# Find triplet with minimum sum

Given an array of distinct integers arr[]. The task is to find a triplet(a group of 3 elements) that has the minimum sum.

Note: The size of the array is always greater than two.

Examples:

```Input : arr[] = {1, 2, 3, 4, -1, 5, -2}
Output : -2
1 - 1 - 2 = -2
Input : arr[] = {5, 6, 0, 0, 1}
Output : 1
0 + 0 + 1.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Naive Approach: The idea is to generate all possible triplets in the array and then compare sum of one triplet with other triplets, then find the minimum sum.

Below is the implementation of the above approach:

## C++

 `// C++ Program to find triplet with minimum sum ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find triplet with minimum sum ` `int` `getMinimumSum(``int` `arr[] , ``int` `n) ` `{ ` `    ``int` `ans = INT_MAX; ` `     `  `    ``// Generate all possible triplets ` `    ``for` `(``int` `i = 0; i < n - 2; i++) { ` `        ``for` `(``int` `j = i + 1; j < n - 1; j++) { ` `            ``for` `(``int` `k = j + 1; k < n; k++) { ` `                ``// Calculate sum of each triplet ` `                ``// and update minimum ` `                ``ans = min(ans, arr[i] + arr[j] + arr[k]); ` `            ``} ` `        ``} ` `    ``} ` `     `  `    ``return` `ans; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 2, 3, 4, 5, -1, 5, -2 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` ` `  `    ``cout << getMinimumSum(arr, n) << endl; ` `     `  `    ``return` `0; ` `} `

## Java

 `// Java Program to find triplet with minimum sum ` `class` `GFG ` `{ ` ` `  `// Function to find triplet with minimum sum ` `static` `int` `getMinimumSum(``int` `arr[] , ``int` `n) ` `{ ` `    ``int` `ans = Integer.MAX_VALUE; ` `     `  `    ``// Generate all possible triplets ` `    ``for` `(``int` `i = ``0``; i < n - ``2``; i++)  ` `    ``{ ` `        ``for` `(``int` `j = i + ``1``; j < n - ``1``; j++)  ` `        ``{ ` `            ``for` `(``int` `k = j + ``1``; k < n; k++) ` `            ``{ ` `                ``// Calculate sum of each triplet ` `                ``// and update minimum ` `                ``ans = Math.min(ans, arr[i] +  ` `                                ``arr[j] + arr[k]); ` `            ``} ` `        ``} ` `    ``} ` `     `  `    ``return` `ans; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `arr[] = { ``1``, ``2``, ``3``, ``4``, ``5``, -``1``, ``5``, -``2` `}; ` `    ``int` `n = arr.length; ` ` `  `    ``System.out.print(getMinimumSum(arr, n) + ``"\n"``); ` `} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `

## Python3

 `# Python3 Program to find triplet with minimum sum ` `import` `sys ` ` `  `# Function to find triplet with minimum sum ` `def` `getMinimumSum(arr, n): ` `    ``ans ``=` `sys.maxsize; ` ` `  `    ``# Generate all possible triplets ` `    ``for` `i ``in` `range``(n ``-` `2``): ` `        ``for` `j ``in` `range``(i ``+` `1``, n ``-` `1``): ` `            ``for` `k ``in` `range``(j ``+` `1``, n): ` `                 `  `                ``# Calculate sum of each triplet ` `                ``# and update minimum ` `                ``ans ``=` `min``(ans, arr[i] ``+` `arr[j] ``+` `arr[k]); ` `    ``return` `ans; ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``arr ``=` `[ ``1``, ``2``, ``3``, ``4``, ``5``, ``-``1``, ``5``, ``-``2` `]; ` `    ``n ``=` `len``(arr); ` ` `  `    ``print``(getMinimumSum(arr, n)); ` `     `  `# This code is contributed by PrinciRaj1992 `

## C#

 `// C# Program to find triplet with minimum sum ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `    ``// Function to find triplet with minimum sum ` `    ``static` `int` `getMinimumSum(``int` `[]arr, ``int` `n) ` `    ``{ ` `        ``int` `ans = ``int``.MaxValue; ` `         `  `        ``// Generate all possible triplets ` `        ``for` `(``int` `i = 0; i < n - 2; i++)  ` `        ``{ ` `            ``for` `(``int` `j = i + 1; j < n - 1; j++)  ` `            ``{ ` `                ``for` `(``int` `k = j + 1; k < n; k++) ` `                ``{ ` `                    ``// Calculate sum of each triplet ` `                    ``// and update minimum ` `                    ``ans = Math.Min(ans, arr[i] +  ` `                                    ``arr[j] + arr[k]); ` `                ``} ` `            ``} ` `        ``} ` `         `  `        ``return` `ans; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `[]arr = { 1, 2, 3, 4, 5, -1, 5, -2 }; ` `        ``int` `n = arr.Length; ` `     `  `        ``Console.WriteLine(getMinimumSum(arr, n)); ` `    ``} ` `} ` ` `  `// This code is contributed by AnkitRai01 `

Output:

