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.

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 <bits/stdc++.h>
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

Javascript

<script>

// JavaScript Program to find
// triplet with minimum sum

// Function to find triplet with minimum sum
function getMinimumSum(arr, n)
{
    let ans = Number.MAX_SAFE_INTEGER;

    // Generate all possible triplets
    for (let i = 0; i < n - 2; i++) {
        for (let j = i + 1; j < n - 1; j++)
        {
            for (let 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
    let arr = [ 1, 2, 3, 4, 5, -1, 5, -2 ];
    let n = arr.length;

    document.write(getMinimumSum(arr, n) + "<br>");


// This code is contributed by Surbhi Tyagi.

</script>

Output:

-2

Time Complexity: 0(n^3) 
Auxiliary Space: 0(1)
Efficient 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 <bits/stdc++.h>
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

Javascript

<script>

// JavaScript Program to find triplet
// with a minimum sum

// Function to find triplet with minimum sum
function getMinimumSum(arr , n)
{
    // fMin: First minimum
    // sMin: Second minimum
    // tMin: Third minimum
    var fMin = 1000000000, sMin = 1000000000,
    tMin = 1000000000;

    for (var 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
var arr = [1, 2, 3, 4, 5, -1, 5, -2];
var n = arr.length;
document.write( getMinimumSum(arr, n));


</script>

Output:

-2

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

Another Approach: Using Sorting

The idea is to sort the array given in the input. After that first three elements of the array will form a triplet that will give a minimum sum because those are the three minimum elements of the array.

Code-

C++

// C++ Program to find triplet with a minimum sum

#include <bits/stdc++.h>
using namespace std;

// Function to find triplet with minimum sum
int getMinimumSum(int arr[], int n)
{
    sort(arr, arr + n);
    return (arr[0] + arr[1] + arr[2]);
}

// 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;
}
// This code is contributed by user_dtewbxkn77n

Java

import java.util.*;

class Main
{

    // Function to find triplet with minimum sum
    static int getMinimumSum(int arr[], int n) {
        Arrays.sort(arr);
        return (arr[0] + arr[1] + arr[2]);
    }

    // Driver code
    public static void main(String[] args) {
        int arr[] = { 1, 2, 3, 4, 5, -1, 5, -2 };
        int n = arr.length;

        System.out.println(getMinimumSum(arr, n));
    }
}

Python3

# Python program to find triplet with a minimum sum

# Function to find triplet with minimum sum
def getMinimumSum(arr, n):
    arr.sort()
    return (arr[0] + arr[1] + arr[2])

# Driver Code
if __name__ == '__main__':
    arr = [1, 2, 3, 4, 5, -1, 5, -2]
    n = len(arr)

    print(getMinimumSum(arr, n))

C#

// C# Program to find triplet with a minimum sum

using System;

class Program {
// Function to find triplet with minimum sum
static int GetMinimumSum(int[] arr, int n) {
Array.Sort(arr);
return (arr[0] + arr[1] + arr[2]);
}
  // Driver Code
static void Main(string[] args) {
    int[] arr = { 1, 2, 3, 4, 5, -1, 5, -2 };
    int n = arr.Length;

    Console.WriteLine(GetMinimumSum(arr, n));
}
}

Javascript

// Function to find triplet with minimum sum
function getMinimumSum(arr) {
    arr.sort((a, b) => a - b);
    return (arr[0] + arr[1] + arr[2]);
}

// Driver Code
const arr = [1, 2, 3, 4, 5, -1, 5, -2];
console.log(getMinimumSum(arr));

Output-

-2

Time Complexity: O(nlogn),in sorting 
Auxiliary Space: O(1)