树 - 二叉树

读了Robert Sedgewick的《算法:C语言实现》（第三版）的第五章，了解了许多关于树，特别是二叉树的知识。这里总结一下。直接看代码(C++)吧。

#include <cstdio>
#include <cstdlib>
#include <queue>
#include <stack>

#define null 0
#define NEXTLINE printf("\n")
#define MAX(x, y) ((x)>(y)?(x):(y))

int max = 1<<31;
int min = ~(1<<31);

typedef int Item;
typedef struct node *link;
struct node {
    Item item;
    link l, r;
};
// 初始化树 
link
InitTree(Item item)
{
    link t = (link)malloc(sizeof *t);
    if (t == null) {
        return null;
    }
    t->item = item;
    t->l = null;
    t->r = null;
    return t;
}
// 加入左子节点 
link
AddLeftNode(link t, Item item)
{
    if (t == null) {
        return null;
    }
    link newNode = (link)malloc(sizeof *newNode);
    if (newNode == null) {
        return null;
    }
    t->l = newNode;
    newNode->item = item;
    newNode->l = null;
    newNode->r = null;
    return newNode;
}
// 加入右子节点 
link
AddRightNode(link t, Item item)
{
    if (t == null) {
        return null;
    }
    link newNode = (link)malloc(sizeof *newNode);
    if (newNode == null) {
        return null;
    }
    t->r = newNode;
    newNode->item = item;
    newNode->l = null;
    newNode->r = null;
    return newNode;
}
// 打印节点中的内容 
void
PrintItem(link t)
{
    printf("%d\t", t->item);
}
// 前序遍历(递归) 
void
PreTraverse(link t)
{
    if (t == null) {
        return;
    }
    PrintItem(t);
    PreTraverse(t->l);
    PreTraverse(t->r);
}
// 中序遍历(递归) 
void
InTraverse(link t)
{
    if (t == null) {
        return;
    }
    InTraverse(t->l);
    PrintItem(t);
    InTraverse(t->r);
}
// 后序遍历(递归) 
void
PostTraverse(link t)
{
    if (t == null) {
        return;
    }
    PostTraverse(t->l);
    PostTraverse(t->r);
    PrintItem(t);
}
// 层次遍历(非递归) 
void
LevelTraverse(link t)
{
    if (t == null) {
        return;
    }
    std::queue<link> linkQueue;
    linkQueue.push(t);
    while (!linkQueue.empty()) {
        PrintItem(t = linkQueue.front());
        linkQueue.pop();
        if (t->l != null) linkQueue.push(t->l);
        if (t->r != null) linkQueue.push(t->r);
    }
}
// 前序遍历(非递归) 
void
PreTraverseNR(link t)
{
    if (t == null) {
        return;
    }
    std::stack<link> linkStack;
    linkStack.push(t);
    while (!linkStack.empty()) {
        PrintItem(t = linkStack.top());
        linkStack.pop();
        if (t->r != null) linkStack.push(t->r);
        if (t->l != null) linkStack.push(t->l);
    }
}
// 找最大节点 
void
FindMax(link t)
{
    if (t == null) {
        return;
    }
    if (max < t->item) {
        max = t->item;
    }
    FindMax(t->l);
    FindMax(t->r);
}
// 找最小节点 
void
FindMin(link t)
{
    if (t == null) {
        return;
    }
    if (min > t->item) {
        min = t->item;
    }
    FindMin(t->l);
    FindMin(t->r);
}
// 计算深度(从0开始计算) 
int
CountDepth(link t)
{
    if (t == null) {
        return -1;
    }
    return MAX(CountDepth(t->l), CountDepth(t->r)) + 1;
}
// 计算所有节点数目 
int
CountNodes(link t)
{
    if (t == null) {
        return 0;
    }
    return CountNodes(t->l) + CountNodes(t->r) + 1;
}
// 计算叶子节点数目 
int
CountLeaves(link t)
{
    if (t == null) {
        return 0;
    }
    if (!CountLeaves(t->l) && !CountLeaves(t->r)) {
        return 1;
    }
    return CountLeaves(t->l) + CountLeaves(t->r);
}
// 清空一棵树 
void
DeleteTree(link t)
{
    if (t == null) {
        return;
    }
    if (!(t->l) && !(t->r)) {
        free(t);
        return;
    }
    DeleteTree(t->l);
    DeleteTree(t->r);
    free(t);
}

int
main(int argc, char** argv)
{
    link t, t1, t2, t3, t4;
    t = InitTree(1);
    t1 = AddLeftNode(t, 2);
    t2 = AddRightNode(t, 3);
    t3 = AddLeftNode(t1, 4);
    t4 = AddRightNode(t1, 5);
    
    
    PreTraverse(t);
    NEXTLINE;
    InTraverse(t);
    NEXTLINE;
    PostTraverse(t);
    NEXTLINE;
    LevelTraverse(t);
    NEXTLINE;
    PreTraverseNR(t);
    NEXTLINE;
 
    FindMax(t);
    FindMin(t);
    printf("Maxima Item in tree: %d\n", max);
    printf("Minima Item in tree: %d\n", min);
    
    printf("Depth of the tree(start from 0): %d\n", CountDepth(t));
 
    printf("Number of the nodes of the tree: %d\n", CountNodes(t));
    
    printf("Number of the leaves of the tree: %d\n", CountLeaves(t));
    
    
    DeleteTree(t);
    
    system("pause");
    return 0;
}