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++



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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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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

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

-2

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

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