700653. Triplet Family
Basic
Triplet Family
Slug: triplet-family Difficulty: Basic Id: 700653 Topic Tags: Arrays, Sorting, Data Structures, Algorithms Company Tags: Arcesium
Summary
The Triplet Family problem involves finding triplets in a given array that satisfy certain conditions. The key concepts involved are arrays and sorting.
A triplet is considered part of the "Triplet Family" if it satisfies three conditions:
- All elements are unique (no duplicates).
- Each element is greater than or equal to 0.
- The sum of any two elements is less than a given target value (T).
Detailed Explanation
To solve this problem, we can use a two-pointer technique along with sorting. Here's the step-by-step approach:
- First, sort the array in ascending order.
- Initialize three pointers:
i,j, andk. Setito 0 (the start of the array),jtoi + 1, andkto the end of the array. - Move the
jpointer towards the end of the array while maintaining the following conditions:- The sum of elements at indices
i,j, andkis less than or equal to T. - The element at index
jis greater than or equal to 0.
- The sum of elements at indices
- If the conditions are met, increment
iby 1 and updatejtoi + 1. This ensures that we consider all possible triplets without duplicates. - Repeat steps 3-4 until
kreaches the end of the array. - When
kreaches the end, decrement it and updateitok - 1, then repeat step 3. - Continue this process until
jis less than or equal tok. This ensures that we have considered all possible triplets.
The time complexity of this algorithm is O(n^2), where n is the size of the array, and the space complexity is O(1) since we only use a few extra variables.
Optimized Solutions
Java
public class TripletFamily {
public static void findTriplets(int[] arr, int T) {
Arrays.sort(arr);
for (int i = 0; i < arr.length - 2; i++) {
int j = i + 1;
int k = arr.length - 1;
while (j < k && arr[i] + arr[j] + arr[k] > T) {
k--;
}
while (j < k && arr[i] + arr[j] + arr[k] <= T) {
System.out.println(arr[i] + " " + arr[j] + " " + arr[k]);
j++;
k--;
}
}
}
}