Extra Characters in a String - Solution & Explanation

In this approach, we use dynamic programming to solve the problem. We define a DP array where dp[i] represents the minimum number of extra characters from index 0 to i of the string s. Initially, we set dp[0] to 0 because there are no extra characters in an empty prefix. For each index i while iterating through the string s, we check every j from 0 to i-1 and see if substring s[j:i] exists in the dictionary. If yes, we update dp[i] to min(dp[i], dp[j]), otherwise, we set dp[i] to dp[i-1] + 1.

This C solution uses a dynamic array to store the minimum number of extra characters needed for each prefix of the string. For each end index i, we check all starting indices to see if a substring is in the dictionary and update the DP accordingly, minimizing extra characters added.

To solve the problem using a Trie and memoization, we first build a Trie from the dictionary. We then use a recursive function with memoization to attempt to decompose the string s into valid segments. For each position in the string, we check possible substrings against the Trie, saving calculated results to avoid redundant computations.

This C solution utilizes a Trie to store dictionary words for fast matching. It also uses memoization to recursively find the minimum extra characters. Each call attempts to split the string from the current index, using the Trie to validate substrings.