3Sum: Unique Triplets
Problem
Print all different triplets (a, b, c) from the array with a + b + c = 0. Each triplet is printed in ascending order as a b c, and the triplets are printed in ascending order too. A triplet uses three different positions but no triplet value is printed twice. Print none if there is no triplet.
Constraints
- 1 <= n <= 3000
Examples
Input
6 -1 0 1 2 -1 -4
Output
-1 -1 2 -1 0 1
Solutions
Checking all triples costs O(n^3). After sorting, one fixed value and two moving pointers need only O(n^2). Skipping repeated values is what keeps the triplets unique.
/*
* Problem : Process an array.
* Input : n, then n integers.
* Output : The triplets.
* Approach: Sort, then two pointers.
* Time : O(n^2)
* Space : O(1) extra
* Java : 8 or newer.
*/
import java.util.Scanner;
public class Main {
// This method solves the task. It receives the input and returns the answer.
static String[] solve(int[] a) {
// Step 1: Sort the array. Then we can use two pointers and skip repeated values easily.
java.util.Arrays.sort(a);
java.util.List<String> found = new java.util.ArrayList<>();
for (int i = 0; i < a.length - 2; i++) {
// Step 2: Skip a first value that is the same as the one before. It would give the same triplets.
if (i > 0 && a[i] == a[i - 1]) {
continue;
}
// Step 3: Two pointers look for a pair with the sum -a[i].
int left = i + 1;
int right = a.length - 1;
while (left < right) {
long sum = (long) a[i] + a[left] + a[right];
if (sum < 0) {
left++;
} else if (sum > 0) {
right--;
} else {
found.add(a[i] + " " + a[left] + " " + a[right]);
left++;
right--;
// Step 4: Skip repeated values on the left side, so the same triplet is not printed twice.
while (left < right && a[left] == a[left - 1]) {
left++;
}
}
}
}
if (found.isEmpty()) {
found.add("none");
}
return found.toArray(new String[0]);
}
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
int size = scanner.nextInt();
int[] a = new int[size];
for (int i = 0; i < size; i++) {
a[i] = scanner.nextInt();
}
System.out.println(String.join("\n", solve(a)));
}
}
Hints (1)
- Why do we sort first?