# 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 ` `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); ` `    ``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

 ` `

Output :

```18
```

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 ` `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); ` `    ``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

 ` `

Output :

```18
```

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 ` `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); ` `    ``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

 ` ``\$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 :

```18
```

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

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