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技术 2022年11月11日
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一、题目:

我们可以用2*1的小矩形横着或者竖着去覆盖更大的矩形。请问用n个2*1的小矩形无重叠地覆盖一个2*n的大矩形,总共有多少种方法?

二、思路:

斐波那契数列

【剑指offer】矩形覆盖

三、代码:

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" 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