Hello! In this tutorial, we will solve the algorithm problem called ‘Finding a Desired Integer’. This problem involves finding a specific integer in a list of n integers. In this process, we will learn about basic algorithms and data structures. I will explain the problem setup and the solution step by step.
Problem Description
Given an integer list nums and an integer target, write a function that returns the index of target in the list nums. If target does not exist in the list, return -1.
Input Examples
nums = [2, 5, 1, 8, 3],target = 8=> Return value:3nums = [2, 5, 1, 8, 3],target = 4=> Return value:-1
Problem Approaches
To solve this problem, we can consider two approaches: linear search and binary search. Each method has its own advantages and disadvantages, and comparing their performance will be a good learning experience.
1. Linear Search
Linear search is a method that searches for target by sequentially checking each element of the list from start to finish. The time complexity is O(n).
Linear Search Implementation
def linear_search(nums, target):
for index in range(len(nums)):
if nums[index] == target:
return index
return -1In the code above, the for loop checks each element of the list one by one. If it finds an element equal to target, it returns that index; if it reaches the end of the list without finding it, it returns -1.
2. Binary Search
Binary search is an efficient search method that can be used on a sorted list. It reduces the search range by comparing the middle value. The time complexity is O(log n). Therefore, this method is useful when search efficiency is important.
Binary Search Implementation
def binary_search(nums, target):
left, right = 0, len(nums) - 1
while left <= right:
mid = (left + right) // 2
if nums[mid] == target:
return mid
elif nums[mid] < target:
left = mid + 1
else:
right = mid - 1
return -1In the binary search implementation above, we use left and right variables to adjust the search range of the list. In each iteration, we calculate the middle value and adjust the search range based on the comparison with target.
Problem Solving Process
Now we will implement both approaches to solve the given problem and compare their performance.
Performance Comparison
To compare the performance of linear search and binary search, we will perform each search algorithm on a list of a fixed size. Here is the test code for performance comparison.
import random
import time
# Data Generation
size = 1000000
nums = sorted(random.sample(range(1, 10000000), size))
target = random.choice(nums)
# Linear Search Performance Test
start_time = time.time()
print("Linear Search Result: ", linear_search(nums, target))
print("Linear Search Time: ", time.time() - start_time)
# Binary Search Performance Test
start_time = time.time()
print("Binary Search Result: ", binary_search(nums, target))
print("Binary Search Time: ", time.time() - start_time)When you run the above code, you can check the execution time and results of both search algorithms. Generally, binary search will show better performance.
Conclusion
In this tutorial, we solved the ‘Finding a Desired Integer’ problem using both linear search and binary search methods. We learned how each algorithm works and in which situations they should be used, which will be a great help in actual coding tests or algorithm problem-solving.
We hope you continue to enhance your coding skills through various algorithm problems. Thank you!