Problem Description
The company is trying to develop a new Blu-ray disc production system. Each Blu-ray disc has a specific size, and it must be optimized to store the maximum amount of data. Based on the given capacity of the Blu-ray and the sizes of each file, write a program that can fit as many files as possible onto the Blu-ray.
Problem Definition: Given N files, each with a positive integer size, and a given capacity C of the Blu-ray, write a program to calculate the maximum number of files that can fit without exceeding the Blu-ray’s capacity.
Input Format:
The first line contains the capacity C of the Blu-ray (1 ≤ C ≤ 10000) and the number of files N (1 ≤ N ≤ 100).
The second line contains the sizes of N files (1 ≤ file size ≤ 1000).
Output Format:
Print the maximum number of files that can fit on the Blu-ray.
Problem Analysis
This problem involves finding the maximum number of files that can be combined without exceeding the capacity C of the Blu-ray. To maximize the number of files that can fit on the Blu-ray, the files must be sorted appropriately in advance, and a suitable search method must be used to solve the problem.
The basic strategy to solve the problem is as follows:
- Sort the file sizes in ascending order.
- Sequentially add the sorted files until the total size exceeds the capacity C of the Blu-ray.
- If it exceeds the capacity, stop adding files and return the count of files added so far.
Problem Solving Process
Let’s look at the process of solving the problem step by step.
Step 1: Input
First, we get the capacity of the Blu-ray, the number of files, and the sizes of the files. Input takes place via standard input. We can use Python’s input() function to receive the data.
Step 2: Data Sorting
Sort the input file sizes in ascending order. This is necessary to ensure we add the smallest files first. Python’s sorted() function can easily sort the data.
Step 3: Add Files and Sum Sizes
While iterating through the sorted file list, check if adding the current file would exceed the total capacity C of the Blu-ray. If it does not exceed, add the current file to the Blu-ray and count the number of files.
Step 4: Output Result
After iterating through all the files, output the final count of files that can fit on the Blu-ray.
Step 5: Complete Code
def maximum_files_in_blu_ray(capacity, files):
# Sort file sizes
files.sort()
count = 0
total_size = 0
for file in files:
if total_size + file <= capacity:
total_size += file
count += 1
else:
break
return count
# Get input
capacity, n = map(int, input().split())
files = list(map(int, input().split()))
# Call function and output result
result = maximum_files_in_blu_ray(capacity, files)
print(result)
Example Input and Output
Example 1
Input:
10 5
1 2 3 4 5
Output:
4
Example 2
Input:
7 4
1 2 3 4
Output:
3
Result Analysis
By using the above code, we can fit the optimal number of files according to the size of the given Blu-ray. This problem serves as a fundamental example of a greedy algorithm, presenting one method that satisfies the problem's conditions.
Conclusion
In this lecture, we have learned about basic list manipulation, sorting, and searching in Python through the Blu-ray making problem. These fundamental problem-solving techniques can be very useful in actual coding tests or algorithm problems. Keep improving your skills through a variety of challenges.