LeetCode 418: Sentence Screen Fitting

Problem Restatement

We are given:

Value	Meaning
sentence	A list of words
rows	Number of screen rows
cols	Number of columns per row

We want to place the sentence repeatedly on the screen.

Rules:

1. Words must appear in the original order.
2. A word cannot be split across lines.
3. Consecutive words are separated by one space.
4. The sentence repeats cyclically.

Return how many complete times the sentence fits on the screen.

The source examples include:

sentence = ["hello", "world"]
rows = 2
cols = 8

whose answer is 1.

The constraints include:

1 <= sentence.length <= 100
1 <= rows, cols <= 20000
1 <= word.length <= 10

Input and Output

Item	Meaning
Input	sentence, rows, cols
Output	Number of complete sentence repetitions
Word rule	Words cannot split across rows
Space rule	One space between adjacent words
Order rule	Sentence order must remain unchanged

Example function shape:

def wordsTyping(sentence: list[str], rows: int, cols: int) -> int:
    ...

Examples

Example 1:

sentence = ["hello", "world"]
rows = 2
cols = 8

The answer is:

1

Screen layout:

hello---
world---

The sentence fits exactly once.

Example 2:

sentence = ["a", "bcd", "e"]
rows = 3
cols = 6

The answer is:

2

One valid layout:

a-bcd-
e-a---
bcd-e-

The sentence repeats twice completely.

Example 3:

sentence = ["i", "had", "apple", "pie"]
rows = 4
cols = 5

The answer is:

1

First Thought: Simulate Word by Word

A direct approach is:

1. Track the current word index.
2. Fill each row greedily.
3. Count how many times we return to word 0.

This works, but repeatedly checking words and spaces row by row can become verbose.

We can simplify the process using a cyclic sentence string.

Key Insight

Join the sentence into one cyclic string:

s = "hello world "

Notice the trailing space.

Now the sentence behaves like an infinite repeating string:

hello world hello world hello world ...

For each row:

1. Pretend we advance exactly cols characters.
2. If we land on a space, we can start the next row immediately after that space.
3. Otherwise, we landed in the middle of a word, so move backward until we reach a space.

This simulates maximal fitting per row.

At the end, the total number of complete sentence repetitions is:

position // len(s)

because every full cycle through s represents one complete sentence.

Algorithm

1. Join the sentence into:

s = " ".join(sentence) + " "

2. Let:

position = 0

3. For each row:
   • Add cols to position.
   • If s[position % len(s)] is a space:
     • Move forward one more character.
   • Otherwise:
     • Move backward until the previous character is a space.
4. Return:

position // len(s)

Correctness

The string:

s = " ".join(sentence) + " "

contains exactly one complete sentence followed by a trailing separator space.

The variable position tracks how many characters of the infinite repeated sentence stream have been consumed by the screen.

For each row, adding cols greedily attempts to place as many characters as possible.

If the landing position is a space, then the row ended exactly at a word boundary, so the next row can start immediately after that space.

If the landing position is inside a word, words are not allowed to split across rows. The algorithm moves backward until it reaches the nearest valid word boundary.

Thus each row contains the maximum valid prefix that fits within cols characters.

After all rows are processed, every complete traversal of s corresponds to one complete sentence placement.

Therefore:

position // len(s)

is exactly the number of complete sentence repetitions that fit on the screen.

Complexity

Metric	Value	Why
Time	O(rows + total_backtracking)	Each row advances once
Space	O(L)	We store the joined sentence string

Here:

Symbol	Meaning
L	Length of the joined sentence string

In practice, the backward adjustment is amortized efficient because the pointer never repeatedly scans long distances overall.

Implementation

from typing import List

class Solution:
    def wordsTyping(self, sentence: List[str], rows: int, cols: int) -> int:
        s = " ".join(sentence) + " "
        n = len(s)

        position = 0

        for _ in range(rows):
            position += cols

            if s[position % n] == " ":
                position += 1
            else:
                while position > 0 and s[(position - 1) % n] != " ":
                    position -= 1

        return position // n

Code Explanation

We first build one cyclic sentence string:

s = " ".join(sentence) + " "

For:

["hello", "world"]

this becomes:

"hello world "

The trailing space is important because it cleanly separates sentence repetitions.

We store the length:

n = len(s)

The variable:

position

tracks how many characters have been consumed from the infinite repeated sentence.

For each row:

position += cols

greedily fills the row.

If we land exactly on a space:

if s[position % n] == " ":

then the next row can begin immediately after that space:

position += 1

Otherwise, we landed in the middle of a word.

Since words cannot split across rows, we move backward:

while position > 0 and s[(position - 1) % n] != " ":
    position -= 1

until we reach the previous space.

Finally:

return position // n

counts how many complete sentence cycles were consumed.

Alternative DP Optimization

When rows is very large, we can precompute row transitions.

For each possible starting word index:

Value	Meaning
Next starting word index after one row
Number of completed sentence cycles in that row

Then each row becomes an O(1) lookup.

This optimization reduces repeated scanning when many rows begin with the same word.

Testing

def test_words_typing():
    s = Solution()

    assert s.wordsTyping(["hello", "world"], 2, 8) == 1

    assert s.wordsTyping(["a", "bcd", "e"], 3, 6) == 2

    assert s.wordsTyping(["i", "had", "apple", "pie"], 4, 5) == 1

    assert s.wordsTyping(["a"], 3, 1) == 3

    assert s.wordsTyping(["abc"], 2, 2) == 0

    assert s.wordsTyping(["a", "b"], 1, 3) == 1

    assert s.wordsTyping(["longword"], 2, 8) == 2

    print("all tests passed")

Test Notes

Test	Why
Standard example 1	Exact row fitting
Standard example 2	Multiple sentence repetitions
Standard example 3	Mixed word lengths
Single short word	Repeated many times
Word longer than row	Cannot fit
Exact fit with space	Boundary handling
Word length equals columns	Full-row single word