algo-sensei

# Algo Sensei's Solution Guide

## Problem: Two Sum

### Understanding the Problem

The problem requires us to find two numbers in an array that add up to a specific target. The solution must return the indices of these two numbers.

### Initial Thoughts

A brute-force approach would involve checking every possible pair of numbers in the array, which would have a time complexity of O(n²). However, we can optimize this using a hash map to reduce the time complexity to O(n).

### Optimized Solution

```python
def two_sum(nums, target):
    num_map = {}
    for i, num in enumerate(nums):
        complement = target - num
        if complement in num_map:
            return [num_map[complement], i]
        num_map[num] = i
    return []
```

### Explanation

1. **Initialization**: We start by creating an empty dictionary `num_map` to store the numbers and their indices.
2. **Iteration**: We iterate through the array using `enumerate` to get both the index and the value of each number.
3. **Complement Calculation**: For each number, we calculate its complement (i.e., the value needed to reach the target sum).
4. **Check for Complement**: If the complement exists in `num_map`, we return the indices of the complement and the current number.
5. **Update Map**: If the complement is not found, we add the current number and its index to `num_map`.

### Edge Cases

- **No Solution**: If no two numbers add up to the target, the function returns an empty list.
- **Duplicate Numbers**: The solution handles duplicate numbers correctly by returning the first occurrence of the complement.

### Time and Space Complexity

- **Time Complexity**: O(n), where n is the number of elements in the array. This is because we traverse the list containing n elements only once. All dictionary operations are O(1) on average.
- **Space Complexity**: O(n), where n is the number of elements in the array. This is due to the extra space required for the dictionary.

### Mock Interview Practice

To further solidify your understanding, try solving similar problems like '3Sum' and '4Sum'. These problems build on the same principles but add additional layers of complexity.

### Next Steps

1. **Practice**: Solve similar problems on LeetCode to reinforce your understanding.
2. **Review**: Go through the solution again and try to explain it to someone else.
3. **Optimize**: Think about how you can further optimize the solution or handle edge cases more efficiently.

Good luck with your preparation for [COMPANY] interviews in [INDUSTRY]!