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128\. Longest Consecutive Sequence

Medium

Given an unsorted array of integers `nums`, return _the length of the longest consecutive elements sequence._

You must write an algorithm that runs in `O(n)` time.

**Example 1:**

**Input:** nums = [100,4,200,1,3,2]

**Output:** 4

**Explanation:** The longest consecutive elements sequence is `[1, 2, 3, 4]`. Therefore its length is 4. 

**Example 2:**

**Input:** nums = [0,3,7,2,5,8,4,6,0,1]

**Output:** 9 

**Constraints:**

*   0 <= nums.length <= 10⁵
*   -10⁹ <= nums[i] <= 10⁹

To solve the "Longest Consecutive Sequence" problem in Java with a `Solution` class, we'll use a HashSet and a greedy approach. Below are the steps:

1. **Create a `Solution` class**: Define a class named `Solution` to encapsulate our solution methods.

2. **Create a `longestConsecutive` method**: This method takes an array `nums` as input and returns the length of the longest consecutive elements sequence.

3. **Initialize a HashSet**: Create a HashSet named `numSet` to store all the numbers in the array `nums`.

4. **Iterate through the array**: Add all the numbers from the array `nums` to the `numSet`.

5. **Find the longest sequence**: Iterate through the array `nums` again. For each number `num` in the array:
   - Check if `num - 1` exists in the `numSet`. If it does not, `num` could be the start of a new sequence.
   - If `num - 1` does not exist, start a new sequence from `num`. Increment `currentNum` by 1 and check if `currentNum` exists in the `numSet`. Keep incrementing `currentNum` until it does not exist in the `numSet`. Update the maximum length of the sequence accordingly.

6. **Return the maximum length**: After iterating through the entire array, return the maximum length of the consecutive sequence.

Here's the Java implementation:

```java
import java.util.HashSet;

class Solution {
    public int longestConsecutive(int[] nums) {
        HashSet numSet = new HashSet<>();
        for (int num : nums) {
            numSet.add(num); // Add all numbers to HashSet
        }
        
        int maxLength = 0;
        for (int num : nums) {
            if (!numSet.contains(num - 1)) { // Check if num - 1 exists in numSet
                int currentNum = num;
                int currentLength = 1;
                
                while (numSet.contains(currentNum + 1)) { // Increment currentNum until it does not exist in numSet
                    currentNum++;
                    currentLength++;
                }
                
                maxLength = Math.max(maxLength, currentLength); // Update maximum length
            }
        }
        
        return maxLength; // Return the maximum length of the consecutive sequence
    }
}
```

This implementation follows the steps outlined above and efficiently calculates the length of the longest consecutive elements sequence in Java.