Maximum triplet sum in array

Given an array, the task is to find maximum triplet sum in the array.

Examples :

Input : arr[] = {1, 2, 3, 0, -1, 8, 10} 
Output : 21
10 + 8 + 3 = 21

Input : arr[] = {9, 8, 20, 3, 4, -1, 0}
Output : 37
20 + 9 + 8 = 37

Recommended: Please solve it on PRACTICE first, before moving on to the solution.

Naive approach : In this method we simply run three loop and one by one add three element and compare with previous sum if the sum of three element is greater then store in previous sum .

C++

// C++ code to find maximum triplet sum 
#include <bits/stdc++.h> 
using namespace std; 
  
int maxTripletSum(int arr[], int n) 
{ 
    // Initialize sum with INT_MIN 
    int sum = INT_MIN; 
  
    for (int i = 0; i < n; i++) 
        for (int j = i + 1; j < n; j++) 
            for (int k = j + 1; k < n; k++)  
                if (sum < arr[i] + arr[j] + arr[k])  
                    sum = arr[i] + arr[j] + arr[k];                 
    return sum;          
} 
  
// Driven code 
int main() 
{ 
    int arr[] = { 1, 0, 8, 6, 4, 2 }; 
    int n = sizeof(arr) / sizeof(arr[0]); 
    cout << maxTripletSum(arr, n); 
    return 0; 
} 

Java

// Java code to find maximum triplet sum 
import java.io.*; 
  
class GFG { 
      
    static int maxTripletSum(int arr[], int n) 
    { 
        // Initialize sum with INT_MIN 
        int sum = -1000000; 
      
        for (int i = 0; i < n; i++) 
            for (int j = i + 1; j < n; j++) 
                for (int k = j + 1; k < n; k++)  
                    if (sum < arr[i] + arr[j] + arr[k])  
                        sum = arr[i] + arr[j] + arr[k];              
        return sum;          
    } 
      
    // Driven code 
    public static void main(String args[]) 
    { 
        int arr[] = { 1, 0, 8, 6, 4, 2 }; 
        int n = arr.length; 
        System.out.println(maxTripletSum(arr, n)); 
    } 
} 
  
// This code is contributed by Nikita Tiwari. 

Python3

# Python 3 code to find 
# maximum triplet sum 
  
def maxTripletSum(arr, n) : 
  
    # Initialize sum with 
    # INT_MIN 
    sm = -1000000
  
    for i in range(0, n) : 
        for j in range(i + 1, n) : 
            for k in range(j + 1, n) : 
      
                if (sm < (arr[i] + arr[j] + arr[k])) : 
                    sm = arr[i] + arr[j] + arr[k]              
    return sm 
      
# Driven code 
arr = [ 1, 0, 8, 6, 4, 2 ] 
n = len(arr) 
  
print(maxTripletSum(arr, n)) 
  
# This code is contributed by Nikita Tiwari. 

C#

// C# code to find maximum triplet sum 
using System; 
  
class GFG { 
  
    static int maxTripletSum(int[] arr, int n) 
    { 
        // Initialize sum with INT_MIN 
        int sum = -1000000; 
  
        for (int i = 0; i < n; i++) 
            for (int j = i + 1; j < n; j++) 
                for (int k = j + 1; k < n; k++) 
                    if (sum < arr[i] + arr[j] + arr[k]) 
                        sum = arr[i] + arr[j] + arr[k]; 
        return sum; 
    } 
  
    // Driven code 
    public static void Main() 
    { 
        int[] arr = { 1, 0, 8, 6, 4, 2 }; 
        int n = arr.Length; 
        Console.WriteLine(maxTripletSum(arr, n)); 
    } 
} 
  
// This code is contributed by vt_m. 

PHP

<?php 
// PHP code to find maximum triplet sum 
  
function maxTripletSum( $arr, $n) 
{ 
      
    // Initialize sum with INT_MIN 
    $sum = PHP_INT_MIN; 
  
    for($i = 0; $i < $n; $i++) 
        for($j = $i + 1; $j < $n; $j++) 
            for($k = $j + 1; $k < $n; $k++)  
                if ($sum < $arr[$i] +  
                           $arr[$j] + 
                           $arr[$k]) 
                             
                    $sum = $arr[$i] +  
                           $arr[$j] + 
                           $arr[$k];          
    return $sum;          
} 
  
    // Driver Code 
    $arr = array(1, 0, 8, 6, 4, 2); 
    $n = count($arr); 
    echo maxTripletSum($arr, $n); 
  
// This code is contributed by anuj_67. 
?> 

Output :

Time complexity : O(n^3)
Space complexity : O(1)

Another approach : In this, we first need to sort the whole array and after that when we add last three element of the array then we find maximum sum of triplates.

