算法作业Latex-20161024

documentclass[UTF8]{article}
usepackage{tikz}
usepackage{CTEX}
usepackage{amssymb}
usepackage{amsmath}
usepackage{xcolor}
egin{document}
	itle{Algorithm homework 2}
author{****\
21617019}
date{2016-10-17}
maketitle
section*{6.3-3}
egin{flushleft}
证明：\
$ecause$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$lfloor n/2 
floor$,叶节点的个数为$Num=n-lfloor n/2
floor=lceil n/2
ceil$。\
高度为h 的节点个数$Num_h$满足:
egin{align*}
&Num_0=lceil n/2
ceil\
&Num_{h+1}=lceil Num_h/2
ceil
end{align*}
$	hereforequad$距离叶节点距离为h，其个数为 $Num/2^h=lceil n/2^{h+1}
ceil$
end{flushleft}
section*{6.4-1}
	ikzset{
box/.style={circle,
minimum width=5pt, inner sep=3pt,
draw=gray,thick, fill=white}
}
egin{center}
%aaaaaaaaaaaaaaaaaaaaaa
egin{tikzpicture}

ode[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
egin{minipage}[t]{0.6	extwidth}
centering
egin{tikzpicture}

ode[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}\
egin{tikzpicture}

ode[box] {25};
end{tikzpicture}\
(b)
end{minipage}
%ccccccccccccccccccccccccccc
egin{minipage}[t]{0.6	extwidth}
centering
egin{tikzpicture}

ode[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}\
egin{tikzpicture}

ode[box] (b) at(4,5){25};

ode[box] (a) at(3,5){20};
 
end{tikzpicture}\
(c)
end{minipage}
\%%%%%%%%ddddddddddddddddddddddd
egin{minipage}[t]{0.6	extwidth}
centering
egin{tikzpicture}

ode[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}\
egin{tikzpicture}

ode[box] (b) at(4,5){25};

ode[box] (a) at(3,5){20};

ode[box] (a) at(2,5){17};
end{tikzpicture}\
(d)
end{minipage}
%%%%%%%eeeeeeeeeeeeeeeeee
egin{minipage}[t]{0.6	extwidth}
centering
egin{tikzpicture}

ode[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}\
egin{tikzpicture}

ode[box] (b) at(4,5){25};

ode[box] (a) at(3,5){20};

ode[box] (a) at(2,5){17};

ode[box] (a) at(1,5){13};
end{tikzpicture}\
(e)
end{minipage}
\%%%%%%%%ffffffffffffffffffffffffff
egin{minipage}[t]{0.6	extwidth}
centering
egin{tikzpicture}

ode[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}\
egin{tikzpicture}

ode[box] (b) at(4,5){25};

ode[box] (a) at(3,5){20};

ode[box] (a) at(2,5){17};

ode[box] (a) at(1,5){13};

ode[box] (a) at(0,5){8};
end{tikzpicture}\
(f)
end{minipage}
%%%%ggggggggggggggggggggggggggggggg
egin{minipage}[t]{0.6	extwidth}
centering
egin{tikzpicture}

ode[box] {5}[sibling distance=80pt]
child {node[box] {4}[sibling distance=40pt]
}
child {node[box] {2}[sibling distance=40pt]
};
end{tikzpicture}\
egin{tikzpicture}

ode[box] (b) at(5,5){25};

ode[box] (a) at(4,5){20};

ode[box] (a) at(3,5){17};

ode[box] (a) at(2,5){13};

ode[box] (a) at(1,5){8};

ode[box] (a) at(0,5){7};
end{tikzpicture}\
(g)
end{minipage}
\%%%%%%%%hhhhhhhhhhhhhhhhhhhhhhhhhhh
egin{minipage}[t]{0.6	extwidth}
centering
egin{tikzpicture}

ode[box] {4}[sibling distance=80pt]
child {node[box] {2}[sibling distance=40pt]
}
;
end{tikzpicture}\
egin{tikzpicture}

ode[box] (b) at(5,5){25};

ode[box] (a) at(4.5,5){20};

ode[box] (a) at(4,5){17};

ode[box] (a) at(3.5,5){13};

ode[box] (a) at(3,5){8};

ode[box] (a) at(2.5,5){7};

ode[box] (a) at(2,5){5};
end{tikzpicture}\
(h)
end{minipage}
%%%%%%%iiiiiiiiiiiiiiiiiiiiiii
egin{minipage}[t]{0.6	extwidth}
centering
egin{tikzpicture}

ode[box] {2};
end{tikzpicture}\
egin{tikzpicture}

ode[box] (b) at(5.6,5){25};

ode[box] (a) at(4.8,5){20};

ode[box] (a) at(4,5){17};

ode[box] (a) at(3.2,5){13};

ode[box] (a) at(2.4,5){8};

ode[box] (a) at(1.6,5){7};

ode[box] (a) at(0.8,5){5};

ode[box] (a) at(0,5){4};
end{tikzpicture}\
(i)
end{minipage}
\\\
排序结果：\
egin{tikzpicture}

ode[box] (b) at(9,5){25};

ode[box] (a) at(8,5){20};

ode[box] (a) at(7,5){17};

ode[box] (a) at(6,5){13};

ode[box] (a) at(5,5){8};

ode[box] (a) at(4,5){7};

ode[box] (a) at(3,5){5};

ode[box] (a) at(2,5){4};

ode[box] (a) at(1,5){2};
end{tikzpicture}\
 
end{document}