinMax(arr, 0, arr_size - 1);
        Console.Write("\nMinimum element is {0}", minmax.min);
        Console.Write("\nMaximum element is {0}", minmax.max);
  
    }
}
 
// This code contributed by Rajput-Ji

Output:

Minimum element is 1
Maximum element is 3000

Time Complexity: O(n)

Total number of comparisons: let number of comparisons be T(n). T(n) can be written as follows:
Algorithmic Paradigm: Divide and Conquer

             
  T(n) = T(floor(n/2)) + T(ceil(n/2)) + 2  
  T(2) = 1
  T(1) = 0

If n is a power of 2, then we can write T(n) as:

   T(n) = 2T(n/2) + 2

After solving above recursion, we get

  T(n)  = 3n/2 -2

Thus, the approach does 3n/2 -2 comparisons if n is a power of 2. And it does more than 3n/2 -2 comparisons if n is not a power of 2.

METHOD 3 (Compare in Pairs)
If n is odd then initialize min and max as first element.
If n is even then initialize min and max as minimum and maximum of the first two elements respectively.
For rest of the elements, pick them in pairs and compare their
maximum and minimum with max and min respectively.

C++

// C++ program of above implementation 
#include<iostream> 
using namespace std; 
 
// Structure is used to return 
// two values from minMax() 
struct Pair 
{ 
    int min; 
    int max; 
}; 
 
struct Pair getMinMax(int arr[], int n) 
{ 
    struct Pair minmax;     
    int i; 
     
    // If array has even number of elements 
    // then initialize the first two elements 
    // as minimum and maximum 
    if (n % 2 == 0) 
    { 
        if (arr[0] > arr[1])     
        { 
            minmax.max = arr[0]; 
            minmax.min = arr[1]; 
        } 
        else
        { 
            minmax.min = arr[0]; 
            minmax.max = arr[1]; 
        } 
         
        // Set the starting index for loop 
        i = 2; 
    } 
     
    // If array has odd number of elements 
    // then initialize the first element as 
    // minimum and maximum 
    else
    { 
        minmax.min = arr[0]; 
        minmax.max = arr[0]; 
         
        // Set the starting index for loop 
        i = 1; 
    } 
     
    // In the while loop, pick elements in 
    // pair and compare the pair with max 
    // and min so far 
    while (i < n - 1) 
    {         
        if (arr[i] > arr[i + 1])         
        { 
            if(arr[i] > minmax.max)     
                minmax.max = arr[i]; 
                 
            if(arr[i + 1] < minmax.min)         
                minmax.min = arr[i + 1];     
        } 
        else       
        { 
            if (arr[i + 1] > minmax.max)     
                minmax.max = arr[i + 1]; 
                 
            if (arr[i] < minmax.min)         
                minmax.min = arr[i];     
        } 
         
        // Increment the index by 2 as 
        // two elements are processed in loop 
        i += 2; 
    }         
    return minmax; 
} 
 
// Driver code 
int main() 
{ 
    int arr[] = { 1000, 11, 445, 
                1, 330, 3000 }; 
    int arr_size = 6; 
     
    Pair minmax = getMinMax(arr, arr_size); 
     
    cout << "nMinimum element is "
        << minmax.min << endl; 
    cout << "nMaximum element is "
        << minmax.max; 
         
    return 0; 
} 
 
// This code is contributed by nik_3112 

C

#include<stdio.h>
 
/* structure is used to return two values from minMax() */
struct pair 
{
  int min;
  int max;
};  
 
struct pair getMinMax(int arr[], int n)
{
  struct pair minmax;     
  int i;  
 
  /* If array has even number of elements then 
    initialize the first two elements as minimum and 
    maximum */
  if (n%2 == 0)
  {         
    if (arr[0] > arr[1])     
    {
      minmax.max = arr[0];
      minmax.min = arr[1];
    }  
    else
    {
      minmax.min = arr[0];
      minmax.max = arr[1];
    }
    i = 2;  /* set the starting index for loop */
  }  
 
   /* If array has odd number of elements then 
    initialize the first element as minimum and 
    maximum */
  else
  {
    minmax.min = arr[0];
    minmax.max = arr[0];
    i = 1;  /* set the starting index for loop */
  }
   
  /* In the while loop, pick elements in pair and 
     compare the pair with max and min so far */   
  while (i < n-1)  
  {          
    if (arr[i] > arr[i+1])          
    {
      if(arr[i] > minmax.max)        
        minmax.max = arr[i];
      if(arr[i+1] < minmax.min)          
        minmax.min = arr[i+1];        
    } 
    else        
    {
      if (arr[i+1] > minmax.max)        
        minmax.max = arr[i+1];
      if (arr[i] < minmax.min)          
        minmax.min = arr[i];        
    }        
    i += 2; /* Increment the index by 2 as two 
               elements are processed in loop */
  }            
 
  return minmax;
}    
 
/* Driver program to test above function */
int main()
{
  int arr[] = {1000, 11, 445, 1, 330, 3000};
  int arr_size = 6;
  struct pair minmax = getMinMax (arr, arr_size);
  printf("nMinimum element is %d", minmax.min);
  printf("nMaximum element is %d", minmax.max);
  getchar();
}

