Font Size

テーマの出所はマイクロソフト社の2016年の春の校閲筆記試験である.
私はまた太ももを抱かれた.(えっ?どうしてこれが第一題なの?水だから.XD)

試験問題の概要

Steven loves reading book on his phone. The book he reads now consists of N paragraphs and the i-th paragraph contains ai characters.
Steven wants to make the characters easier to read, so he decides to increase the font size of characters. But the size of Steven’s phone screen is limited. Its width is W and height is H. As a result, if the font size of characters is S then it can only show ⌊W/S⌋ characters in a line and ⌊H/S⌋ lines in a page. (⌊x⌋ is the largest integer no more than x)
So here’s the question, if Steven wants to control the number of pages no more than P, what’s the maximum font size he can set? Note that paragraphs must start in a new line and there is no empty line between paragraphs.

入力フォーマット

Input may contain multiple test cases.
The first line is an integer TASKS, representing the number of test cases.
For each test case, the first line contains four integers N, P, W and H, as described above.
The second line contains N integers a1,a2,…,aN , indicating the number of characters in each paragraph.
For all test cases,

1 <= N <= 103 ,

1 <= W, H, ai <= 103 ,

1 <= P <= 106 ,

There is always a way to control the number of pages no more than P.

出力フォーマット

For each testcase, output a line with an integer Ans, indicating the maximum font size Steven can set.

問題を解く構想.

この問題は次のように変換できます.
∑i=1N⌈ai⌊W/S⌋⌉≤P×⌊H/S⌋
二分検索とかしようと思っていたら、一度順番を巡ってもタイムアウトしない.

問題

最初はMath.floor関数を使用しなかったが、結果は30%のデータしか通過できなかった.なぜか全く理解できません.Math.floor(height / currentFontSize)とheight / currentFontSizeは等価ではありませんか?

ソースコード

package edu.hit;

import java.util.Scanner;

public class Solution {
    public int getFontSize(int numberOfParagraphs, int[] numberOfCharacters, 
        int numberOfPages, int width, int height) {
        int minFontSize = 1, 
            maxFontSize = width;

        for ( int currentFontSize = maxFontSize; currentFontSize >= minFontSize; -- currentFontSize ) {
            double linesOccupied = 0, 
                   totalLines = numberOfPages * Math.floor(height / currentFontSize);

            for ( int i = 0; i < numberOfParagraphs; ++ i ) {
                linesOccupied += Math.ceil(numberOfCharacters[i] / Math.floor(width / currentFontSize));
            }
            if ( linesOccupied <= totalLines ) {
                return currentFontSize;
            }
        }
        return 1;
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);

        Solution s = new Solution();
        int numberOfTestCases = in.nextInt();

        for ( int i = 0; i < numberOfTestCases; ++ i ) {
            int numberOfParagraphs = in.nextInt(), 
                numberOfPages = in.nextInt(), 
                width = in.nextInt(), 
                height = in.nextInt();
            int[] numberOfCharacters = new int[numberOfParagraphs];

            for ( int j = 0; j < numberOfParagraphs; ++ j ) {
                numberOfCharacters[j] = in.nextInt();
            }
            int fontSize = s.getFontSize(numberOfParagraphs, numberOfCharacters, numberOfPages, width, height);

            System.out.println(fontSize);
        }
        in.close();
    }
}