Two Sum
Given an array of integers and a target, return the indices of the two numbers that add up to the target.
Assume exactly one solution exists. Output two indices space-separated.
Example:
2,7,11,15 9
0 1
- The input array is [2,7,11,15] and the target sum is 9.
- We iterate through the array to find two numbers that add up to the target: 2+7=9$, which matches the target.
- The indices of these two numbers in the array are 0 and 1, since array indices start at 0.
- The final output is the space-separated indices: 01
Constraints:
- 2 <= len(nums) <= 10^4
- -10^9 <= nums[i] <= 10^9
- Exactly one valid answer exists
Background Knowledge
The "Two Sum" problem is a classic example of a problem that can be solved using hash maps. A hash map is a data structure that stores key-value pairs in a way that allows for efficient lookup, insertion, and deletion of elements. In the context of this problem, we can use a hash map to store the numbers in the array as keys and their indices as values. This allows us to quickly look up the index of a number in the array.
The problem also involves the concept of array indexing, where we need to return the indices of the two numbers that add up to the target. This requires us to keep track of the indices of the numbers as we iterate through the array. Additionally, the problem assumes that exactly one solution exists, which means that we can stop searching as soon as we find a pair of numbers that add up to the target.
The "Two Sum" problem is often used to introduce the concept of trade-offs in algorithm design. In this case, we can trade off time complexity for space complexity by using a hash map to store the numbers and their indices. This allows us to solve the problem in linear time, but it requires us to use extra space to store the hash map.
Algorithm/Approach
The general approach to solving this type of problem is to use a single pass through the array, where we iterate through the numbers and use a hash map to keep track of the numbers we have seen so far and their indices. We can use the hash map to look up the index of a number in constant time, which allows us to solve the problem in linear time.
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