From c5d9485d44bfc86270536612e9078fd01f12927e Mon Sep 17 00:00:00 2001 From: Shine wOng <1551885@tongji.edu.cn> Date: Fri, 14 Jun 2019 10:59:42 +0800 Subject: [PATCH] Correct the format of latex formula. --- thu_dsa/chp7/AVL.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/thu_dsa/chp7/AVL.md b/thu_dsa/chp7/AVL.md index a6986b9..492d305 100644 --- a/thu_dsa/chp7/AVL.md +++ b/thu_dsa/chp7/AVL.md @@ -41,7 +41,7 @@ $$ 对于树高为h的AVL树,我们说它的结点数不少于$fib(h + 3) - 1$,其中$fib(1) = 1, fib(2) = 1$。从而包含n个结点的AVL树其高度不超过$O(logn)$,从而AVL树是一棵适度平衡的BST。其证明如下: + 首先对于树高为1的平凡的情况,$n = 1, h = 0$,$fib(h + 3) - 1 = 2 - 1 = 1$,满足上述结论。 -+ 对于任意树高h,结点最少的情况下,其左右子树树高分别为$h - 1, h - 2$,从而结点数$T(h) \ge T(h - 1) + T(h - 2) + 1 \ge = fib(h + 2) + fib(h + 1) - 1 = fib(h + 3) - 1$。故得证。 ++ 对于任意树高h,结点最少的情况下,其左右子树树高分别为$h - 1, h - 2$,从而结点数$T(h) \ge T(h - 1) + T(h - 2) + 1 \ge fib(h + 2) + fib(h + 1) - 1 = fib(h + 3) - 1$。故得证。 由于Fibonacci数呈现一个指数级数,所以反过来,任意含n个结点的AVL树,其树高不高于$O(logn)$。