Find the prime numbers between 1 to 100
Detailed guide and Python implementation for the 'Find the prime numbers between 1 to 100' problem.
1. Concept Overview
The 'Find the prime numbers between 1 to 100' problem is a key challenge in the Numbers section.
This implementation focuses on easy-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Find the prime numbers between 1 to 100.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Find the prime numbers between 1 to 100 carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
Write a function primes_up_to_100() that takes no arguments and returns a list of all prime numbers between 1 and 100 (inclusive of 100 if it were prime).
A prime number is a number greater than 1 that has no divisors other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, ...
- •The range is fixed: 1 to 100
- •Return a list sorted in ascending order
Examples
primes_up_to_100()
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
There are 25 prime numbers between 1 and 100. Each number in the list is only divisible by 1 and itself.
len(primes_up_to_100())
25
The total count of primes between 1 and 100 is 25.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
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Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def primes_1_to_100_opt():
sieve = [True] * 101
for p in range(2, 11):
if sieve[p]:
for i in range(p * p, 101, p):
sieve[i] = False
return [p for p in range(2, 101) if sieve[p]]Brute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def primes_1_to_100_brute():
res = []
for num in range(2, 101):
is_prime = True
for i in range(2, num):
if num % i == 0:
is_prime = False
break
if is_prime:
res.append(num)
return resAlgorithm Pattern Checklist
When dealing with Numbers data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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