C++

// C++ code to find maximum triplet sum 
#include <bits/stdc++.h> 
using namespace std; 
  
// This function assumes that there are at least  
// three elements in arr[]. 
int maxTripletSum(int arr[], int n) 
{ 
    // sort the given array 
    sort(arr, arr + n); 
  
    // After sorting the array.  
    // Add last three element of the given array 
    return arr[n - 1] + arr[n - 2] + arr[n - 3]; 
} 
  
// Driven code 
int main() 
{ 
    int arr[] = { 1, 0, 8, 6, 4, 2 }; 
    int n = sizeof(arr) / sizeof(arr[0]); 
    cout << maxTripletSum(arr, n); 
    return 0; 
} 

Java

// Java code to find maximum triplet sum 
import java.io.*; 
import java.util.*; 
  
  
class GFG { 
      
    // This function assumes that there are 
    // at least three elements in arr[]. 
    static int maxTripletSum(int arr[], int n) 
    { 
        // sort the given array 
        Arrays.sort(arr); 
      
        // After sorting the array.  
        // Add last three element  
        // of the given array 
        return arr[n - 1] + arr[n - 2] + arr[n - 3]; 
    }  
      
    // Driven code 
    public static void main(String args[]) 
    { 
        int arr[] = { 1, 0, 8, 6, 4, 2 }; 
        int n = arr.length; 
        System.out.println(maxTripletSum(arr, n)); 
    } 
} 
  
  
// This code is contributed by Nikita Tiwari. 

Python3

# Python 3 code to find  
# maximum triplet sum 
  
# This function assumes  
# that there are at least  
# three elements in arr[]. 
def maxTripletSum(arr, n) : 
  
    # sort the given array 
    arr.sort() 
  
    # After sorting the array.  
    # Add last three element  
    # of the given array 
    return (arr[n - 1] + arr[n - 2] + arr[n - 3]) 
      
      
# Driven code 
arr = [ 1, 0, 8, 6, 4, 2 ] 
n = len(arr) 
  
print(maxTripletSum(arr, n)) 
  
# This code is contributed by Nikita Tiwari. 

C#

// C# code to find maximum triplet sum 
using System; 
  
class GFG { 
  
    // This function assumes that there are 
    // at least three elements in arr[]. 
    static int maxTripletSum(int[] arr, int n) 
    { 
        // sort the given array 
        Array.Sort(arr); 
  
        // After sorting the array. 
        // Add last three element 
        // of the given array 
        return arr[n - 1] + arr[n - 2] + arr[n - 3]; 
    } 
  
    // Driven code 
    public static void Main() 
    { 
        int[] arr = { 1, 0, 8, 6, 4, 2 }; 
        int n = arr.Length; 
        Console.WriteLine(maxTripletSum(arr, n)); 
    } 
} 
  
// This code is contributed by vt_m. 

PHP

<?php 
// PHP code to find  
// maximum triplet sum 
  
// This function assumes that 
// there are at least  
// three elements in arr[]. 
function maxTripletSum( $arr, $n) 
{ 
    // sort the given array 
    sort($arr); 
  
    // After sorting the array.  
    // Add last three element  
    // of the given array 
    return $arr[$n - 1] + $arr[$n - 2] + 
                          $arr[$n - 3]; 
} 
  
// Driver code 
$arr = array( 1, 0, 8, 6, 4, 2 ); 
$n = count($arr); 
echo maxTripletSum($arr, $n); 
  
// This code is contributed by anuj_67. 
?> 

Output :

Time complexity : O(nlogn)
Space complexity : O(1)

Efficent approach : Scan the array and compute Maximum, second maximum and third maximum element present in the array and return the sum of its and it would be maximum sum .

C++

// C++ code to find maximum triplet sum 
#include <bits/stdc++.h> 
using namespace std; 
  
// This function assumes that there are at least  
// three elements in arr[]. 
int maxTripletSum(int arr[], int n) 
{ 
    // Initialize Maximum, second maximum and third 
    // maximum element 
    int maxA = INT_MIN, maxB = INT_MIN, maxC = INT_MIN; 
  
    for (int i = 0; i < n; i++) { 
  
        // Update Maximum, second maximum and third 
        // maximum element 
        if (arr[i] > maxA) { 
            maxC = maxB; 
            maxB = maxA; 
            maxA = arr[i]; 
        } 
  
        // Update second maximum and third maximum 
        // element 
        else if (arr[i] > maxB) { 
            maxC = maxB; 
            maxB = arr[i]; 
        } 
  
        // Update third maximum element 
        else if (arr[i] > maxC) 
            maxC = arr[i]; 
    } 
  
    return (maxA + maxB + maxC); 
} 
  
// Driven code 
int main() 
{ 
    int arr[] = { 1, 0, 8, 6, 4, 2 }; 
    int n = sizeof(arr) / sizeof(arr[0]); 
    cout << maxTripletSum(arr, n); 
    return 0; 
} 

