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Decode Ways

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 10

Write a JavaScript program to count the number of ways to decode a string of digits. A message containing letters from A-Z can be encoded into numbers using the mapping A=1, B=2, ..., Z=26. Given a string containing only digits, determine the total number of ways to decode it back to letters.

Example 1
    
      
  • Input: s = "12"
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  • Output: 2
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  • Explanation: 
    • The string "12" can be decoded in multiple ways. 
    • First way: "12" can be decoded as "1" + "2" which gives "AB". 
    • Second way: "12" can be decoded as "12" which gives "L". 
    • Both decodings are valid since 1→A, 2→B, and 12→L are all valid mappings. 
    • Therefore, there are 2 total ways to decode the string.
    •
Example 2
    
      
  • Input: s = "226"
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  • Output: 3
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  • Explanation: 
    • The string "226" has multiple valid decoding combinations. 
    • First way: "2" + "2" + "6" which decodes to "BBF". 
    • Second way: "22" + "6" which decodes to "VF" (since 22→V). 
    • Third way: "2" + "26" which decodes to "BZ" (since 26→Z). 
    • All three combinations use valid letter mappings, so the answer is 3.
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Constraints
    
      
  • 1 <= s.length <= 100
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  • s contains only digits
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  • s may contain leading zeros
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  • Valid encodings are from "1" to "26" (A to Z)
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  • Return 0 if the string cannot be decoded
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  • Time Complexity: O(n)
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  • Space Complexity: O(n) for DP array, O(1) for optimized version
    •
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Hint
Solution

Solution Hints

    
      
  • Use dynamic programming where dp[i] represents the number of ways to decode the first i characters
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  • For each position, check if single digit (1-9) and two digits (10-26) form valid decodings
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  • If current digit is valid (1-9), add dp[i-1] to current ways
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  • If current two digits form valid number (10-26), add dp[i-2] to current ways
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  • Handle edge cases like leading zeros and invalid digit combinations
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Steps to solve by this approach:

 Step 1: Handle base cases - return 0 if string is empty or starts with '0' (invalid)

 Step 2: Create a DP array where dp[i] represents number of ways to decode first i characters

 Step 3: Initialize dp[0] = 1 (empty string) and dp[1] = 1 (first valid character)

 Step 4: For each position i from 2 to string length, check single digit decoding possibility

 Step 5: If current single digit (1-9) is valid, add dp[i-1] ways to dp[i]

 Step 6: Check two-digit combination from previous and current character (10-26)

 Step 7: If two digits form valid encoding (10-26), add dp[i-2] ways to dp[i]

 Step 8: Return dp[s.length] which contains total ways to decode the entire string

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