Chap3: question: 11 - 18

11. double 数值的整数次方

note: 浮点数表示时有误差，判等时必须自己根据精度要求实现。

#include <iostream>
#include <ctime>
using namespace std;
bool Power_Input_Invalid = false; // set a Global variant to check the input.

bool equal(double num1, double num2) // key 1
{
	if(num1 - num2 >= -0.0000001 && num1 - num2 <= 0.0000001)
		return true;
	return false;
} 

double Power(double base, int exponent)
{
	Power_Input_Invalid = false;
	if(equal(base,0.0) && exponent <= 0) /* 无意义 */
	{
		Power_Input_Invalid = true;
		return 0.0;
	}
	if(exponent == 0) return 1.0;
	bool sigmal = false; // 0 denote positive exp
	bool overflow = false;
	if(exponent < 0)
	{
		if(exponent == INT_MIN) { overflow = true; exponent++;}
		exponent *= -1;
		sigmal = true;   // 1 denote negative exp
	} 

	double result = base, tem = 1.0;
	while(exponent - 1 != 0)                // key 2
	{
		if(exponent & 1) tem *= result;
		result *= result;
		exponent >>= 1;
	}
	result *= tem;
	if(overflow) result *= base;
	if(sigmal) result = 1.0 / result;
	return result;
} 

int main()
{
	double d;
	int v;
	clock_t start;
	int k = 0;
	while(cin >> d >> v)
	{
		start = clock();
		double result = Power(d, v);
		if(!Power_Input_Invalid)
			cout << "Case " << k++ << ": " << Power(d, v) <<
			"   time:" << (clock()-start) << "ms" << endl;
		else
			cout << "Invalid input." << endl;
	}
	return 0;
}

12.打印 1 到最大的 n 位数

note: n 可能很大，如 100，就容易溢出

a. 字符串模拟法

 #include <stdio.h>
 #include <string.h>
 bool Increment(char *);
 void printNumber(char *);

 void print1ToMax(int n)
 {
     if(n <= ) return;
     char *number = new char[n+];
     memset(number, '', n);
     number[n] = '\0';
     while(!Increment(number)) // Increment() return true denote overflow
     {
         printNumber(number);
     }
     delete[] number;
 }

 bool Increment(char *number)
 {
     bool overflow = false;
     int carry = , len = strlen(number);
     for(int i = len -; i >= ; --i)   /*   note: 从最右端开始增 is more easy    */
     {
         number[i] += carry;
         if(i == len -)  ++number[i];
         if(number[i] > '')
         {
             if(i == )
                 overflow = true;
             else
             {
                 number[i] -= ;
                 carry = ;
             }
         }
         else break;
     }
     return overflow;
 }

 void printNumber(char *number)
 {
     if(number == NULL) return;
     bool begin = false;
     for(int i = ; number[i] != '\0'; ++i)
     {
         if(begin)
         {
             printf("%c", number[i]);
         }
         else if(number[i] != '')
         {
             begin = true;
             printf("%c", number[i]);
         }
     }
     printf("\t");
 }

 int main()
 {
     int N;
     while(scanf("%d", &N) == )
     {
         print1ToMax(N);
     }
     return ;
 }

Code

b. 数字排列法（由后到前，递归增加）

void printNumber(char *);
void AddRecursively(char *, int, int);

void print1ToMax(int n)
{
    if(n <= 0) return;
    char *number = new char[n +1];
    memset(number, '0', n);
    number[n] = 0;
    AddRecursively(number, n, 0);
    delete[] number;
}

void AddRecursively(char *number, int length, int begin)
{
    if(begin == length)
    {
        printNumber(number);
        return;
    }
    for(int i = '0'; i <= '9'; ++i)
    {
        number[begin] = i;
        AddRecursively(number, length, begin +1);
    }
}

void printNumber(char *number)
{
    if(number == NULL) return;
    bool begin = false;
    for(int i = 0; number[i] != '\0'; ++i)
    {
        if(begin)
        {
            printf("%c", number[i]);
        }
        else if(number[i] != '0')
        {
            begin = true;
            printf("%c", number[i]);
        }
    }
    if(!begin) return;
    printf("\t");
}

运行结果如上。
13. O(1) 时间删除链表结点

其值赋为后继的值，删除后继结点。时间：[O(1) * (n-1) + O(n)] / n ≈ O(1).          //  若检测欲删除结点是否在链表内，则 O(n) .

