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 sumint 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 Codeint 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 sumclass GFG{ // Function to find triplet with minimum sumstatic 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 Codepublic 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 sumimport sys # Function to find triplet with minimum sumdef 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 Codeif __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 sumusing 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 <bits/stdc++.h>using namespace std; // Function to find triplet with minimum sumint 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 Codeint 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 sumstatic 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 Codepublic 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 sumimport sys # Function to find triplet with minimum sumdef 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 Codeif __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 sumusing System; class GFG{ // Function to find triplet with minimum sumstatic 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 Codepublic 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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