算法作业Latex-20161024
来源:互联网 发布:淘宝售馨图片 编辑:程序博客网 时间:2024/05/27 00:33
\documentclass[UTF8]{article}\usepackage{tikz}\usepackage{CTEX}\usepackage{amssymb}\usepackage{amsmath}\usepackage{xcolor}\begin{document}\title{Algorithm homework 2}\author{****\\21617019}\date{2016-10-17}\maketitle\section*{6.3-3}\begin{flushleft}证明:\\$\because$\quad 下标为 i 的父节点的子节点为 2i 和 2i+1 ,所以节点为 n 的叶节点的父节点应该为$\lfloor n/2 \rfloor$,叶节点的个数为$Num=n-\lfloor n/2\rfloor=\lceil n/2\rceil$。\\高度为h 的节点个数$Num_h$满足:\begin{align*}&Num_0=\lceil n/2\rceil\\&Num_{h+1}=\lceil Num_h/2\rceil\end{align*}$\therefore\quad$距离叶节点距离为h,其个数为 $Num/2^h=\lceil n/2^{h+1}\rceil$\end{flushleft}\section*{6.4-1}\tikzset{box/.style={circle,minimum width=5pt, inner sep=3pt,draw=gray,thick, fill=white}}\begin{center}%aaaaaaaaaaaaaaaaaaaaaa\begin{tikzpicture}\node[box] {25}[sibling distance=80pt]child {node[box] {13}[sibling distance=40pt]child {node[box] {8}[sibling distance=40pt]child {node[box] {5}}child {node[box] {4}}}child {node[box] {7}}}child {node[box] {20}[sibling distance=40pt]child {node[box] {17}}child {node[box] {2}}};\end{tikzpicture}\\a.最大堆\end{center}%bbbbbbbbbbbbbbbbbbbbbbbbbbb\begin{minipage}[t]{0.6\textwidth}\centering\begin{tikzpicture}\node[box] {20}[sibling distance=80pt]child {node[box] {13}[sibling distance=40pt]child {node[box] {8}[sibling distance=40pt]child {node[box] {5}}}child {node[box] {7}}}child {node[box] {17}[sibling distance=40pt]child {node[box] {4}}child {node[box] {2}}}; \end{tikzpicture}\\\begin{tikzpicture}\node[box] {25};\end{tikzpicture}\\(b)\end{minipage}%ccccccccccccccccccccccccccc\begin{minipage}[t]{0.6\textwidth}\centering\begin{tikzpicture}\node[box] {17}[sibling distance=80pt]child {node[box] {13}[sibling distance=40pt]child {node[box] {8}[sibling distance=40pt]}child {node[box] {7}}}child {node[box] {5}[sibling distance=40pt]child {node[box] {4}}child {node[box] {2}}};\end{tikzpicture}\\\begin{tikzpicture}\node[box] (b) at(4,5){25};\node[box] (a) at(3,5){20}; \end{tikzpicture}\\(c)\end{minipage}\\%%%%%%%%ddddddddddddddddddddddd\begin{minipage}[t]{0.6\textwidth}\centering\begin{tikzpicture}\node[box] {13}[sibling distance=80pt]child {node[box] {8}[sibling distance=40pt]child {node[box] {2}[sibling distance=40pt]}child {node[box] {7}}}child {node[box] {5}[sibling distance=40pt]child {node[box] {4}}};\end{tikzpicture}\\\begin{tikzpicture}\node[box] (b) at(4,5){25};\node[box] (a) at(3,5){20};\node[box] (a) at(2,5){17};\end{tikzpicture}\\(d)\end{minipage}%%%%%%%eeeeeeeeeeeeeeeeee\begin{minipage}[t]{0.6\textwidth}\centering\begin{tikzpicture}\node[box] {8}[sibling distance=80pt]child {node[box] {7}[sibling distance=40pt]child {node[box] {2}[sibling distance=40pt]}child {node[box] {4}}}child {node[box] {5}[sibling