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68. Text Justification

Description

Given an array of strings words and a width maxWidth, format the text such that each line has exactly maxWidth characters and is fully (left and right) justified.

You should pack your words in a greedy approach; that is, pack as many words as you can in each line. Pad extra spaces ' ' when necessary so that each line has exactly maxWidth characters.

Extra spaces between words should be distributed as evenly as possible. If the number of spaces on a line does not divide evenly between words, the empty slots on the left will be assigned more spaces than the slots on the right.

For the last line of text, it should be left-justified, and no extra space is inserted between words.

Note:

  • A word is defined as a character sequence consisting of non-space characters only.
  • Each word's length is guaranteed to be greater than 0 and not exceed maxWidth.
  • The input array words contains at least one word.

 

Example 1:

Input: words = ["This", "is", "an", "example", "of", "text", "justification."], maxWidth = 16
Output:
[
   "This    is    an",
   "example  of text",
   "justification.  "
]

Example 2:

Input: words = ["What","must","be","acknowledgment","shall","be"], maxWidth = 16
Output:
[
  "What   must   be",
  "acknowledgment  ",
  "shall be        "
]
Explanation: Note that the last line is "shall be    " instead of "shall     be", because the last line must be left-justified instead of fully-justified.
Note that the second line is also left-justified because it contains only one word.

Example 3:

Input: words = ["Science","is","what","we","understand","well","enough","to","explain","to","a","computer.","Art","is","everything","else","we","do"], maxWidth = 20
Output:
[
  "Science  is  what we",
  "understand      well",
  "enough to explain to",
  "a  computer.  Art is",
  "everything  else  we",
  "do                  "
]

 

Constraints:

  • 1 <= words.length <= 300
  • 1 <= words[i].length <= 20
  • words[i] consists of only English letters and symbols.
  • 1 <= maxWidth <= 100
  • words[i].length <= maxWidth

Solutions

Solution 1: Simulation

Thinking

The first idea is to pack as many words as possible into a line, then pad with spaces. There are at most \(300\) words and the width is at most \(100\), so a linear scan is enough; no backtracking.

The bottleneck is not runtime but the spacing rules: the last line and a one-word line must be left-aligned; every other line must spread extra spaces as evenly as possible, leftover spaces going to the left gaps first.

So we greedily take the words that fit, then branch on “last line / single word” versus even distribution. Process lines from left to right.

We can simulate the process according to the problem's requirements. Note that if it is the last line, or if there is only one word in the line, then we should align to the left. Otherwise, we should distribute the spaces evenly.

The time complexity is \(O(L)\), and the space complexity is \(O(L)\). Here, \(L\) is the sum of the lengths of all words.

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class Solution:
    def fullJustify(self, words: List[str], maxWidth: int) -> List[str]:
        ans = []
        i, n = 0, len(words)
        while i < n:
            t = []
            cnt = len(words[i])
            t.append(words[i])
            i += 1
            while i < n and cnt + 1 + len(words[i]) <= maxWidth:
                cnt += 1 + len(words[i])
                t.append(words[i])
                i += 1
            if i == n or len(t) == 1:
                left = ' '.join(t)
                right = ' ' * (maxWidth - len(left))
                ans.append(left + right)
                continue
            space_width = maxWidth - (cnt - len(t) + 1)
            w, m = divmod(space_width, len(t) - 1)
            row = []
            for j, s in enumerate(t[:-1]):
                row.append(s)
                row.append(' ' * (w + (1 if j < m else 0)))
            row.append(t[-1])
            ans.append(''.join(row))
        return ans

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class Solution {
    public List<String> fullJustify(String[] words, int maxWidth) {
        List<String> ans = new ArrayList<>();
        for (int i = 0, n = words.length; i < n;) {
            List<String> t = new ArrayList<>();
            t.add(words[i]);
            int cnt = words[i].length();
            ++i;
            while (i < n && cnt + 1 + words[i].length() <= maxWidth) {
                cnt += 1 + words[i].length();
                t.add(words[i++]);
            }
            if (i == n || t.size() == 1) {
                String left = String.join(" ", t);
                String right = " ".repeat(maxWidth - left.length());
                ans.add(left + right);
                continue;
            }
            int spaceWidth = maxWidth - (cnt - t.size() + 1);
            int w = spaceWidth / (t.size() - 1);
            int m = spaceWidth % (t.size() - 1);
            StringBuilder row = new StringBuilder();
            for (int j = 0; j < t.size() - 1; ++j) {
                row.append(t.get(j));
                row.append(" ".repeat(w + (j < m ? 1 : 0)));
            }
            row.append(t.get(t.size() - 1));
            ans.add(row.toString());
        }
        return ans;
    }
}

