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[游戏] 蹬高游戏

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王守恩
发表于 2019-4-12 11:00:02 | 显示全部楼层 |阅读模式

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蹬高台阶共35级，每次可以蹬 2 级或 3 级，
个位数是 4 的不能蹬，个位数是 8 的必须蹬，问有多少种蹬法？
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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倪举鹏
发表于 2019-4-12 11:56:42 | 显示全部楼层
母函数加排除法
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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zeroieme
发表于 2019-4-12 12:29:26 | 显示全部楼层
你们真的觉得论坛里爬楼梯的题目不够多吗

逢8必蹬，于是中间段是$x^n$，前后段生成函数计算，相乘。
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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markfang2050
发表于 2019-4-12 17:03:29 | 显示全部楼层
真的觉得论坛里爬楼梯的题目不够多吗
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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markfang2050
发表于 2019-4-12 18:51:09 | 显示全部楼层
倪举鹏 发表于 2019-4-12 11:56
母函数加排除法

期待大佬写程序
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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王守恩
 楼主| 发表于 2019-4-13 06:40:23 | 显示全部楼层
本帖最后由 王守恩 于 2019-4-13 06:41 编辑
markfang2050 发表于 2019-4-12 18:51
期待大佬写程序


谢谢 zeroieme ！   逢\(\ \ 8\ \ \)必蹬！于是中间段是\(\ \ x^n\)，前后段生成函数计算，相乘。
前段：第 1 级到第 8 级有 3 种蹬法，
中间段：分2节，8——18——28，每节有 5 种蹬法，
后段：第 28 级到第 35 级有 3 种蹬法，
合计：3×5^2×3=225 种蹬法。

毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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markfang2050
发表于 2019-4-13 16:27:05 | 显示全部楼层
程序计算得
-------------------
225
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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markfang2050
发表于 2019-4-13 17:02:22 | 显示全部楼层
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  15, 18, 21, 23, 25, 28, 30, 33, 35}, {3, 6, 8, 11, 13, 15, 18, 21,
  23, 25, 28, 31, 33, 35}, {3, 6, 8, 11, 13, 15, 18, 21, 23, 26, 28,
  30, 32, 35}, {3, 6, 8, 11, 13, 15, 18, 21, 23, 26, 28, 30, 33,
  35}, {3, 6, 8, 11, 13, 15, 18, 21, 23, 26, 28, 31, 33, 35}, {3, 6,
  8, 11, 13, 16, 18, 20, 22, 25, 28, 30, 32, 35}, {3, 6, 8, 11, 13,
  16, 18, 20, 22, 25, 28, 30, 33, 35}, {3, 6, 8, 11, 13, 16, 18, 20,
  22, 25, 28, 31, 33, 35}, {3, 6, 8, 11, 13, 16, 18, 20, 23, 25, 28,
  30, 32, 35}, {3, 6, 8, 11, 13, 16, 18, 20, 23, 25, 28, 30, 33,
  35}, {3, 6, 8, 11, 13, 16, 18, 20, 23, 25, 28, 31, 33, 35}, {3, 6,
  8, 11, 13, 16, 18, 20, 23, 26, 28, 30, 32, 35}, {3, 6, 8, 11, 13,
  16, 18, 20, 23, 26, 28, 30, 33, 35}, {3, 6, 8, 11, 13, 16, 18, 20,
  23, 26, 28, 31, 33, 35}, {3, 6, 8, 11, 13, 16, 18, 21, 23, 25, 28,
  30, 32, 35}, {3, 6, 8, 11, 13, 16, 18, 21, 23, 25, 28, 30, 33,
  35}, {3, 6, 8, 11, 13, 16, 18, 21, 23, 25, 28, 31, 33, 35}, {3, 6,
  8, 11, 13, 16, 18, 21, 23, 26, 28, 30, 32, 35}, {3, 6, 8, 11, 13,
  16, 18, 21, 23, 26, 28, 30, 33, 35}, {3, 6, 8, 11, 13, 16, 18, 21,
  23, 26, 28, 31, 33, 35}}
225种登高方案。@守恩王

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