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Asked: 2024-09-24T07:49:42+05:30 In:

You are given a string of digits that represent an encoded message. Each digit can correspond to letters (1 for A, 2 for B, …, 26 for Z). Your task is to determine the total number of different ways to decode this string into letters. For example, the string “12” can be decoded as “AB” (1, 2) or “L” (12), resulting in 2 possible decodings. The input consists of a string of digits, and you need to return the count of unique decodings that can be made from this string. Consider edge cases such as strings that begin with ‘0’ or contain invalid two-digit numbers. What is the method for calculating the number of distinct ways to decode a given numeric string?

I have a fun coding puzzle for you! Imagine you come across a string of digits, and each digit represents a letter according to a simple mapping: 1 for A, 2 for B, all the way up to 26 for Z. Your challenge is to figure out how many ways we can decode this string into letters.

For instance, if you have the string “12,” it can be decoded in two ways: as “AB” (where 1 = A and 2 = B) or as “L” (where 12 = L). So that’s 2 possible decodings, pretty straightforward, right?

But things can get tricky! What if the string starts with a ‘0’ or has some two-digit numbers that are not valid? For example, “230” can be decoded as “BC” (2, 3) or “W” (23). However, “00” is a no-go because there’s no mapping for that.

So, my question for you is: how do we calculate the total number of unique decodings for a given numeric string? What considerations do we need to take into account, particularly in terms of edge cases like leading zeros or invalid two-digit combinations?

To tackle this problem, you could think about using a dynamic programming approach. You can create an array where each index represents the number of ways to decode the string up to that point.

Imagine starting with the first letter and deciding how to build up. As you go through the digits, you can work out how many ways exist at each stage by checking if the previous digit or the last two digits can form valid letters.

But what if the string length is large or filled with tricky combinations? How do you ensure that you cover every potential decoding without getting lost in the number crunching?

Give it a shot! Lay out your thoughts, maybe even sketch out a small example to visualize how you’d break it down. I’m interested to see how you approach this decoding challenge!

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    2 Answers


    1. Decoding a String of Digits

      Okay, so I’ve got this string of digits, and I’m supposed to figure out how many ways I can decode it into letters, right? Like, 1 for A, 2 for B, all the way up to 26 for Z. Sounds fun!

      Let’s take an example: if I have the string “12,” I can think of it as:

      • 1 = A, 2 = B -> “AB”
      • 12 = L -> “L”

      So there are 2 ways to decode “12”. Neat!

      But, oh boy, what about cases like “230”? I can see:

      • 2 = B, 3 = C -> “BC”
      • 23 = W -> “W”

      That gives me 2 ways again! But wait – if the string starts with ‘0’ or has ’00’, then it’s a no-go because there’s no mapping for that. Like, I can’t translate “00” into anything.

      How to Calculate Unique Decodings?

      So here’s how I think I can approach this. I might use something called dynamic programming. I could create an array where each index is the number of ways to decode up to that point. Sounds a bit complex, but let’s see!

      1. Start with something like an array `dp` where `dp[i]` is the number of ways to decode the substring up to index `i`.

      2. Initialize `dp[0]` to 1 because there’s one way to decode an empty string.

      3. For each digit in the string, I’ll check:

      • If the current digit is not ‘0’, it can be decoded by itself. So, I add `dp[i – 1]` to `dp[i]`.
      • If the last two digits form a valid number (10 to 26), I add `dp[i – 2]` to `dp[i]`.

      Edge Cases!

      Definitely need to think about edge cases:

      • Strings starting with ‘0’ should instantly return 0.
      • Two-digit numbers like ’30’ or ’00’ are invalid, so I’d avoid counting those.

      Hmm, and if the string gets long or has tricky combos, I guess I just keep building up my `dp` array. As long as I keep the rules in mind, I should be able to cover every possibility, right?

      Alright, time to give it a whirl with some code if I can figure it out! This decoding challenge seems like it could get pretty fun! 🤔



    2. To solve the decoding challenge, we can utilize a dynamic programming approach. First, we need to establish a valid mapping for the digits from ‘1’ to ’26’ corresponding to letters ‘A’ through ‘Z’. We will maintain an array, say dp, where dp[i] will represent the number of ways to decode the substring of length i. The length of this array will be n + 1, where n is the length of the input string. We’ll initialize dp[0] = 1 because an empty string has one way to decode — by not decoding at all. For the first character, if it’s between ‘1’ and ‘9’, we’ll set dp[1] to 1; if it’s ‘0’, decoding is impossible, and we leave it as 0.

      Next, we iterate through the string starting from the second character. For each digit, we check if it’s a valid single-digit number (from ‘1’ to ‘9’). If valid, we add the count from the previous character (i.e., dp[i] += dp[i-1]). We also check the two-digit combination with the previous character (i.e., from s[i-2]s[i-1]). If this combination forms a number between ’10’ and ’26’, we add the count from dp[i-2]. Special cases such as leading zeros and invalid combinations need to be handled explicitly — for example, ’00’ should immediately return 0. Thus, by following this methodology, we can robustly compute the number of unique decodings, even for larger strings.


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