Dynamic Programming Questions Medium
Dynamic Programming can be used to solve the Decode Ways problem by breaking it down into smaller subproblems and using the results of these subproblems to build up the solution to the original problem.
To solve the Decode Ways problem, we can define a dynamic programming array dp, where dp[i] represents the number of ways to decode the substring from index 0 to i.
We can start by initializing dp[0] and dp[1] to 1, as there is only one way to decode a single-digit number or a two-digit number if it is valid.
Then, we iterate through the string from index 2 to n, where n is the length of the input string. At each index i, we check if the current digit and the previous digit form a valid two-digit number. If they do, we can add the number of ways to decode the substring from index 0 to i-2 to dp[i]. This is because we can either decode the current two-digit number as a single character or as two separate characters.
Additionally, if the current digit is not zero, we can add the number of ways to decode the substring from index 0 to i-1 to dp[i]. This is because we can decode the current digit as a single character.
Finally, the answer to the problem will be stored in dp[n], which represents the number of ways to decode the entire string.
The time complexity of this dynamic programming solution is O(n), where n is the length of the input string, as we iterate through the string once. The space complexity is also O(n) as we use an array of size n to store the intermediate results.