数据结构考研复习 | 2021王道第2章·线性表的顺序表示之综合应用题(C语言实现)

#include "stdafx.h"
#include <iostream>
#define MAXSIZE 100
typedef int ElemType;
typedef int DataType;

typedef struct
{
	ElemType data[MAXSIZE];
	int length;
} SqList;

bool InitList(SqList *L)
{
	L->length = 0;
	return true;
}

bool ListInsert(SqList *L, int i, ElemType e)
{
	if (i < 1 || i > L->length + 1)
		return false;
	if (L->length == MAXSIZE)
		return false;
	for (int k = L->length; k >= i - 1; k--)
	{
		L->data[k + 1] = L->data[k];
	}
	L->data[i - 1] = e;
	L->length++;
	return true;
}

bool ListDelete(SqList *L, int i, ElemType *e)
{
	if (i > L->length || i <= 0)
		return false;
	if (L->length == 0)
		return false;
	*e = L->data[i - 1];
	for (i = i - 1; i < L->length - 1; i++)
	{
		L->data[i] = L->data[i + 1];
	}
	L->length--;
	return true;
}

bool LocateElem(SqList L, ElemType e)
{
	int i;
	for (i = 0; i < L.length; i++)
	{
		if (L.data[i] == e)
			return i + 1;
	}
	return false;
}

bool ListEmpty(SqList L)
{
	/*判断线性表是否为空*/
	if (L.length == 0)
		return true;
	else
		return false;
}

bool ClearList(SqList *L)
{
	L->length = 0;
	return true;
}

bool ListLength(SqList L)
{
	return L.length;
}

bool GetElem(SqList L, int i, ElemType *e)
{
	if (L.length == 0 || i < 1 || i > L.length)
		return false;
	*e = L.data[i - 1];
	return true;
}

void Union(SqList *La, SqList Lb)
{
	int La_len = La->length;
	int Lb_len = ListLength(Lb);
	ElemType e;
	int i = 1;
	for (i = 1; i < Lb_len; i++)
	{
		GetElem(Lb, i, &e);
		if (!LocateElem(*La, e))
			ListInsert(La, ++La_len, e);
	}
}

int printList(SqList L)
{
	if (L.length == 0)
	{
		printf("链表为空\n");
		return 0;
	}
	for (int i = 0; i < L.length; i++)
	{
		printf("%d ", L.data[i]);
	}
	printf("\n");
	return 1;
}

bool delMin(SqList *L,ElemType *e)//2.2-1
{
	if (L->length == 0)
		return false;
	*e = L->data[0];
	int pos = 0;
	for (int j = 0; j < L->length; j++) {
		if (*e > L->data[j]) {
			*e = L->data[j];
			pos = j;
		}
	}
	printf("min:%d,pos:%d\n", *e, pos);
	L->data[pos] = L->data[L->length - 1];
	return true;
}

bool reverse(SqList *L) {//2.2-2
	if (L->length == 0)
		return false;
	ElemType temp;
	for (int i = 0; i < L->length/2; i++) {
		temp = L->data[i];
		L->data[i] = L->data[L->length - i - 1];
		L->data[L->length - i - 1] = temp;
	}
	return true;
}

void del_x_1(SqList *L, ElemType x) {//2.2-3 时间复杂度为O(n^2)
	for (int i = 0; i < L->length; i++) {
		if (L->data[i] == x) {
			for (int j = i; j < L->length; j++) {
				L->data[j] = L->data[j + 1];
			}
			L->length = L->length -1;
		}
	}
}

void del_x_2(SqList *L, ElemType x) {//2.2-3 时间复杂度为O(n)
	int k = 0;
	for (int i = 0; i < L->length; i++) {
		if (L->data[i] != x) {
			L->data[k] = L->data[i];
			k++;
		}
	}
	L->length = k;
}

void del_x_3(SqList *L, ElemType x) {//2.2-3 时间复杂度为O(n)
	int k = 0;
	for (int i = 0; i < L->length; i++) {
		if (L->data[i] == x)
			k++;
		else
			L->data[i - k] = L->data[i];
	}
	L->length -= k;
}

