Programming Team: Practice Contest,
Mt Lebanon HS 2004-5
Link to the Programming Team Home Page.
Q1: Read in three doubles: x1, x2, and
y2, followed by an integer n. The doubles represent triangle T1
which has vertices at (0,0), (x1,0), and (x2,y2). Triangle T2
is formed by connecting the midpoints of the sides of triangle T1,
and in general, triangle Tk+1 is formed by connecting the midpoints
of the sides of triangle Tk. Print out the perimeter of
Q2: Read in a positive integer n1 followed by a positive integer n2, where n2 > n1. Print out the number of prime numbers in the range [n1,n2]. Note: your program must run in under 1 second when n1=0 and n2 = 1 million.
Q3: There are four unique digits a, b, c, and d such that the number abcd equals abcd. For example, the digits are not 2, 3, 4, 5 because 2345 equals 8 * 1024 which equals 8192, which does not equal 2345. Find these digits and print out the number abcd.
Q4: Read in an integer n>2, followed by n pairs of integers xi,yi which represent the vertices of a possibly-concave polygon. The points are listed in clockwise order around the polygon, and you are guaranteed that the first and last pairs of points are identical. Find the area of the polygon
Q5: Read in an all-lowercase-letter string "s" and an integer "k" and print out the kth permutation of the letters in the string "s" when these permutations are listed uniquely in alphabetical order.