🚀 Day 43 System Design & DSA Journey Update 🌐💻
Today's exploration delved deep into problems based on binary search. Here's a recap of the problems I've tackled and the approaches I've explored:
1️⃣ Find Peak Element:
- Brute Force Approach: Utilizing linear search to find the peak element.
- Time Complexity: O(n)
- Space Complexity: O(1)
- Optimal Approach: Leveraging binary search to efficiently locate the peak element.
- Time Complexity: O(log n)
- Space Complexity: O(1)
- Intuition: The optimal approach leverages the property that a peak element, in a given array, will always be located where the ascending sequence turns into a descending one. By iteratively narrowing down the search space through binary search, we efficiently locate the peak element.
2️⃣ Find Nth Root Of M:
- Brute Force Approach: Employing linear search to find the nth root of m.
- Time Complexity: O(m)
- Space Complexity: O(1)
- Optimal Approach: Utilizing binary search for an efficient search for the nth root of m.
- Time Complexity: O(log m)
- Space Complexity: O(1)
- Intuition: In the optimal approach, we exploit the monotonic nature of the root function. By iteratively narrowing down the search space using binary search, we efficiently converge to the desired nth root of m.
3️⃣ Koko Eating Bananas:
- Brute Force Approach: Using linear search to determine the minimum rate to eat bananas.
- Time Complexity: O(*max(arr) * n)
- Space Complexity: O(1)
- Optimal Approach: Employing binary search to efficiently find the minimum rate to eat bananas.
- Time Complexity: O(*max(arr) * n)
- Space Complexity: O(1)
- Intuition: By realizing the monotonic nature of the eating rate function and the problem's objective, we apply binary search to efficiently converge to the minimum rate at which Koko can eat bananas within the given time constraints.
4️⃣ Rose Garden:
- Brute Force Approach: Utilizing linear search to find the minimum number of days required to make bouquets.
- Time Complexity: O(*max(arr) * n)
- Space Complexity: O(1)
- Optimal Approach: Leveraging binary search to efficiently find the minimum number of days required to make bouquets.
- Time Complexity: O(*max(arr) * n)
- Space Complexity: O(1)
- Intuition: Recognizing the monotonic relationship between the number of days and the feasibility of making bouquets, binary search efficiently converges to the minimum number of days required, ensuring the optimal solution.
Solutions: https://lnkd.in/g9KGrPK7
Each problem was approached with both brute force and optimal strategies, highlighting the efficiency gains achieved through binary search algorithms. By honing these problem-solving skills, I'm enhancing my ability to tackle diverse challenges in algorithmic programming.
#DSA #BinarySearch #ProblemSolving #Optimization #Algorithms
Co-founder & CEO @ Objective, Inc | PhD, Artificial Intelligence
1moIt's been such a pleasure and an honor to partner up with Nadine ElAshkar, Javier Araya Kopaitic and team! 🚀 Congrats on all the progress so far and thanks for making us a little part of that success story!