Count possible decoding of a given digit sequence
Detailed guide and Python implementation for the 'Count possible decoding of a given digit sequence' problem.
1. Concept Overview
The 'Count possible decoding of a given digit sequence' 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 Count possible decoding of a given digit sequence.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Count possible decoding of a given digit sequence 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 count_decodings(digits) that takes a string of digits and returns the number of possible ways to decode it, where 'A' = 1, 'B' = 2, ..., 'Z' = 26.
For example, '12' can be decoded as 'AB' (1, 2) or 'L' (12), giving 2 ways.
If the string contains '0' in an invalid position (e.g., leading '0' or '30'), those paths are invalid and should not be counted.
- •1 <= len(digits) <= 20
- •digits contains only characters '0' through '9'
Examples
count_decodings('12')2
'12' can be decoded as 'AB' (1,2) or 'L' (12). So 2 ways.
count_decodings('226')3
'226' can be decoded as 'BBF' (2,2,6), 'BZ' (2,26), or 'VF' (22,6). So 3 ways.
count_decodings('06')0
'06' cannot be decoded because '0' has no letter mapping and '06' is not a valid code.
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 count_decodings_opt(s):
if not s or s[0] == '0': return 0
n = len(s)
dp = [0] * (n + 1)
dp[0], dp[1] = 1, 1
for i in range(2, n + 1):
if s[i-1] != '0':
dp[i] += dp[i-1]
if s[i-2] == '1' or (s[i-2] == '2' and s[i-1] < '7'):
dp[i] += dp[i-2]
return dp[n]Brute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def count_decodings_brute(s):
def solve(idx):
if idx == len(s): return 1
if s[idx] == '0': return 0
res = solve(idx + 1)
if idx + 1 < len(s) and (s[idx] == '1' or (s[idx] == '2' and s[idx+1] < '7')):
res += solve(idx + 2)
return res
return solve(0)Algorithm Pattern Checklist
When dealing with Numbers data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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