Problem Link :- leetcode-875
Problem statement
Koko loves to eat bananas. There are n piles of bananas, the ith pile has piles[i] bananas. The guards have gone and will come back in h hours.
Koko can decide her bananas-per-hour eating speed of k. Each hour, she chooses some pile of bananas and eats k bananas from that pile. If the pile has less than k bananas, she eats all of them instead and will not eat any more bananas during this hour.
Koko likes to eat slowly but still wants to finish eating all the bananas before the guards return.
Return the minimum integer k such that she can eat all the bananas within h hours.
Koko can decide her bananas-per-hour eating speed of k. Each hour, she chooses some pile of bananas and eats k bananas from that pile. If the pile has less than k bananas, she eats all of them instead and will not eat any more bananas during this hour.
Koko likes to eat slowly but still wants to finish eating all the bananas before the guards return.
Return the minimum integer k such that she can eat all the bananas within h hours.
Significance of problem
The significance of the problem statement, determining the minimum eating speed for Koko to finish consuming bananas within a specific time frame, extends beyond its apparent simplicity. At its core, this problem mirrors real-world scenarios where efficiency and optimization are paramount.
In everyday terms, think of Koko as a person with a limited amount of time (represented by hours) and a pile of bananas to eat. The problem captures the essence of time management and resource utilization—an essential skill in various aspects of life. The ability to find the minimum eating speed translates into a practical understanding of how to make the most effective use of available time.
The application of binary search in this context is particularly significant. Binary search, commonly used in computer science, is like a smart guessing game where you progressively narrow down possibilities. Here, it efficiently homes in on the optimal eating speed within a range, reflecting a practical use of a fundamental algorithmic concept.
Furthermore, the problem involves mathematical considerations, introducing the idea of precision in calculations. Koko needs to calculate how many bananas can be eaten at a given speed, and the use of functions like ceil ensures accurate calculations. This mathematical precision is akin to the precision required in everyday tasks involving measurements and quantities.
The iterative decision-making process embedded in the solution aligns with problem-solving approaches in various fields. It's akin to adjusting a strategy based on ongoing feedback. In this scenario, Koko iteratively checks if a specific eating speed is feasible, a skill analogous to adapting plans based on real-time circumstances.
In essence, the problem statement goes beyond bananas and eating speeds. It encapsulates fundamental principles applicable in time management, algorithmic efficiency, mathematical precision, and adaptive decision-making—skills with broad significance in both the digital realm of coding and the practical landscape of everyday challenges. Thus, mastering this seemingly simple problem provides a foundation for tackling more complex problems across diverse domains.
In everyday terms, think of Koko as a person with a limited amount of time (represented by hours) and a pile of bananas to eat. The problem captures the essence of time management and resource utilization—an essential skill in various aspects of life. The ability to find the minimum eating speed translates into a practical understanding of how to make the most effective use of available time.
The application of binary search in this context is particularly significant. Binary search, commonly used in computer science, is like a smart guessing game where you progressively narrow down possibilities. Here, it efficiently homes in on the optimal eating speed within a range, reflecting a practical use of a fundamental algorithmic concept.
Furthermore, the problem involves mathematical considerations, introducing the idea of precision in calculations. Koko needs to calculate how many bananas can be eaten at a given speed, and the use of functions like ceil ensures accurate calculations. This mathematical precision is akin to the precision required in everyday tasks involving measurements and quantities.
The iterative decision-making process embedded in the solution aligns with problem-solving approaches in various fields. It's akin to adjusting a strategy based on ongoing feedback. In this scenario, Koko iteratively checks if a specific eating speed is feasible, a skill analogous to adapting plans based on real-time circumstances.
In essence, the problem statement goes beyond bananas and eating speeds. It encapsulates fundamental principles applicable in time management, algorithmic efficiency, mathematical precision, and adaptive decision-making—skills with broad significance in both the digital realm of coding and the practical landscape of everyday challenges. Thus, mastering this seemingly simple problem provides a foundation for tackling more complex problems across diverse domains.
Easiest Explanation
Imagine Koko is a very hungry monkey who loves to eat bananas. She has a bunch of banana piles, and she wants to eat them all before the guards come back.
She can only eat a certain number of bananas per hour, and she wants to eat them slowly so she can enjoy them. We need to help Koko find the minimum number of bananas she needs to eat per hour so she can finish all the bananas before the guards come back.
We can use a special search called binary search to quickly find the answer.
It starts with an initial range of possible bananas per hour from 1 to the maximum number of bananas in any pile. Then it repeatedly divides the range in half until it finds the minimum number of bananas per hour that allows the person to eat all the bananas within h hours.
I hope that explanation helps! If you find any difficulty in solving, feel free to comment with your doubts.
She can only eat a certain number of bananas per hour, and she wants to eat them slowly so she can enjoy them. We need to help Koko find the minimum number of bananas she needs to eat per hour so she can finish all the bananas before the guards come back.
We can use a special search called binary search to quickly find the answer.
It starts with an initial range of possible bananas per hour from 1 to the maximum number of bananas in any pile. Then it repeatedly divides the range in half until it finds the minimum number of bananas per hour that allows the person to eat all the bananas within h hours.
