876825. Find All Triplets with Zero Sum
Medium
Here is a detailed Markdown blog post for the "Find All Triplets with Zero Sum" problem:
Find All Triplets with Zero Sum
Summary
Given an array of integers, find all triplets in the array that sum up to zero. This problem involves sorting arrays and hash tables.
Detailed Explanation
The problem requires us to find all unique triplets in a given array of integers such that their sum is equal to zero.
Here's how we can approach this problem:
- First, sort the array of integers.
- Iterate through each element in the sorted array.
- For each element, use two pointers (start and end) initialized at the next element and the last element respectively.
- Move the start pointer towards the end if the sum of the current element and the elements pointed by start and end is less than zero.
- If the sum is greater than zero, move the end pointer towards the start.
- When the sum becomes equal to zero, add the triplet to our result set and move both pointers.
- Repeat this process until the start pointer meets the end pointer.
This solution has a time complexity of O(n^2) due to the nested loops, where n is the number of elements in the array. The space complexity is O(1) as we are not using any extra space that scales with the input size.
Here's an ASCII art diagram illustrating the algorithm:
+---------------+
| Iterate |
| through each|
| element |
+---------------+
|
v
+---------------+
| Start |
| pointer at |
| next elem. |
+---------------+
|
v
+---------------+
| End |
| pointer at |
| last elem.|
+---------------+
|
v
+---------------+
| Move start |
| if sum < 0 |
+---------------+
|
v
+---------------+
| Move end |
| if sum > 0 |
+---------------+
|
v
+---------------+
| Check sum =|
| 0, add to |
| result set |
+---------------+
Optimized Solutions
Java
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
public class Solution {
public List<List<Integer>> findTriplets(int[] nums) {
Arrays.sort(nums);
List<List<Integer>> triplets = new ArrayList<>();
for (int i = 0; i < nums.length - 2; i++) {
if (i > 0 && nums[i] == nums[i - 1]) continue;
int start = i + 1;
int end = nums.length - 1;
while (start < end) {
int sum = nums[i] + nums[start] + nums[end];
if (sum > 0) {
end--;
} else if (sum < 0) {
start++;
} else {
triplets.add(Arrays.asList(nums[i], nums[start], nums[end]));
while (start < end && nums[start] == nums[start + 1]) start++;
while (start < end && nums[end] == nums[end - 1]) end--;
start++;
end--;
}
}
}
return triplets;
}
}