Problem E: Word Cloud

Before describing the algorithm Tagg uses for generating clouds, we digress for a quick lesson in typography. The basic unit of measure is known as a point (typically abbreviated as pt). A font's size is described based on the vertical number of points from one line to the next, including any interline spacing. For example, with a 12pt font, the vertical space from the top of one character to the top of a character below it is 12 points. We assume that a character's height is precisely equal to the font's point size (regardless of whether the character is upper or lower case).

For this problem, we focus on a fixed-width font, such as Courier, in which each character of the alphabet is also given the same amount of width. The character width for such a font depends on the font size and the aspect ratio. For Courier, a word with t characters rendered in a font of size P has a total width of $\left\lceil \frac{9}{16} \cdot t \cdot P \right\rceil$ when measured in points. Note well the use of the ceiling operator, which converts any noninteger to the next highest integer. For example, a 5-letter word in a 20pt font would be rendered with a height of 20 points and a width equal to $\left\lceil \frac{900}{16} \right\rceil = \left\lceil 56.25 \right\rceil = 57$ points.

Now we can describe Tagg's algorithm for creating a word cloud. He pre-sorts his word list into alphabetical order and removes words that do not occur at least five times. For each word w, he computes a point size based on the formula $P = 8 + \left\lceil \frac{40(c_w - 4)}{(c_{max}-4)} \right\rceil$, where $c_w$ is the number of occurrences of the word, and $c_{max}$ is the number of occurrences of the most frequent word in the data set. Note that by this formula, every word will be rendered with anywhere from a 9pt font to a 48pt font. He then places the words in rows, with a 10pt horizontal space between adjacent words, placing as many words as fit in the row, subject to a maximum width W for his entire cloud. The height of a given row is equal to the maximum font size of any word rendered in that row.

As a tangible example, consider the following data set and word cloud.

word	count
apple	10
banana	5
grape	20
kiwi	18
orange	12
strawberry	10

Input: Each data set begins with a line containing two integers: W and N. The value W denotes the maximum width of the cloud; W ≤ 5000 will be at least as wide as any word at its desired font size. The value 1 ≤ N ≤ 100 denotes the number of words that appear in the cloud. Following the first line are N additional lines, each having a string S that is the word (with no whitespace), and an integer C that is a count of the number of occurrences of that word in the original data set, with 5 ≤ C ≤ 1000. Words will be given in the same order that they are to be displayed within the cloud.

Output: For each data set, output the word CLOUD followed by a space, a serial number indicating the data set, a colon, another space, and the integer height of the cloud, measured in font points.