 #include <stdio.h>
 struct ListNode{
     int v;
     ListNode * next;
 };
 enum{ N = }; // set the number of Node in ListNode
 /*************************************************************************/
 /********  Basic function which were needed ******************************/
 /*  creat a List with the value of Node is 1, 2, …，N-1.  */
 ListNode* creatList(){
     ListNode * pHead = NULL, *p;
     for(int i = ; i < N; ++i){
         ListNode *s = new ListNode;
         s->v = i;
         s->next = NULL;
         if(pHead != NULL){
             p->next = s;
             p = p->next;
         }else{
             pHead = s;
             p = pHead;
         }
     }
     return pHead;
 }
 void printList(ListNode *pHead){
     if(pHead == NULL) { printf("NULL"); return; }
     printf("%d —> ", pHead->v);
     printList(pHead->next);
 }
 void release(ListNode *pHead) {
     if(pHead == NULL) return;
     release(pHead->next);
     delete[] pHead;
     pHead = NULL;
 }
 /****************************************************************************************/
 void deleteNode(ListNode *pHead, ListNode * pToBeDeleted){
     if(pHead == NULL || pToBeDeleted == NULL) return;
     /*   not the last one  */
     if(pToBeDeleted->next != NULL){
         ListNode *pNext = pToBeDeleted->next;
         pToBeDeleted->v = pToBeDeleted->next->v;
         pToBeDeleted->next = pToBeDeleted->next->next;
         delete[] pNext;
         pNext = NULL;
     }else{
         if(pToBeDeleted == pHead) {  // List only has one Node
             delete [] pHead;
             pHead = NULL;
             return;
         }else {                     // the last one && not the head
             ListNode *p = pHead;
             while(p->next != pToBeDeleted && p->next != NULL) p = p->next;
             if(p->next == NULL) return;
             else{
                 ListNode *s = p->next;
                 p->next = NULL;
                 delete[] s;
             }
         }
     }
 }

 int main()
 {
     ListNode *pHead = creatList();
     printList(pHead);
     printf("\ndelete 3: \n");

     deleteNode(pHead, pHead->next->next); // delete 3 (among)
     printList(pHead);
     printf("\ndelete 1: \n");

     deleteNode(pHead, pHead);      // delete 1 (head)
     printList(pHead);
     printf("\ndelete 4: \n");

     deleteNode(pHead, pHead->next); // delete 4 (tail)
     printList(pHead);
     printf("\n");
 /*
     ListNode *s = new ListNode; // not in the list, if wanted more robust , need check before deleteNode
     deleteNode(pHead, s);
     printList(pHead);
     printf("\n");
     delete[] s;
 */
     release(pHead);
     return ;
 }

Code

14. 使整数数组中奇数位于前部分，偶数位于后部分。

解耦合，使 Reorder函数可以复用。如代码：

 #include <stdio.h>

 bool isEven(int v)
 {
     return (v & ) == ;
 }

 bool isPositive(int v)
 {
     return v > ;
 }

 void Reorder(int data[], int length, bool (*fcn)(int))
 {
     if(length <= ) return;
     int low = , high = length - ;
     while(low < high)
     {
         while(low < high && fcn(data[low])) ++low;
         while(low < high && !fcn(data[high])) --high;
         if(low < high)
         {
             int tem = data[low];
             data[low] = data[high];
             data[high] = tem;
         }
     }
 }

 void printf(int data[], int length)
 {
     for(int i = ; i < length; ++i)
     {
         printf("%-3d", data[i]);
     }
     printf("\n");
 }
 int main()
 {
     printf("Test 1: odd element before even element. \n");
     int test1[] = {, , , , , , };
     printf(test1, sizeof(test1)/sizeof(int));
     Reorder(test1,sizeof(test1)/, isEven);   /*  奇数放前面    */
     printf(test1, sizeof(test1)/);

     printf("Test 2: positive before Non-positive. \n");
     int test2[] = {-, , -, , , -, };
     printf(test2, sizeof(test2)/sizeof(int));
     Reorder(test2,sizeof(test2)/, isPositive); /*  正数放前面  */
     printf(test2, sizeof(test2)/);

     return ;
 }

Code

 15. 链表中倒数第 k 个结点

note: k = 0 或 k > LinkList.length().

