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10110: Light, more light

10110: Light, more light. ★☆☆☆☆ 題組： Problem Set Archive with Online Judge 題號： 1 0110: Light, more light 解題者： 陳泓宇 解題日期： 200 9 年 5 月 15 日 題意： 輸入 n 代表走廊上有 n 個燈泡，依序編號為 1 到 n ，而管理員走 n 趟來開關燈泡，每當走第 i 趟時則切換編號能被 i 整除的燈泡，初始所有燈泡為關，求 n 趟結束後，第 n 個燈泡為開或關。 n ≤ 2^32-1. 題意範例： Sample input 3 6241

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10110: Light, more light

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  1. 10110: Light, more light • ★☆☆☆☆ • 題組：Problem Set Archive with Online Judge • 題號：10110:Light, more light • 解題者：陳泓宇 • 解題日期：2009年5月15日 • 題意： 輸入n代表走廊上有n個燈泡，依序編號為1到n，而管理員走n趟來開關燈泡，每當走第i趟時則切換編號能被i整除的燈泡，初始所有燈泡為關，求n趟結束後，第n個燈泡為開或關。 n ≤ 2^32-1

  2. 題意範例：Sample input3 6241 8191 0 Output for Sample Inputno yes no Example:

  3. 解法：解法一： • 如果i是n的因數，則切換燈泡， • So, continue (i = 1 to n) : i++ • =>TLE (Time Limit Exceed) 解法二： • (1) 使用unsigned long或long long，格式為%I64d。 • (2) 考慮n有幾個因數，若為奇數個則燈泡為開。 • (3) A number have Odd number of factors if and only if it is a Perfect Square • (4)So, if (sqrt (n) = Integer) then output: Yes otherwise No.

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