扔鸡蛋问题 （动态规划） （Balls）

                                                      Balls

Time Limit: 1000MS		Memory Limit: 65536K

Description

The classic Two Glass Balls brain-teaser is often posed as:

"Given two identical glass spheres, you would like to determine the lowest floor in a 100-story building from which they will break when dropped. Assume the spheres are undamaged when dropped below this point. What is the strategy that will minimize the worst-case scenario for number of drops?"
Suppose that we had only one ball. We'd have to drop from each floor from 1 to 100 in sequence, requiring 100 drops in the worst case.
Now consider the case where we have two balls. Suppose we drop the first ball from floor n. If it breaks we're in the case where we have one ball remaining and we need to drop from floors 1 to n-1 in sequence, yielding n drops in the worst case (the first ball is dropped once, the second at most n-1 times). However, if it does not break when dropped from floor n, we have reduced the problem to dropping from floors n+1 to 100. In either case we must keep in mind that we've already used one drop. So the minimum number of drops, in the worst case, is the minimum over all n.

You will write a program to determine the minimum number of drops required, in the worst case, given B balls and an M-story building.

Input

The first line of input contains a single integer P, (1 ≤ P ≤ 1000), which is the number of data sets that follow. Each data set consists of a single line containing three(3) decimal integer values: the problem number, followed by a space, followed by the number of balls B, (1 ≤ B ≤ 50), followed by a space and the number of floors in the building M, (1 ≤ M ≤ 1000).

Output

For each data set, generate one line of output with the following values: The data set number as a decimal integer, a space, and the minimum number of drops needed for the corresponding values of B and M.

Sample Input

4 
1 2 10 
2 2 100 
3 2 300 
4 25 900

Sample Output

1 4
2 14
3 24
4 10

推荐一篇写的很好的博客  https://blog.csdn.net/joylnwang/article/details/6769160

解题思路：
这是一个比较经典的 DP 问题，又叫做 “扔鸡蛋问题”，假设 dp[n,w] 表示 n 层楼、w 个鸡蛋时找到摔鸡蛋不碎的最少判断次数。则一个鸡蛋从第 i 层扔下，如果碎了，还剩 w−1 个鸡蛋，为确定下面楼层中的安全位置，还需要dp[i−1,w−1] 次（子问题）；不碎的话，上面还有 n−i 层，还需要 dp[n−i,w]次（子问题，实体 n 层楼的上 n−i 层需要的最少判断次数和一个新的问题的 n−i 层楼需要的最少判断次数其实是一样的）。

#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include