distance=40pt]};\end{tikzpicture}\\\begin{tikzpicture}\node[box] (b) at(4,5){25};\node[box] (a) at(3,5){20};\node[box] (a) at(2,5){17};\node[box] (a) at(1,5){13};\end{tikzpicture}\\(e)\end{minipage}\\%%%%%%%%ffffffffffffffffffffffffff\begin{minipage}[t]{0.6\textwidth}\centering\begin{tikzpicture}\node[box] {7}[sibling distance=80pt]child {node[box] {4}[sibling distance=40pt]child {node[box] {2}[sibling distance=40pt]}}child {node[box] {5}[sibling distance=40pt]};\end{tikzpicture}\\\begin{tikzpicture}\node[box] (b) at(4,5){25};\node[box] (a) at(3,5){20};\node[box] (a) at(2,5){17};\node[box] (a) at(1,5){13};\node[box] (a) at(0,5){8};\end{tikzpicture}\\(f)\end{minipage}%%%%ggggggggggggggggggggggggggggggg\begin{minipage}[t]{0.6\textwidth}\centering\begin{tikzpicture}\node[box] {5}[sibling distance=80pt]child {node[box] {4}[sibling distance=40pt]}child {node[box] {2}[sibling distance=40pt]};\end{tikzpicture}\\\begin{tikzpicture}\node[box] (b) at(5,5){25};\node[box] (a) at(4,5){20};\node[box] (a) at(3,5){17};\node[box] (a) at(2,5){13};\node[box] (a) at(1,5){8};\node[box] (a) at(0,5){7};\end{tikzpicture}\\(g)\end{minipage}\\%%%%%%%%hhhhhhhhhhhhhhhhhhhhhhhhhhh\begin{minipage}[t]{0.6\textwidth}\centering\begin{tikzpicture}\node[box] {4}[sibling distance=80pt]child {node[box] {2}[sibling distance=40pt]};\end{tikzpicture}\\\begin{tikzpicture}\node[box] (b) at(5,5){25};\node[box] (a) at(4.5,5){20};\node[box] (a) at(4,5){17};\node[box] (a) at(3.5,5){13};\node[box] (a) at(3,5){8};\node[box] (a) at(2.5,5){7};\node[box] (a) at(2,5){5};\end{tikzpicture}\\(h)\end{minipage}%%%%%%%iiiiiiiiiiiiiiiiiiiiiii\begin{minipage}[t]{0.6\textwidth}\centering\begin{tikzpicture}\node[box] {2};\end{tikzpicture}\\\begin{tikzpicture}\node[box] (b) at(5.6,5){25};\node[box] (a) at(4.8,5){20};\node[box] (a) at(4,5){17};\node[box] (a) at(3.2,5){13};\node[box] (a) at(2.4,5){8};\node[box] (a) at(1.6,5){7};\node[box] (a) at(0.8,5){5};\node[box] (a) at(0,5){4};\end{tikzpicture}\\(i)\end{minipage}\\\\\\排序结果:\\\begin{tikzpicture}\node[box] (b) at(9,5){25};\node[box] (a) at(8,5){20};\node[box] (a) at(7,5){17};\node[box] (a) at(6,5){13};\node[box] (a) at(5,5){8};\node[box] (a) at(4,5){7};\node[box] (a) at(3,5){5};\node[box] (a) at(2,5){4};\node[box] (a) at(1,5){2};\end{tikzpicture}\\ \end{document}
0 0
- 算法作业Latex-20161024
- Latex:算法
- Latex算法排版
- LaTeX算法排版例子
- Latex 算法编辑
- latex算法排版
- LaTeX算法排版例子
- latex中输入算法
- LaTex:算法排版
- Latex 算法Algorithm
- latex 插入算法
- LaTex:算法排版
- LaTex算法插入
- latex算法流程图
- Latex.算法分页
- latex算法书写
- LaTeX 算法排版
- latex 算法,算法包 algorithm
- Linux 下的sqlite
- View的绘制流程
- CAN 总线 5 分钟入门
- 遗传算法实现 解车辆路径问题(vrp)
- 无法获得锁 /var/lib/dpkg/lock - open (11: 资源临时不可用)
- 算法作业Latex-20161024
- java数组
- 解决python3 UnicodeEncodeError: 'gbk' codec can't encode character '\xXX' in position XX
- 加快Android Studio 编译速度
- 个人PC克隆公司数据库简单步骤
- 嵌入式LINUX C学习之笔记(第一天)
- LeetCode 442. Find All Duplicates in an Array
- JavaScript笔记
- cookie 设置浏览器在关闭5秒后 cookie还是存在的