Understanding the Problem
The Two Sum problem asks us to find two numbers in a given array that add up to a specific target value. Our goal is to return the indices of these two numbers.
For example, if the array is [2, 7, 11, 15]
and the target is 9
, then 2 + 7 = 9
, so we return the indices [0, 1]
.
Step-by-Step Solution for Beginners
Step 1: Loop through each element
We’ll use a loop to go through each element in the array one by one.
Step 2: For each element, check all elements after it
This helps us avoid repeating the same pairs and ensures we check each possible combination of two numbers.
Step 3: Add the two numbers and check if they equal the target
If they do, we immediately return their indices.
Step 4: Stop once a valid pair is found
The problem guarantees that only one solution exists, so we can stop as soon as we find it.
Let’s Walk Through an Example
Input:
nums = [2, 7, 11, 15], target = 9
Steps:
- Start with index 0: value is 2
- Check with index 1: 2 + 7 = 9 ✅ → Match found
- Return [0, 1]
Handling Edge Cases
Case 1: Duplicate Numbers
If array is [3, 3]
and target is 6
, the same number can be used as long as the indices are different. Return [0, 1]
.
Case 2: No Valid Pair
If no combination adds up to the target, like [1, 2, 3]
with target 10
, return []
.
Case 3: Empty Array
With input []
, there are no elements to form a pair. Return []
.
Case 4: Single Element
With input [5]
, one element cannot form a pair. Return []
.
Finally
This brute force method is simple and ideal for learning. It helps build an intuitive understanding of how nested loops can be used to compare all pairs.
However, it is not efficient for large arrays since its time complexity is O(n²).
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