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Decode Ways

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

Write a C# program to determine 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. To decode an encoded message, all the digits must be grouped then mapped back into letters using the reverse mapping. For example, "11106" can be mapped to "AAJF" (1 1 10 6) or "KJF" (11 10 6). Return the number of ways to decode the given string.

Example 1
    
  
  • Input: s = "12"
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  • Output: 2
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  • Explanation: "12" could be decoded as "AB" (1 2) or "L" (12).
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Example 2
    
  
  • Input: s = "226"
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  • Output: 3
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  • Explanation: "226" could be decoded as "BZ" (2 26), "VF" (22 6), or "BBF" (2 2 6).
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Constraints
    
  
  • 1 ≤ s.length ≤ 100
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  • s contains only digits and may contain leading zero(s)
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  • Time Complexity: O(n)
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  • Space Complexity: O(n)
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StringsNumberGoogleGoldman Sachs
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Hint
Solution

Solution Hints

    
  
  • Use dynamic programming to solve this problem
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  • Create a dp array where dp[i] represents the number of ways to decode the substring s[0...i-1]
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  • For each position, check if the current digit is valid (not '0') and if the last two digits form a valid number (between 10 and 26)
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  • Handle the special case of '0' carefully, as it can't be decoded on its own
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  • The final answer is dp[n], where n is the length of the string
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Steps to solve by this approach:

 Step 1: Handle edge cases - empty string or string starting with '0'.
 Step 2: Create a dp array of size n+1 to store the number of ways to decode each prefix of the string.
 Step 3: Initialize dp[0] = 1 (base case - one way to decode empty string) and dp[1] = 1 if s[0] is not '0'.
 Step 4: For each position i from 2 to n:
 Step 5: If the current digit s[i-1] is not '0', add dp[i-1] to dp[i] (can be decoded independently).
 Step 6: Check if the last two digits form a valid number between 10 and 26. If yes, add dp[i-2] to dp[i].
 Step 7: Return dp[n] which represents the total number of ways to decode the entire string.

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