Last non-zero digit in factorial
Detailed guide and Python implementation for the 'Last non-zero digit in factorial' problem.
1. Concept Overview
The 'Last non-zero digit in factorial' problem is a key challenge in the Recursion 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 Last non-zero digit in factorial.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Last non-zero digit in factorial 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 last_non_zero_digit(n) that returns the last non-zero digit of n! (n factorial). For example, 5! = 120, and the last non-zero digit is 2. The function takes a non-negative integer n and returns a single digit (1-9).
- •0 <= n <= 1000
Examples
n = 5
2
5! = 120. Ignoring trailing zeros, the last non-zero digit is 2.
n = 10
8
10! = 3628800. The last non-zero digit is 8.
n = 1
1
1! = 1. The last non-zero digit is 1.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
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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 last_non_zero_digit(n):
dig = [1, 1, 2, 6, 4, 2, 2, 4, 2, 8]
if n < 10: return dig[n]
if (n // 10) % 2 == 0:
return (6 * last_non_zero_digit(n // 5) * dig[n % 10]) % 10
return (4 * last_non_zero_digit(n // 5) * dig[n % 10]) % 10Brute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def last_non_zero(n):
f = 1
for i in range(1, n + 1): f *= i
return int(str(f).rstrip('0')[-1])Algorithm Pattern Checklist
When dealing with Recursion data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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