Maximum Number of Words Found in Sentences - Solution & Explanation

Problem Overview: You receive an array of sentences where each sentence contains words separated by single spaces. The task is simple: determine the maximum number of words that appear in any single sentence.

The key observation is that the number of words in a sentence equals the number of spaces plus one. Every space separates two words, so counting spaces becomes the fastest way to compute the word count. Since each sentence is processed independently, the goal is to scan each string and track the maximum word count seen so far.

Approach 1: Counting Spaces Method (Time: O(n), Space: O(1))

This approach relies on the observation that words are separated by exactly one space. Iterate through each sentence in the array and count how many spaces it contains using a simple loop or built‑in string operation. The number of words equals spaces + 1. Maintain a variable that stores the maximum word count encountered while iterating through the list of sentences.

The algorithm scans every character once across all sentences, so the total time complexity is O(n), where n is the total number of characters across the input array. Space complexity remains O(1) because only a few integer counters are used. This is the most direct solution and works well for problems involving simple string processing inside an array.

Approach 2: Iterative Character Count Method (Time: O(n), Space: O(1))

This method performs a full character scan for each sentence while explicitly counting words. Start with a word counter initialized to 1 for every non-empty sentence, then iterate through each character. Every time you encounter a space character (' '), increment the word counter. After processing the sentence, compare the result with the global maximum and update it if necessary.

The complexity remains O(n) because each character is visited exactly once. Space usage stays O(1). While this approach produces the same result as the previous one, it makes the counting logic explicit and is sometimes easier to adapt if the delimiter rules change (for example, handling multiple spaces or different separators).

Recommended for interviews: The Counting Spaces Method is the expected solution. Interviewers want to see that you recognize the relationship between spaces and word counts instead of splitting strings or allocating extra arrays. A brute approach using split() also works but increases memory usage to O(w) where w is the number of words. Demonstrating the space-count insight shows strong attention to problem constraints and efficient string traversal.