Java

// Java program of above implementation
public class GFG {
 
/* Class Pair is used to return two values from getMinMax() */
    static class Pair {
 
        int min;
        int max;
    }
 
    static Pair getMinMax(int arr[], int n) {
        Pair minmax = new Pair();
        int i;
        /* If array has even number of elements then  
    initialize the first two elements as minimum and  
    maximum */
        if (n % 2 == 0) {
            if (arr[0] > arr[1]) {
                minmax.max = arr[0];
                minmax.min = arr[1];
            } else {
                minmax.min = arr[0];
                minmax.max = arr[1];
            }
            i = 2;
            /* set the starting index for loop */
        } /* If array has odd number of elements then  
    initialize the first element as minimum and  
    maximum */ else {
            minmax.min = arr[0];
            minmax.max = arr[0];
            i = 1;
            /* set the starting index for loop */
        }
 
        /* In the while loop, pick elements in pair and  
     compare the pair with max and min so far */
        while (i < n - 1) {
            if (arr[i] > arr[i + 1]) {
                if (arr[i] > minmax.max) {
                    minmax.max = arr[i];
                }
                if (arr[i + 1] < minmax.min) {
                    minmax.min = arr[i + 1];
                }
            } else {
                if (arr[i + 1] > minmax.max) {
                    minmax.max = arr[i + 1];
                }
                if (arr[i] < minmax.min) {
                    minmax.min = arr[i];
                }
            }
            i += 2;
            /* Increment the index by 2 as two  
               elements are processed in loop */
        }
 
        return minmax;
    }
 
    /* Driver program to test above function */
    public static void main(String args[]) {
        int arr[] = {1000, 11, 445, 1, 330, 3000};
        int arr_size = 6;
        Pair minmax = getMinMax(arr, arr_size);
        System.out.printf("\nMinimum element is %d", minmax.min);
        System.out.printf("\nMaximum element is %d", minmax.max);
 
    }
}

Python3

# Python3 program of above implementation 
def getMinMax(arr):
     
    n = len(arr)
     
    # If array has even number of elements then 
    # initialize the first two elements as minimum 
    # and maximum 
    if(n % 2 == 0):
        mx = max(arr[0], arr[1])
        mn = min(arr[0], arr[1])
         
        # set the starting index for loop 
        i = 2
         
    # If array has odd number of elements then 
    # initialize the first element as minimum 
    # and maximum 
    else:
        mx = mn = arr[0]
         
        # set the starting index for loop 
        i = 1
         
    # In the while loop, pick elements in pair and 
    # compare the pair with max and min so far 
    while(i < n - 1):
        if arr[i] < arr[i + 1]:
            mx = max(mx, arr[i + 1])
            mn = min(mn, arr[i])
        else:
            mx = max(mx, arr[i])
            mn = min(mn, arr[i + 1])
             
        # Increment the index by 2 as two 
        # elements are processed in loop 
        i += 2
     
    return (mx, mn)
     
# Driver Code
if __name__ =='__main__':
     
    arr = [1000, 11, 445, 1, 330, 3000]
    mx, mn = getMinMax(arr)
    print("Minimum element is", mn)
    print("Maximum element is", mx)
     
# This code is contributed by Kaustav

C#

// C# program of above implementation
using System;
     
class GFG 
{
 
    /* Class Pair is used to return 
       two values from getMinMax() */
    public class Pair 
    {
        public int min;
        public int max;
    }
 
    static Pair getMinMax(int []arr, int n)
    {
        Pair minmax = new Pair();
        int i;
         
        /* If array has even number of elements 
        then initialize the first two elements 
        as minimum and maximum */
        if (n % 2 == 0) 
        {
            if (arr[0] > arr[1])
            {
                minmax.max = arr[0];
                minmax.min = arr[1];
            } 
            else
            {
                minmax.min = arr[0];
                minmax.max = arr[1];
            }
            i = 2;
        }
         
        /* set the starting index for loop */
        /* If array has odd number of elements then 
        initialize the first element as minimum and 
        maximum */
        else
        {
            minmax.min = arr[0];
            minmax.max = arr[0];
            i = 1;
            /* set the starting index for loop */
        }
 
        /* In the while loop, pick elements in pair and 
        compare the pair with max and min so far */
        while (i < n - 1) 
        {
            if (arr[i] > arr[i + 1]) 
            {
                if (arr[i] > minmax.max) 
                {
                    minmax.max = arr[i];
                }
                if (arr[i + 1] < minmax.min)
                {
                    minmax.min = arr[i + 1];
                }
            } 
            else
            {
                if (arr[i + 1] > minmax.max)
                {
                    minmax.max = arr[i + 1];
                }
                if (arr[i] < minmax.min)
                {
                    minmax.min = arr[i];
                }
            }
            i += 2;
             
            /* Increment the index by 2 as two 
            elements are processed in loop */
        }
        return minmax;
    }
 
    // Driver Code
    public static void Main(String []args) 
    {
        int []arr = {1000, 11, 445, 1, 330, 3000};
        int arr_size = 6;
        Pair minmax = getMinMax(arr, arr_size);
        Console.Write("Minimum element is {0}",
                                   minmax.min);
        Console.Write("\nMaximum element is {0}", 
                                     minmax.max);
    }
}
 
// This code is contributed by 29AjayKumar

Output:

Minimum element is 1
Maximum element is 3000

Time Complexity: O(n)

Total number of comparisons: Different for even and odd n, see below:

       If n is odd:    3*(n-1)/2  
       If n is even:   1 Initial comparison for initializing min and max, 
                           and 3(n-2)/2 comparisons for rest of the elements  
                      =  1 + 3*(n-2)/2 = 3n/2 -2

Second and third approaches make equal number of comparisons when n is a power of 2.
In general, method 3 seems to be the best.
Please write comments if you find any bug in the above programs/algorithms or a better way to solve the same problem.

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