```-2
```

Time Complexity: 0(n^3)
Auxiliary Space: 0(1)

Efficent approach: The idea is to traverse the array and compute minimum, second minimum and third minimum element present in the array and print the sum of these three elements.

Below is the implementation of the above approach:

## CPP

 `// C++ Program to find triplet with a minimum sum ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to find triplet with minimum sum ` `int` `getMinimumSum(``int` `arr[] , ``int` `n) ` `{ ` `    ``// fMin: First minimum ` `    ``// sMin: Second minimum ` `    ``// tMin: Third minimum ` `    ``int` `fMin = INT_MAX, sMin = INT_MAX, tMin = INT_MAX; ` `     `  `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``// Update the first, second and third minimum ` `        ``if` `(arr[i] < fMin) { ` `            ``tMin = sMin; ` `            ``sMin = fMin; ` `            ``fMin = arr[i]; ` `        ``} ` `        ``// update second and third minimum ` `        ``else` `if` `(arr[i] < sMin) { ` `            ``tMin = sMin; ` `            ``sMin = arr[i]; ` `        ``} ` `        ``else` `if` `(arr[i] < tMin) { ` `            ``tMin = arr[i]; ` `        ``} ` `    ``} ` `     `  `    ``return` `(fMin + sMin + tMin); ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 2, 3, 4, 5, -1, 5, -2 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` ` `  `    ``cout << getMinimumSum(arr, n) << endl; ` `     `  `    ``return` `0; ` `} `

## Java

 `// Java Program to find triplet with a minimum sum ` ` `  `class` `GFG ` `{ ` ` `  `// Function to find triplet with minimum sum ` `static` `int` `getMinimumSum(``int` `arr[] , ``int` `n) ` `{ ` `    ``// fMin: First minimum ` `    ``// sMin: Second minimum ` `    ``// tMin: Third minimum ` `    ``int` `fMin = Integer.MAX_VALUE, ` `            ``sMin = Integer.MAX_VALUE,  ` `            ``tMin = Integer.MAX_VALUE; ` `     `  `    ``for` `(``int` `i = ``0``; i < n; i++)  ` `    ``{ ` `         `  `        ``// Update the first, second and third minimum ` `        ``if` `(arr[i] < fMin)  ` `        ``{ ` `            ``tMin = sMin; ` `            ``sMin = fMin; ` `            ``fMin = arr[i]; ` `        ``} ` `         `  `        ``// update second and third minimum ` `        ``else` `if` `(arr[i] < sMin) ` `        ``{ ` `            ``tMin = sMin; ` `            ``sMin = arr[i]; ` `        ``} ` `        ``else` `if` `(arr[i] < tMin) ` `        ``{ ` `            ``tMin = arr[i]; ` `        ``} ` `    ``} ` `    ``return` `(fMin + sMin + tMin); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `arr[] = { ``1``, ``2``, ``3``, ``4``, ``5``, -``1``, ``5``, -``2` `}; ` `    ``int` `n = arr.length; ` ` `  `    ``System.out.print(getMinimumSum(arr, n) +``"\n"``); ` `} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `

## Python3

 `# Python3 Program to find triplet with a minimum sum ` `import` `sys ` ` `  `# Function to find triplet with minimum sum ` `def` `getMinimumSum(arr, n): ` ` `  `    ``# fMin: First minimum ` `    ``# sMin: Second minimum ` `    ``# tMin: Third minimum ` `    ``fMin ``=` `sys.maxsize;  ` `    ``sMin ``=` `sys.maxsize; ` `    ``tMin ``=` `sys.maxsize; ` ` `  `    ``for` `i ``in` `range``(n): ` ` `  `        ``# Update the first, second and third minimum ` `        ``if` `(arr[i] < fMin): ` `            ``tMin ``=` `sMin; ` `            ``sMin ``=` `fMin; ` `            ``fMin ``=` `arr[i]; ` `         `  `        ``# update second and third minimum ` `        ``elif``(arr[i] < sMin): ` `            ``tMin ``=` `sMin; ` `            ``sMin ``=` `arr[i]; ` `        ``elif``(arr[i] < tMin): ` `            ``tMin ``=` `arr[i]; ` `         `  `    ``return` `(fMin ``+` `sMin ``+` `tMin); ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``arr ``=` `[ ``1``, ``2``, ``3``, ``4``, ``5``, ``-``1``, ``5``, ``-``2``]; ` `    ``n ``=` `len``(arr); ` ` `  `    ``print``(getMinimumSum(arr, n)); ` ` `  `# This code is contributed by 29AjayKumar `

## C#

 `// C# Program to find triplet with a minimum sum ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to find triplet with minimum sum ` `static` `int` `getMinimumSum(``int` `[]arr, ``int` `n) ` `{ ` `    ``// fMin: First minimum ` `    ``// sMin: Second minimum ` `    ``// tMin: Third minimum ` `    ``int` `fMin = ``int``.MaxValue, ` `        ``sMin = ``int``.MaxValue,  ` `        ``tMin = ``int``.MaxValue; ` `     `  `    ``for` `(``int` `i = 0; i < n; i++)  ` `    ``{ ` `         `  `        ``// Update the first, second and third minimum ` `        ``if` `(arr[i] < fMin)  ` `        ``{ ` `            ``tMin = sMin; ` `            ``sMin = fMin; ` `            ``fMin = arr[i]; ` `        ``} ` `         `  `        ``// update second and third minimum ` `        ``else` `if` `(arr[i] < sMin) ` `        ``{ ` `            ``tMin = sMin; ` `            ``sMin = arr[i]; ` `        ``} ` `        ``else` `if` `(arr[i] < tMin) ` `        ``{ ` `            ``tMin = arr[i]; ` `        ``} ` `    ``} ` `    ``return` `(fMin + sMin + tMin); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `[]arr = { 1, 2, 3, 4, 5, -1, 5, -2 }; ` `    ``int` `n = arr.Length; ` ` `  `    ``Console.Write(getMinimumSum(arr, n) +``"\n"``); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```-2
```

Time Complexity: 0(n)
Auxiliary Space: 0(1)

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