1 #include<iostream> 2 using namespace std; 3 int main() 4 { 5 float c; 6 while((cin>>c)&&c!=0) 7 { 8 float sum=0; 9 int n=2; 10 while(sum<c) 11 { 12 sum=sum+1.00/n; 13 n++; 14 } 15 cout<<n-2; 16 } 17 return 0; 18 }
How far can you make a stack of cards overhang a table? If you have one card, you can create a maximum overhang of half a card length. (We're assuming that the cards must be perpendicular to the table.) With two cards you can make the top card overhang the bottom one by half a card length, and the bottom one overhang the table by a third of a card length, for a total maximum overhang of 1/2 + 1/3 = 5/6 card lengths. In general you can make n cards overhang by 1/2 + 1/3 + 1/4 + ... + 1/(n + 1) card lengths, where the top card overhangs the second by 1/2, the second overhangs tha third by 1/3, the third overhangs the fourth by 1/4, etc., and the bottom card overhangs the table by 1/(n + 1). This is illustrated in the figure below.
The input consists of one or more test cases, followed by a line containing the number 0.00 that signals the end of the input. Each test case is a single line containing a positive floating-point number c whose value is at least 0.01 and at most 5.20; c will contain exactly three digits.
For each test case, output the minimum number of cards necessary to achieve an overhang of at least c card lengths. Use the exact output format shown in the examples.
Example input:
1.00
3.71
0.04
5.19
题目大意：你可以把一叠卡片放的离桌子多远？如果有一张卡片，那么可达到的最远距离是卡片唱的的一半（假设卡片必须与桌子的边缘垂直），是用两张卡片，是上面一张能放到的最远距离超过下面长度的一半，而下面一张超过桌子的是卡片长度的1/3，所以能达到的最远距离是：1/2+1/3=5/6。一半来说，n张卡片能达到的最远距离是1/2+1/3+1/4+....+1/(n+1)，也就是最顶上的卡片超出第二张的1/2，第二张超出第三张的1/3，第三张超出第四张的1/4，等等，输入一行数字0.00时表示输入结束，每个测试例一行，是一个浮点数c（0.01<=c<=5.20），c刚好是3位数字。对每个测试例，输出达到距离c所需要的最少卡片的数量。注意输出格式！
算法分析：其实这道题就是1/2+1/3+...+1/(n+1)<=c，利用循环语句知道上面的等式超过c为止
0.00
Example output:
3 card(s)
61 card(s)
1 card(s)
273 card(s)