北京大學(xué)ACM題
Here is a geometric problem. You have an angle and some squares in the first quadrant of the plane rectangular coordinates. The vertex of the angle is fixed on the origin O of the coordinates, and both of its radial lines are specified by the input. The sizes of the squares are also specified by the input, and the squares can shift vertically and horizontally. Now your job is to use the squares and the radial lines of the angle to enclose the maximum area, which excludes the area of the squares (see Figure 1). You should note that the edges of the squares must be parallel to the axes.
北京大學(xué)ACM比賽題
The game of Scrabble is played with tiles. A tile either has a single letter written on it, or it is blank. In the latter case, the tile may be used to represent a letter of your choice. On your turn, you arrange the tiles to form a word. Each tile may be used at most once, but not all tiles need to be used. Given several Scrabble tiles and a dictionary, determine how many words in the dictionary can be formed using the given Scrabble tiles.
北京大學(xué)ACM比賽題目
In 1742, Christian Goldbach, a German amateur mathematician, sent a letter to Leonhard Euler in which he made the following conjecture:
Every even number greater than 4 can be
written as the sum of two odd prime numbers.
For example:
8 = 3 + 5. Both 3 and 5 are odd prime numbers.
20 = 3 + 17 = 7 + 13.
42 = 5 + 37 = 11 + 31 = 13 + 29 = 19 + 23.
Today it is still unproven whether the conjecture is right. (Oh wait, I have the proof of course, but it is too long to write it on the margin of this page.)
Anyway, your task is now to verify Goldbach s conjecture for all even numbers less than a million.
北京大學(xué)ACM比賽題目
Consider an infinite full binary search tree (see the figure below), the numbers in the nodes are 1, 2, 3, .... In a subtree whose root node is X, we can get the minimum number in this subtree by repeating going down the left node until the last level, and we can also find the maximum number by going down the right node. Now you are given some queries as "What are the minimum and maximum numbers in the subtree whose root node is X?" Please try to find answers for there queries.
北京大學(xué)ACM比賽題目
Write a program to read four lines of upper case (i.e., all CAPITAL LETTERS) text input (no more than 72 characters per line) from the input file and print a vertical histogram that shows how many times each letter (but not blanks, digits, or punctuation) appears in the all-upper-case input. Format your output exactly as shown.
