UVa 10110 - Light, more light

最新推荐文章于 2025-12-01 18:53:18 发布

最新推荐文章于 2025-12-01 18:53:18 发布 · 87 阅读

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本文详细解析UVa10110-Light,morelight问题，通过理解题意，抽象为数学问题，即判断给定整数n的因子个数是奇数还是偶数，进而确定最后灯泡的状态。提供简洁的代码实现，通过计算n的平方根判断其是否为完全平方数来解决此问题。

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UVa 10110 - Light, more light

1 题目
2 思路
3 代码
4 参考

1题目

===================

Light, more light

The Problem

There is man named "mabu" for switching on-off light in our University. He switches on-off the lights in a corridor. Every bulb has its own toggle switch. That is, if it is pressed then the bulb turns on. Another press will turn it off. To save power consumption (or may be he is mad or something else) he does a peculiar thing. If in a corridor there is `n' bulbs, he walks along the corridor back and forth `n' times and in i'th walk he toggles only the switches whose serial is divisable by i. He does not press any switch when coming back to his initial position. A i'th walk is defined as going down the corridor (while doing the peculiar thing) and coming back again.

Now you have to determine what is the final condition of the last bulb. Is it on or off?

The Input

The input will be an integer indicating the n'th bulb in a corridor. Which is less then or equals 2^32-1. A zero indicates the end of input. You should not process this input.

The Output

Output " yes " if the light is on otherwise " no " , in a single line.

Sample Input

Sample Output

no
yes
no

Sadi Khan
Suman Mahbub
01-04-2001

===================

2思路

这题关键是理解题目的意思，抽象成数学问题就是1~n中n的因子个数是奇数还是偶数，由于因子都是成对出现的，所以问题其实就是在问n是否是完全平方数。

3代码

/*
 * Problem: UVa 10110 - Light, more light
 * Lang: ANSI C
 * Time: 0.029
 * Author: minix
 */


#include <stdio.h>
#include <math.h>

int main() {
  long long n, qn;

  while (scanf ("%lld", &n) != EOF) {
    if (n == 0) break;

    qn = (long long)sqrt(n);

    if (qn*qn == n) printf ("yes\n");
    else printf ("no\n");
  }

  return 0;
}