The time complexity for searching a string in a Trie of N nodes is O(M), where M is the length of the searched string. Let's understand why this is the case:

Trie Data Structure:
A Trie is a tree-like data structure that is commonly used for efficient string searching operations. It is built using a set of nodes where each node represents a character. The nodes are connected with edges, and each edge represents a character from the alphabet.

Searching a String in a Trie:
When searching a string in a Trie, we start from the root node and follow the edges based on the characters of the string. If at any point, we reach a node that represents the last character of the string, it means that the string exists in the Trie. Otherwise, the string is not present.

Time Complexity Analysis:
To analyze the time complexity, let's consider the worst-case scenario:

- Best Case: The string we are searching for is not present in the Trie. In this case, the time complexity would be O(1) because we can quickly determine that the string is not present after traversing a single character.

- Worst Case: The string we are searching for is present in the Trie, and we need to traverse the entire path from the root to the last character of the string. This would require traversing M edges, where M is the length of the searched string.

Since the time complexity depends on the length of the string, the time complexity for searching a string in a Trie is O(M).

Explanation:
- The time complexity for searching a string in a Trie of N nodes is O(M), where M is the length of the searched string.
- The worst-case scenario is when we need to traverse the entire path from the root to the last character of the string.
- In this case, the time complexity is directly proportional to the length of the string.
- The time complexity for searching a string in a Trie is not constant (O(1)), logarithmic (O(log N)), or linear (O(N)). It is linear with respect to the length of the string (O(M)).
- This is because we need to check each character of the string and follow the corresponding edges in the Trie.