Hello! Today, we will conduct a lecture to prepare for coding tests using Kotlin. The main topic of this lecture is ‘Time Complexity’. We will learn how to analyze and optimize time complexity when solving coding problems. Additionally, we will solve a real problem and calculate its time complexity.
Problem Description
We will address the problem of finding two numbers in a given integer array nums whose sum equals a specific value target and returning the indices of those numbers.
Problem: Given an integer array nums and an integer target, return the indices i and j such that nums[i] + nums[j] = target. Each input should have only one output, and the same element cannot be used twice.
Input Example
nums = [2, 7, 11, 15], target = 9
Output Example
[0, 1]
Problem Solving Process
To solve this problem, we will first design an algorithm. Common methods include brute-force and using a hashmap.
1. Brute-force Method
The simplest way is to use two nested loops to check all possible combinations. In this case, the time complexity is O(n^2).
fun twoSum(nums: IntArray, target: Int): IntArray {
for (i in nums.indices) {
for (j in i + 1 until nums.size) {
if (nums[i] + nums[j] == target) {
return intArrayOf(i, j)
}
}
}
throw IllegalArgumentException("No two sum solution")
}
2. Optimization using Hashmap
Using a hashmap allows us to solve it with just one iteration. The basic idea of this method is to check if the required value (target – current value) already exists in the hashmap while iterating through each element. In this case, the time complexity is reduced to O(n).
fun twoSum(nums: IntArray, target: Int): IntArray {
val map = mutableMapOf()
for (i in nums.indices) {
val complement = target - nums[i]
if (map.containsKey(complement)) {
return intArrayOf(map[complement]!!, i)
}
map[nums[i]] = i
}
throw IllegalArgumentException("No two sum solution")
}
Time Complexity Analysis
The time complexity of the brute-force method is O(n^2) due to the nested loops, while the hashmap method has a time complexity of O(n) since it only uses one loop. Therefore, although using a hashmap may require more memory, it is much more advantageous in terms of execution speed.
Conclusion
In this lecture, we explored the process of solving the two-sum problem using Kotlin and learned how to analyze and optimize the time complexity of each approach. Please remember that time complexity analysis is a very important factor in efficient algorithm design. As you prepare for coding tests, it is essential to practice solving various problems and develop your time complexity skills.
Reference Material
- Kotlin Official Documentation
- Try solving various problems on LeetCode
- Study algorithm materials on GeeksforGeeks
This concludes our lecture. We will return with more interesting and beneficial topics next time. Thank you!