C语言实现，100个整数构造平衡二叉树，以树的形式输出
#include <stdlib.h>
#include <stdio.h>
#define NUM 100
int a[100];
typedef struct node {
int value;
int bf;
struct node* left;
struct node* right;
}NODE, *NODEP;
NODEP adjust(NODEP p);
/*将100个整数随机打乱*/
void init()
{
int i, j, k, n;
for(i=0;i < 100;i++)
a[i] = i;
srand((int)time(0));
for(i = 0;i < 100;i++){
j = rand()%100;
k = rand()%100;
n = a[j];
a[j] = a[k];
a[k] = n;
}
}
/*输出1被打乱的100个整数*/
void output()
{
int i;
for(i =0;i < NUM;i++)
printf(((i+1)%10 == 0)?"%5d\n":"%5d", a[i]);
putchar('\n');
}
/*取得节点的深度*/
int get_deep(NODEP p)
{
int l, r, max;
if (p == NULL)
return 0;
l = get_deep(p->left);
r = get_deep(p->right);
max = (l >=r)?l:r;
return 1+max;
}
/*设置节点的bf（平衡因子）位，再调整树满足平衡二叉树*/
NODEP set_bf(NODEP p)
{
int l, r;
if (p == NULL)
return NULL;
p->left = set_bf(p->left);
p->right = set_bf(p->right);
l = get_deep(p->left);
r = get_deep(p->right);
p->bf = l-r;
p->left = set_bf(p->left);
p->right = set_bf(p->right);
if ((p->bf ==2)||(p->bf == -2)) {
p = adjust(p);
return p;
}
return p;
}
/*在平衡二叉树中插入节点*/
void insert(NODEP p, int i)
{
NODEP q;
if (p->value < i) {
if(p->right == NULL) {
q = (NODEP)malloc(sizeof(NODE));
q->value = i;
q->bf = 0;
q->left = NULL;
q->right = NULL;
p->right = q;
}
else
insert(p->right, i);
}
if (p->value > i) {
if (p->left == NULL) {
q= (NODEP)malloc(sizeof(NODE));
q->value = i;
q->bf = 0;
q->left = NULL;
q->right = NULL;
p->left = q;
}
else
insert(p->left, i);
}
}
/*调整插入节点后的树，使其仍满足平衡二叉树特性*/
NODEP adjust(NODEP p)
{
NODEP n, m;
if (p->bf == 2) {
n = p->left;
/*LL*/
if (n->bf == 1) {
p->left = n->right;
n->right = p;
return n;
}
/*LR*/
else {
m = n->right;
n->right = m->left;
m->left = n;
p->left = m->right;
m->right = p;
return m;
}
}
if (p->bf == -2) {
n = p->right;
/*RR*/
if (n->bf == -1) {
p->right = n->left;
n->left = p;
return n;
}
/*RL*/
else {
m = n->left;
n->left = m->right;
m->right = n;
p->right = m->left;
m->left= p;
return m;
}
}
}
void output1(NODEP root);
/*构建平衡二叉树*/
NODEP insert_all()
{
int i;
NODEP root;
root = (NODEP)malloc(sizeof(NODE));
root->left = NULL;
root->right = NULL;
for(i = 0,root->value = a[i++];i < NUM;i++) {
insert(root, a[i]);
root = set_bf(root);
}
return root;
}
/*以树的结构输出*/
void output1(NODEP root)
{
if (root == NULL)
return;
printf("%d", root->value);
putchar('(');
output1(root->left);
putchar(',');
output1(root->right);
putchar(')');
}
int main()
{
init();
output();
NODEP root;
root = insert_all();
output1(root);
return 1;
}
输出：
71 96 84 3 82 5 0 75 8 89
10 15 12 16 14 51 66 4 87 26
20 76 97 23 24 31 63 85 22 93
78 38 35 33 34 56 73 88 50 47
42 59 40 94 57 45 41 7 72 37
2 18 1 74 54 55 32 79 46 70
60 99 80 83 64 44 62 6 48 29
52 11 36 19 58 90 17 77 30 68
43 67 65 27 49 92 39 53 9 13
25 28 91 21 81 69 98 61 86 95
47(26(8(5(3(1(0(,),2(,)),4(,)),7(6(,),)),15(12(10(9(,),11(,)),14(13(,),)),20(18(16(,17(,)),19(,)),23(22(21(,),),24(,25(,)))))),35(31(29(27(,28(,)),30(,)),33(32(,),34(,))),40(37(36(,),38(,39(,))),44(42(41(,),43(,)),45(,46(,)))))),71(56(51(49(48(,),50(,)),54(52(,53(,)),55(,))),63(59(57(,58(,)),61(60(,),62(,))),66(64(,65(,)),68(67(,),70(69(,),))))),84(76(73(72(,),75(74(,),)),79(78(77(,),),82(80(,81(,)),83(,)))),93(89(87(85(,86(,)),88(,)),91(90(,),92(,))),96(94(,95(,)),98(97(,),99(,)))))))
总结：1、一直没找到一个办法以树的结构输出书，那样看起来更直观，目前就是一个“（）”代表一对二叉树，代表一层。
2、对于二叉排序树，采用中序输出，正好是由小到大
3、在递归程序中，改变程序先后顺序，可决定是从内层向外层执行，还是层外层向内层执行
后续：用树的结构形象地输出树。
1、算法应该是在脑袋中有一定思想再去编程，而不是在编程过程中尝试
#include <stdlib.h>
#include <stdio.h>
/*50个整数输出更容易观察，超过50就会换行，所以设置50*/
#define NUM 50
int a[100];
typedef struct node {
