[POJ] #1003# Hangover : 浮点数运算

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.

• 按照固定的累加方式：从高层到低层，相对于其相邻下层可以伸出的长度为(1/2),(1/3),...,(1/n)
• 给定一个指定长度 S，问最少需要累加多上块板，使其相对于桌面的伸出长度大于或等于 S

三. 分析

• 算法核心: 此题比较简单，无需考虑任何算法
• 实现细节: 简单的浮点数累加运算即可

四. 题解

 1 #include <stdio.h>
 2 
 3 int main()
 4 {
 5     int i;
 6     float length, sum;
 7 
 8     while (1) {
 9         sum = 0;
10         scanf("%f\n", &length);
11         if (!length) break;
12 
13         for (i = 2; ; i++) {
14             sum += (1 / (float)i);
15 
16             if (sum >= length) {
17                 printf("%d card(s)\n", i - 1);
18                 break;
19             }
20         }
21     }
22 
23     return 0;
24 }