#include <stdio.h>
struct ListNode{
	int v;
	ListNode * next;
};
enum{ N = 5}; // set the number of Node in ListNode
/*************************************************************************/
/********  Basic function which were needed ******************************/
/*  creat a List with the value of Node is 1, 2, …，N-1.  */
ListNode* creatList(){
	ListNode * pHead = NULL, *p;
	for(int i = 1; i < N; ++i){
		ListNode *s = new ListNode;
		s->v = i;
		s->next = NULL;
		if(pHead != NULL){
			p->next = s;
			p = p->next;
		}else{
			pHead = s;
			p = pHead;
		}
	}
	return pHead;
}
void printList(ListNode *pHead){
	if(pHead == NULL) { printf("NULL"); return; }
	printf("%d —> ", pHead->v);
	printList(pHead->next);
}
void release(ListNode *pHead) {
	if(pHead == NULL) return;
	release(pHead->next);
	delete[] pHead;
	pHead = NULL;
}
/****************************************************************************************/

ListNode* FindKthTOTail(ListNode *pListHead, unsigned int k)
{
	if(pListHead == NULL || k == 0) return NULL; // Note 1: for robust
	ListNode *pA, *pB;
	pA = pB = pListHead;
	for(unsigned int i = 0; i < k-1; ++i) // go ahead k-1 steps
	{
		if(pB->next == NULL) return NULL; // Note 2: the length of LinkList if less than k
		else pB = pB->next;
	}
	while(pB->next != NULL)
	{
		pA = pA->next;
		pB = pB->next;
	}
	return pA;
}

int main()
{
	ListNode *pHead = creatList();
	printf("LinkList: ");
	printList(pHead);
	printf("\nTest: \n");

	ListNode *p;
	for(int k = 0; k <= N; ++k)
	{
		p = FindKthTOTail(pHead, k);
		if(p != NULL) printf("倒数第 %d 个数: %d\n", k, p->v);
		else printf("倒数第 %d 个数: Not Exist.\n", k);
	}

	release(pHead);
	return 0;
}

16. 反转链表

#include <stdio.h>
struct ListNode{
	int v;
	ListNode * next;
};
enum{ N = 10}; // set the number of Node in ListNode
/*************************************************************************/
/********  Basic function which were needed ******************************/
/*  creat a List with the value of Node is 1, 2, …，N.  */
ListNode* creatList(){
	ListNode * pHead = NULL, *p;
	for(int i = 1; i < N; ++i){
		ListNode *s = new ListNode;
		s->v = i;
		s->next = NULL;
		if(pHead != NULL){
			p->next = s;
			p = p->next;
		}else{
			pHead = s;
			p = pHead;
		}
	}
	return pHead;
}
void printList(ListNode *pHead){
	if(pHead == NULL) { printf("NULL"); return; }
	printf("%d —> ", pHead->v);
	printList(pHead->next);
}
void release(ListNode *pHead) {
	if(pHead == NULL) return;
	release(pHead->next);
	delete[] pHead;
	pHead = NULL;
}
/******************************************************/

ListNode* ReverseList(ListNode *pListHead)
{
	ListNode *pPre, *pCur, *pPost;
	pPre = NULL, pCur = pListHead;
	while(pCur != NULL)
	{
		pPost = pCur->next;
		pCur->next = pPre;
		pPre = pCur;
		pCur = pPost;
	}
	/* pCur == pPost == NULL, pPre point to the new ListHead   */
	return pPre;
}

int main()
{
	ListNode *pHead = creatList();
	printf("LinkList: ");
	printList(pHead);
	printf("\n");

	pHead = ReverseList(pHead);
	printf("Reverse1: ");
	printList(pHead);
	printf("\n");

	pHead = ReverseList(pHead);
	printf("Reverse2: ");
	printList(pHead);
	printf("\n");

	release(pHead);
	return 0;
}

a.    b.   c.