int value;
int bf;
struct node* left;
struct node* right;
}NODE, *NODEP;
NODEP adjust(NODEP p);
void init()
{
int i, j, k, n;
for(i=0;i < 100;i++)
a[i] = i;
srand((int)time(0));
for(i = 0;i < 100;i++){
j = rand()%100;
k = rand()%100;
n = a[j];
a[j] = a[k];
a[k] = n;
}
}
void output()
{
int i;
for(i =0;i < NUM;i++)
printf(((i+1)%10 == 0)?"%5d\n":"%5d", a[i]);
putchar('\n');
}
int get_deep(NODEP p)
{
int l, r, max;
if (p == NULL)
return 0;
l = get_deep(p->left);
r = get_deep(p->right);
max = (l >=r)?l:r;
return 1+max;
}
NODEP set_bf(NODEP p)
{
int l, r;
if (p == NULL)
return NULL;
p->left = set_bf(p->left);
p->right = set_bf(p->right);
l = get_deep(p->left);
r = get_deep(p->right);
p->bf = l-r;
p->left = set_bf(p->left);
p->right = set_bf(p->right);
if ((p->bf ==2)||(p->bf == -2)) {
p = adjust(p);
return p;
}
return p;
}
void insert(NODEP p, int i)
{
NODEP q;
if (p->value < i) {
if(p->right == NULL) {
q = (NODEP)malloc(sizeof(NODE));
q->value = i;
q->bf = 0;
q->left = NULL;
q->right = NULL;
p->right = q;
}
else
insert(p->right, i);
}
if (p->value > i) {
if (p->left == NULL) {
q= (NODEP)malloc(sizeof(NODE));
q->value = i;
q->bf = 0;
q->left = NULL;
q->right = NULL;
p->left = q;
}
else
insert(p->left, i);
}
}
NODEP adjust(NODEP p)
{
NODEP n, m;
if (p->bf == 2) {
n = p->left;
if (n->bf == 1) {
p->left = n->right;
n->right = p;
return n;
}
else {
m = n->right;
n->right = m->left;
m->left = n;
p->left = m->right;
m->right = p;
return m;
}
}
if (p->bf == -2) {
n = p->right;
if (n->bf == -1) {
p->right = n->left;
n->left = p;
return n;
}
else {
m = n->left;
n->left = m->right;
m->right = n;
p->right = m->left;
m->left= p;
return m;
}
}
}
void output1(NODEP root);
NODEP insert_all()
{
int i;
NODEP root;
root = (NODEP)malloc(sizeof(NODE));
root->left = NULL;
root->right = NULL;
for(i = 0,root->value = a[i++];i < NUM;i++) {
insert(root, a[i]);
root = set_bf(root);
}
return root;
}
void output1(NODEP root)
{
if (root == NULL)
return;
printf("%d", root->value);
putchar('(');
output1(root->left);
putchar(',');
output1(root->right);
putchar(')');
}
/*构造另外一棵树，树分为deep层，该树为一个矩阵，left指向下（为下一层），right指向右（为一层），每一层为之前树中每一层的元素，下一层为之前树中下一层的元素*/
NODEP get_output(NODEP root, NODEP head, int n, int deep)
{
int m = n;
NODEP head_next = head;
NODEP p;
while(m--)
head_next = head_next->left;
while(head_next->right != NULL)
head_next = head_next->right;
p = (NODEP)malloc(sizeof(NODE));
head_next->right = p;
p->right = NULL;
p->left = NULL;
if (root == NULL)
p->value = 100;
else
p->value = root->value;
++n;
if (n < deep) {
/*如果树不为空，则将左右子孩子传入*/
if (root != NULL) {
head = get_output(root->left, head, n, deep);
head = get_output(root->right, head, n, deep);
}
/*如果树为空，为了保持新树的结构，继续向其中传入空值*/
else {
head = get_output(root, head, n, deep);
head = get_output(root, head, n, deep);
}
}
return head;
}
int main()
{
int deep, i, j, k;
init();
output();
NODEP root, head, p, q;
root = insert_all();
output1(root);
deep = get_deep1(root);
printf("\n%d\n", deep);
for (i = 0,head = (NODEP)malloc(sizeof(NODE)), head->left = NULL, head->right = NULL , p = head;i < (deep - 1);i++) {
q = (NODEP)malloc(sizeof(NODE));
q->right = NULL;
q->left = NULL;
p->left = q;
p = q;
}
head = get_output(root, head, 0, deep);
for (p = head, i = deep;p != NULL;p = p->left, i--, putchar('\n')) {
j = i-1;
k = 1;
while(j--)
k *= 2;
k--;
while(k--)
printf(" ");
for(q = p->right;q != NULL;q = q->right) {
/*空节点输出NO*/
printf((q->value == 100)?"NO":"%2d", q->value);
j = i;
k = 1;
while(j--)
k*=2;
k--;
while(k--)
printf(" ");
}
}
return 1;
}
