若一头小母牛,从出生起第四个年头开始每年生一头母牛,按此规律,第n年有多少头母牛?
具体分析:
1.分析题目:(从出生起第四个年头开始每年生一头母牛)
时间(年) 未成熟母牛(头) 成熟母牛(头) 母牛总数(头)
1 1 0 1
2 1 0 1
3 1 0 1
4 0 1 1
5 1 1 2
6 2 1 3
7 3 1 4
8 3 2 5
9 4 3 7
10 6 4 10
从图中可以看出A1=1,A2=2,A3=3,A4=4,A5=A4+A1等,则依此规律,An=An-1+An-4.这个规律很重要的,因为我们可以从中得到类似问题的规律(例如:从出生起第m个年头开始每年生一头母牛,则得到的规律是Fn=Fn-1+Fn-m (n>m)).
递归算法:
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