whuwarming.pdf

-1- The Problem Set Problem A: Cup Problem B: Find The Path Problem C: Five in a Row, Again Problem D: Minimum Heap Problem E: Name PK Problem F: Pendant Problem G: Radar Problem H: Ring Problem I: Run Problem J: Toxophily Totally： 10 problems，20 pages. March 29, 2009 -2- Problem A: Cup The WHU ACM Team has a big cup, with which every member drinks water. Now, we know the volume of the water in the cup, can you tell us it height? The radius of the cups top and bottom circle is known, the cups height is also known. Input: The input consists of several test cases. The first line of input contains an integer T, indicating the num of test cases. Each test case is on a single line, and it consists of four floating point numbers: r, R, H, V, representing the bottom radius, the top radius, the height and the volume of the hot water. Technical Specification 1. T = 20. 2. 1 = r, R, H = 100; 0 = V = 1000,000,000. 3. r = R. 4. r, R, H, V are separated by ONE whitespace. 5. There is NO empty line between two neighboring cases. -3- Output For each test case, output the height of hot water on a single line. Please round it to six fractional digits. Sample Input 1 100 100 100 3141562 Sample Output 99.999024 -4- Problem B: Find the Path Scofield is a hero in American show “Prison Break”. He had broken the prison and started a big runaway. Scofield has a map of US with cities and bidirectional roads between them. The lengths of roads are known. Some cities get a lot of cops who are very troublesome. Now Scofield needs your help to arrange his runaway route. He needs a shortest path between two cities, while the quantity of the police in any city, except the start city and end city, on the route is no more than k. You should know that it is very hard to escape. Scofield is very smart but not good at computer. Now Scofield is in trouble, can you help him with your computer? Input The input consists of several test cases. There is an integer T on the first line indi