I hope that explanation helps! If you find any difficulty in solving, feel free to comment with your doubts.
class Solution { public: int minEatingSpeed(vector<int>& piles, int h) { int l = 1; int r = piles[0]; for (int i = 0; i < piles.size(); i++) { r = max(r, piles[i]); } int ans = -1; while (l <= r) { int m = (l + r) / 2; if (check(piles, h, m)) { r = m - 1; ans = m; } else { l = m + 1; } } return ans; } bool check(vector<int>& piles, int h, int k) { if (k == 0) { return false; } int i = 0; while (h >= 0 && i < piles.size()) { h -= ceil((double)piles[i] / k); i++; } return h >= 0 && i == piles.size(); } };
Here's how the function works:
The code uses binary search to find the answer quickly.Here's what the code is doing:
The code has two main functions:
minEatingSpeed : It takes in the vector of piles of bananas and the maximum number of hours h the person has to finish eating all the bananas. It initializes the range of possible bananas per hour and then uses binary search to find the minimum number of bananas per hour. It returns the minimum number of bananas per hour.
check: It takes in the vector of piles of bananas, the maximum number of hours h the person has to finish eating all the bananas, and a guess for the minimum number of bananas the person can eat per hour. It uses a loop to simulate the person eating the bananas one by one, and it checks if he can finish eating all the bananas within h hours with the given guess for the minimum number of bananas per hour. It returns true if he can finish eating all the bananas within h hours with the given guess, and false otherwise.
The code has two main functions:
minEatingSpeed : It takes in the vector of piles of bananas and the maximum number of hours h the person has to finish eating all the bananas. It initializes the range of possible bananas per hour and then uses binary search to find the minimum number of bananas per hour. It returns the minimum number of bananas per hour.
check: It takes in the vector of piles of bananas, the maximum number of hours h the person has to finish eating all the bananas, and a guess for the minimum number of bananas the person can eat per hour. It uses a loop to simulate the person eating the bananas one by one, and it checks if he can finish eating all the bananas within h hours with the given guess for the minimum number of bananas per hour. It returns true if he can finish eating all the bananas within h hours with the given guess, and false otherwise.
Learning Outcomes
Solving the problem of determining the minimum eating speed for Koko to consume all the bananas within a given time frame provides valuable insights into algorithmic problem-solving, optimization, and binary search techniques. The approach taken in the provided code demonstrates a thoughtful strategy to efficiently search for the optimal eating speed, showcasing key learning outcomes.
Firstly, the problem necessitates a nuanced understanding of binary search. The code employs a binary search algorithm to find the minimum eating speed, recognizing that the eating speed is a discrete parameter and can be efficiently searched within a defined range. This application of binary search optimally narrows down the potential speeds, highlighting the significance of this algorithmic technique in solving problems with monotonic and sorted search spaces.
Moreover, the code emphasizes the importance of optimization in algorithm design. The binary search is intelligently implemented to efficiently explore the feasible range of eating speeds, reducing the time complexity of the solution. This efficiency is crucial when dealing with large datasets or time-sensitive applications, and the experience gained here contributes to the development of optimized coding practices.
Additionally, the problem fosters a deeper appreciation for mathematical considerations in algorithmic solutions. The utilization of the ceil function to ensure accurate calculations of the time required to consume bananas at a given speed demonstrates the coder's ability to handle real-world constraints and nuances. This mathematical precision is a valuable skill when dealing with computational challenges that involve intricate calculations or constraints.
Furthermore, the problem inherently involves iterative reasoning and condition checking. The check function, employed within the binary search, iteratively assesses whether the current eating speed satisfies the conditions for consuming all the bananas within the given time frame. This iterative decision-making process is fundamental to algorithmic thinking and problem-solving in various domains.
Firstly, the problem necessitates a nuanced understanding of binary search. The code employs a binary search algorithm to find the minimum eating speed, recognizing that the eating speed is a discrete parameter and can be efficiently searched within a defined range. This application of binary search optimally narrows down the potential speeds, highlighting the significance of this algorithmic technique in solving problems with monotonic and sorted search spaces.
Moreover, the code emphasizes the importance of optimization in algorithm design. The binary search is intelligently implemented to efficiently explore the feasible range of eating speeds, reducing the time complexity of the solution. This efficiency is crucial when dealing with large datasets or time-sensitive applications, and the experience gained here contributes to the development of optimized coding practices.
Additionally, the problem fosters a deeper appreciation for mathematical considerations in algorithmic solutions. The utilization of the ceil function to ensure accurate calculations of the time required to consume bananas at a given speed demonstrates the coder's ability to handle real-world constraints and nuances. This mathematical precision is a valuable skill when dealing with computational challenges that involve intricate calculations or constraints.
Furthermore, the problem inherently involves iterative reasoning and condition checking. The check function, employed within the binary search, iteratively assesses whether the current eating speed satisfies the conditions for consuming all the bananas within the given time frame. This iterative decision-making process is fundamental to algorithmic thinking and problem-solving in various domains.
Conclusion
In conclusion, the problem of finding Koko's minimum eating speed may revolve around bananas, but its significance extends to practical aspects of life. It teaches us the value of time management and resource optimization—essential skills in various situations. The use of binary search introduces a smart and efficient way to make decisions within a range, a concept applicable beyond the world of coding. Additionally, the need for mathematical precision reflects everyday scenarios where accurate calculations matter.
The iterative approach mirrors real-world adaptability, adjusting strategies based on ongoing feedback. Overall, while seemingly about bananas, this problem imparts valuable lessons applicable in navigating time constraints, optimizing resources, and making effective decisions in both coding challenges and real-life situations.
The iterative approach mirrors real-world adaptability, adjusting strategies based on ongoing feedback. Overall, while seemingly about bananas, this problem imparts valuable lessons applicable in navigating time constraints, optimizing resources, and making effective decisions in both coding challenges and real-life situations.
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