Decode Ways 🎯

Welcome to our comprehensive guide on Decode Ways! This lesson is designed to help you understand the fascinating world of Dynamic Programming through a practical example.

Introduction 📝

In this lesson, we will solve a problem called Decode Ways, which is a classic example of Dynamic Programming. Dynamic Programming is a powerful algorithmic technique used to solve complex problems by breaking them down into simpler, overlapping sub-problems.

What is Decode Ways? 💡

Given a non-negative integer n represented as a string, write a function to check whether it represents a valid number that can be formed by an arbitrary number of digits (which means that leading zeros are allowed) using the digits from 0-9. The function should return the count of valid ways to represent n.

For example, given the number 111, there are 3 ways to represent it: 111, 10 - 11, and 1 - 10 - 1.

Breaking Down the Problem 📝

Let's break down the problem into smaller steps:

If n is 0, there is only 1 way to represent it (just 0).
For numbers greater than 0, we can consider two cases:
- The number does not start with 0 (i.e., it starts with a digit other than 0). In this case, the first digit cannot be 0.
- The number starts with 0, but it is not the first digit (i.e., it has at least one digit before 0). In this case, the number before 0 must represent a valid number, and the number after 0 can be any valid number.

Implementing the Solution ✅

Now, let's implement the solution in Python.

python

def numDecodings(self, s: str) -> int:
    # Initialize the base case
    dp = [1] * len(s)
    dp[0] = 1 if s[0] != '0' else 0

    for i in range(1, len(s)):
        if s[i] != '0':
            dp[i] += dp[i - 1]

        tens = int(s[i - 1: i + 1])
        if 10 <= tens <= 26 and dp[i - 1] > 0:
            dp[i] += dp[i - 2]

    return dp[-1]

In the above code, we are using dynamic programming to calculate the number of ways to represent the given number. We create a dp array to store the number of ways to represent each substring of the input string. We start from the base case and calculate the ways for each subsequent substring based on the previous ones.

Quiz Time 🎯

That's it for today! By understanding the Decode Ways problem, you've taken a significant step towards mastering Dynamic Programming. In our next lesson, we'll dive deeper into Dynamic Programming and explore more problems and solutions.

Stay tuned and keep coding! 🚀