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class Solution {
public:
    vector<string> fullJustify(vector<string>& words, int maxWidth) {
        vector<string> ans;
        for (int i = 0, n = words.size(); i < n;) {
            vector<string> t = {words[i]};
            int cnt = words[i].size();
            ++i;
            while (i < n && cnt + 1 + words[i].size() <= maxWidth) {
                cnt += 1 + words[i].size();
                t.emplace_back(words[i++]);
            }
            if (i == n || t.size() == 1) {
                string left = t[0];
                for (int j = 1; j < t.size(); ++j) {
                    left += " " + t[j];
                }
                string right = string(maxWidth - left.size(), ' ');
                ans.emplace_back(left + right);
                continue;
            }
            int spaceWidth = maxWidth - (cnt - t.size() + 1);
            int w = spaceWidth / (t.size() - 1);
            int m = spaceWidth % (t.size() - 1);
            string row;
            for (int j = 0; j < t.size() - 1; ++j) {
                row += t[j] + string(w + (j < m ? 1 : 0), ' ');
            }
            row += t.back();
            ans.emplace_back(row);
        }
        return ans;
    }
};

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func fullJustify(words []string, maxWidth int) (ans []string) {
    for i, n := 0, len(words); i < n; {
        t := []string{words[i]}
        cnt := len(words[i])
        i++
        for i < n && cnt+1+len(words[i]) <= maxWidth {
            cnt += 1 + len(words[i])
            t = append(t, words[i])
            i++
        }
        if i == n || len(t) == 1 {
            left := strings.Join(t, " ")
            right := strings.Repeat(" ", maxWidth-len(left))
            ans = append(ans, left+right)
            continue
        }
        spaceWidth := maxWidth - (cnt - len(t) + 1)
        w := spaceWidth / (len(t) - 1)
        m := spaceWidth % (len(t) - 1)
        row := strings.Builder{}
        for j, s := range t[:len(t)-1] {
            row.WriteString(s)
            row.WriteString(strings.Repeat(" ", w))
            if j < m {
                row.WriteString(" ")
            }
        }
        row.WriteString(t[len(t)-1])
        ans = append(ans, row.String())
    }
    return
}

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function fullJustify(words: string[], maxWidth: number): string[] {
    const ans: string[] = [];
    for (let i = 0, n = words.length; i < n;) {
        const t: string[] = [words[i]];
        let cnt = words[i++].length;
        while (i < n && cnt + 1 + words[i].length <= maxWidth) {
            t.push(words[i]);
            cnt += 1 + words[i++].length;
        }
        if (i === n || t.length === 1) {
            const left: string = t.join(' ');
            const right: string = ' '.repeat(maxWidth - left.length);
            ans.push(left + right);
            continue;
        }
        const spaceWidth: number = maxWidth - (cnt - t.length + 1);
        const w: number = Math.floor(spaceWidth / (t.length - 1));
        const m: number = spaceWidth % (t.length - 1);
        const row: string[] = [];
        for (let j = 0; j < t.length - 1; ++j) {
            row.push(t[j]);
            row.push(' '.repeat(w + (j < m ? 1 : 0)));
        }
        row.push(t[t.length - 1]);
        ans.push(row.join(''));
    }
    return ans;
}

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public class Solution {
    public IList<string> FullJustify(string[] words, int maxWidth) {
        var ans = new List<string>();
        for (int i = 0, n = words.Length; i < n;) {
            var t = new List<string>();
            t.Add(words[i]);
            int cnt = words[i].Length;
            ++i;
            while (i < n && cnt + 1 + words[i].Length <= maxWidth) {
                t.Add(words[i]);
                cnt += 1 + words[i].Length;
                ++i;
            }
            if (i == n || t.Count == 1) {
                string left = string.Join(" ", t);
                string right = new string(' ', maxWidth - left.Length);
                ans.Add(left + right);
                continue;
            }
            int spaceWidth = maxWidth - (cnt - t.Count + 1);
            int w = spaceWidth / (t.Count - 1);
            int m = spaceWidth % (t.Count - 1);
            var row = new StringBuilder();
            for (int j = 0; j < t.Count - 1; ++j) {
                row.Append(t[j]);
                row.Append(new string(' ', w + (j < m ? 1 : 0)));
            }
            row.Append(t[t.Count - 1]);
            ans.Add(row.ToString());
        }
        return ans;
    }
}

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