Java

// Java code to find maximum triplet sum 
import java.io.*; 
import java.util.*; 
  
  
class GFG { 
      
    // This function assumes that there  
    // are at least  three elements in arr[]. 
    static int maxTripletSum(int arr[], int n) 
    { 
        // Initialize Maximum, second maximum and third 
        // maximum element 
        int maxA = -100000000, maxB = -100000000; 
        int maxC = -100000000; 
      
        for (int i = 0; i < n; i++) { 
      
            // Update Maximum, second maximum  
            // and third maximum element 
            if (arr[i] > maxA)  
            { 
                maxC = maxB; 
                maxB = maxA; 
                maxA = arr[i]; 
            } 
      
            // Update second maximum and third maximum 
            // element 
            else if (arr[i] > maxB)  
            { 
                maxC = maxB; 
                maxB = arr[i]; 
            } 
      
            // Update third maximum element 
            else if (arr[i] > maxC) 
                maxC = arr[i]; 
        } 
      
        return (maxA + maxB + maxC); 
    } 
  
    // Driven code 
    public static void main(String args[]) 
    { 
        int arr[] = { 1, 0, 8, 6, 4, 2 }; 
        int n = arr.length; 
        System.out.println(maxTripletSum(arr, n)); 
    } 
} 
  
  
// This code is contributed by Nikita Tiwari. 

Python3

# Python 3 code to find  
# maximum triplet sum 
  
# This function assumes  
# that there are at least  
# three elements in arr[]. 
def maxTripletSum(arr, n) : 
  
    # Initialize Maximum, second  
    # maximum and third maximum  
    # element 
    maxA = -100000000
    maxB = -100000000
    maxC = -100000000
  
    for i in range(0, n) : 
      
        # Update Maximum, second maximum 
        # and third  maximum element 
        if (arr[i] > maxA) : 
            maxC = maxB 
            maxB = maxA 
            maxA = arr[i] 
  
        # Update second maximum and  
        # third maximum element 
        elif (arr[i] > maxB) : 
            maxC = maxB 
            maxB = arr[i] 
          
        # Update third maximum element 
        elif (arr[i] > maxC) : 
            maxC = arr[i] 
              
    return (maxA + maxB + maxC) 
      
# Driven code 
arr = [ 1, 0, 8, 6, 4, 2 ] 
n = len(arr) 
  
print(maxTripletSum(arr, n)) 
  
# This code is contributed by Nikita Tiwari. 

C#

// C# code to find maximum triplet sum 
using System; 
  
class GFG { 
  
    // This function assumes that there 
    // are at least three elements in arr[]. 
    static int maxTripletSum(int[] arr, int n) 
    { 
        // Initialize Maximum, second maximum 
        // and third maximum element 
        int maxA = -100000000, maxB = -100000000; 
        int maxC = -100000000; 
  
        for (int i = 0; i < n; i++) { 
  
            // Update Maximum, second maximum 
            // and third maximum element 
            if (arr[i] > maxA) { 
                maxC = maxB; 
                maxB = maxA; 
                maxA = arr[i]; 
            } 
  
            // Update second maximum and third 
            // maximum element 
            else if (arr[i] > maxB) { 
                maxC = maxB; 
                maxB = arr[i]; 
            } 
  
            // Update third maximum element 
            else if (arr[i] > maxC) 
                maxC = arr[i]; 
        } 
  
        return (maxA + maxB + maxC); 
    } 
  
    // Driven code 
    public static void Main() 
    { 
        int[] arr = { 1, 0, 8, 6, 4, 2 }; 
        int n = arr.Length; 
        Console.WriteLine(maxTripletSum(arr, n)); 
    } 
} 
  
// This code is contributed by vt_m. 

PHP

<?php 
// PHP code to find  
// maximum triplet sum 
  
// This function assumes that  
// there are at least three 
// elements in arr[]. 
function maxTripletSum($arr, $n) 
{ 
    // Initialize Maximum,  
    // second maximum and  
    // third maximum element 
    $maxA = PHP_INT_MIN;  
    $maxB = PHP_INT_MIN;  
    $maxC = PHP_INT_MIN; 
  
    for ( $i = 0; $i < $n; $i++)  
    { 
  
        // Update Maximum, 
        // second maximum and  
        // third maximum element 
        if ($arr[$i] > $maxA)  
        { 
            $maxC = $maxB; 
            $maxB = $maxA; 
            $maxA = $arr[$i]; 
        } 
  
        // Update second maximum and  
        // third maximum element 
        else if ($arr[$i] > $maxB)  
        { 
            $maxC = $maxB; 
            $maxB = $arr[$i]; 
        } 
  
        // Update third maximum element 
        else if ($arr[$i] > $maxC) 
            $maxC = $arr[$i]; 
    } 
  
    return ($maxA + $maxB + $maxC); 
} 
  
// Driven code 
$arr = array( 1, 0, 8, 6, 4, 2 ); 
$n = count($arr); 
echo maxTripletSum($arr, $n); 
  
// This code is contributed by anuj_67. 
?> 

Output :

Time complexity : O(n)
Space complexity : O(1)

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My Personal Notes

Recommended: Please solve it on PRACTICE first, before moving on to the solution.

C++

Java

Python3

C#

PHP

C++

Java

Python3

C#

PHP

C++

Java

Python3

C#

PHP

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