17.合并两个排序的链表（递归）

 #include <stdio.h>
 struct ListNode{
     int v;
     ListNode * next;
 };
 /*************************************************************************/
 /********  Basic functions which were needed ******************************/
 /*  creat a List with the value of Node is 1, 2, …，N.  */
 ListNode* creatList(int begin, int N){
     ListNode * pHead = NULL, *p;
     for(int i = begin; i <= N; ++i){
         ListNode *s = new ListNode;
         s->v = i;
         s->next = NULL;
         if(pHead != NULL){
             p->next = s;
             p = p->next;
         }else {
             pHead = s;
             p = pHead;
         }
     }
     return pHead;
 }
 void printList(ListNode *pHead){
     if(pHead == NULL) { printf("NULL"); return; }
     printf("%d —> ", pHead->v);
     printList(pHead->next);
 }
 void release(ListNode *pHead) {
     if(pHead == NULL) return;
     release(pHead->next);
     delete[] pHead;
     pHead = NULL;
 }
 /********************************************************************************/

 ListNode* Merge(ListNode *pHead1, ListNode *pHead2) //not create any new Node again
 {
     if(pHead1 == NULL) return pHead2;
     if(pHead2 == NULL) return pHead1;
     ListNode *pMergedHead = NULL;
     if(pHead1->v <= pHead2->v)
     {
         pMergedHead = pHead1;
         pMergedHead->next = Merge(pHead1->next, pHead2);
     }
     else
     {
         pMergedHead = pHead2;
         pMergedHead->next = Merge(pHead1, pHead2->next);
     }
     return pMergedHead; // key point
 }

 int main()
 {
     ListNode *pHead1 = creatList(, );
     printf("LinkList1: ");
     printList(pHead1);
     printf("\n");
     ListNode *pHead2 = creatList(, );
     printf("LinkList1: ");
     printList(pHead2);
     printf("\n");

     ListNode *pHead3 = Merge(pHead1, pHead2);
     printf("MergeList: ");
     printList(pHead3);
     printf("\n");

     release(pHead3);
     return ;
 } 

Code

18. 判断树 B 是否为树 A 的子结构（递归）

#include <iostream>
using namespace std;
struct BTNode{
	int v;  // default positive Integer.
	BTNode *pLeft;
	BTNode *pRight;
	BTNode(int x) : v(x), pLeft(NULL), pRight(NULL) {}
};
/********************************************************/
/*****        Basic functions          ***********/
BTNode* createBinaryTree(int r)
{
	BTNode *pRoot = new BTNode(r);
	int u, v;
	cin >> u >> v;
	if(u != 0)
		pRoot->pLeft = createBinaryTree(u);
	if(v != 0)
		pRoot->pRight = createBinaryTree(v);
	return pRoot;
}
void release(BTNode *root){
	if(root == NULL) return;
	release(root->pLeft);
	release(root->pRight);
	delete[] root;
	root = NULL;
}
/******************************************************************/

bool treeAHasTreeB(BTNode *pRootA, BTNode *pRootB){   /* check from every node in the BinaryTeee pRoot1 */
	if(pRootB == NULL) return true;
	if(pRootA == NULL) return false;
	if(pRootA->v != pRootB->v) return false;
	return treeAHasTreeB(pRootA->pLeft, pRootB->pLeft) && treeAHasTreeB(pRootA->pRight, pRootB->pRight);
}

bool isSubTree(BTNode *pRoot1, BTNode *pRoot2){
	bool result = false;
	/* define the output when A or B is NULL */
	if(pRoot2 == NULL) return true;
	if(pRoot1 == NULL) return false;
	result = treeAHasTreeB(pRoot1, pRoot2);
	if(!result) result = treeAHasTreeB(pRoot1->pLeft, pRoot2);
	if(!result) result = treeAHasTreeB(pRoot1->pLeft, pRoot2);

	return result;
}

int main(){
	int TestTime = 3, k = 1;
	while(k <= TestTime)
	{
		cout << "Test " << k++ << ":" << endl;
		cout << "Create Tree A: " << endl;
		BTNode *pRoot1 = createBinaryTree(8);
		cout << "Create Tree B: " << endl;
		BTNode *pRoor2 = createBinaryTree(8);
		if(isSubTree(pRoot1, pRoor2))
			cout << "Tree A has Tree B." << endl;
		else
			cout << "Tree A has not Tree B." << endl;

		release(pRoot1);
		release(pRoor2);
	}
	return 0;
}