bool del_s_t_1(SqList *L, ElemType s, ElemType t) {//2.2-4 删除s-t元素
	if (L->length == 0 || s >= t) {
		printf("error");
		return false;
	}
	int count = 0;
	int pos = 0;
	for (int i = 0; i < L->length; i++) {
		if (L->data[i] > s && L->data[i] < t) {
			//printf("%d\n", L->data[i]);
			count++;
			pos = i;
		}
	}
	for (int j = pos-count+1; j < L->length; j++) {
		L->data[j] = L->data[j + count];
	}
	L->length-=count;
}

bool del_s_t_2(SqList *L,ElemType s,ElemType t) {//2.2-5 删除s-t元素
	if (L->length == 0 || s >= t) {
		printf("error");
		return false;
	}
	for (int i = 0; i < L->length; i++) {
		if (L->data[i] >= s && L->data[i] <= t) {
			//printf("%d\n", L->data[i]);
			for (int j = i; j < L->length; j++) {
				L->data[j] = L->data[j + 1];
			}
			L->length--;
			i--;
		}
	}
}

void del_repeated(SqList *L) {//2.2-6 删除重复元素
	//int count = 0;
	//bool found = false;
	//for (int i = 0; i < L->length; i++) {
	//	if (L->data[i] == L->data[i + 1]) {
	//		found = true;
	//		count++;
	//	}
	//	else if (found == true) {
	//		for (int j = i - 1; j < L->length; j++) {
	//			L->data[j] = L->data[j + count];
	//		}
	//		L->length -= count;
	//		found = false;
	//	}
	//}
	int i = 0;
	for (int j = 1; j < L->length; j++) {
		if (L->data[i] != L->data[j])
			L->data[++i] = L->data[j];
	}
}
bool list_merge(SqList L1,SqList L2,SqList &L3) {//2.2-7 有序表合并
	//if (L1.length + L2.length > L3.length)
	//	return false;
	int i = 0,j = 0, k = 0;
	
	while (i < L1.length && j < L2.length) {
		if (L1.data[i] <= L2.data[j])
			L3.data[k++] = L1.data[i++];
		else
			L3.data[k++] = L2.data[j++];
	}
	while (i < L1.length)
		L3.data[k++] = L1.data[i++];
	while (j < L2.length)
		L3.data[k++] = L2.data[j++];
	L3.length = k;
	return true;
 }

void reverse(DataType *a,int m,int n) {//2.2-8 顺序表位置互换
	DataType b[MAXSIZE];
	memset(b, 0, m * sizeof(DataType));
	memcpy(b, a, m * sizeof(DataType));
	for (int i = 0; i < n; i++)
		b[i] = a[m + i];
	for (int i = n; i < m + n; i++)
		b[i] = a[i - n];
	for (int i = 0; i < m + n; i++) {
		a[i] = b[i];
	}
}

void search_x(SqList *L, DataType x) {//2.2-9 查找x
	int i = 0, j = L->length - 1;
	while (i <= j) {
		int m = (i + j) / 2;
		if (L->data[m] < x && L->data[m + 1] > x) {
			//printf("not found\n");
			L->length++;
			for (int ii = L->length - 1; ii > m; ii--)
				L->data[ii] = L->data[ii-1];
			L->data[m + 1] = x;
			return;
		}
		else if (L->data[m] > x) {
			j = m;
		}
		else if (L->data[m] < x) {
			i = m;
		}
		else {
			//printf("found\n");
			DataType temp = L->data[m];
			L->data[m] = L->data[m+1];
			L->data[m + 1] = temp;
			return;
		}
	}
}

void moving(DataType *r,int p,int n) {//2.2-10 循环左移P个位置
	DataType b[MAXSIZE];
	memset(b, 0, n * sizeof(DataType));
	memcpy(b, r, n * sizeof(DataType));
	for (int i = 0; i < p; i++)
		b[n-p+i] = r[i];
	for (int i = 0; i < n-p; i++)
		b[i] = r[p+i];
	for (int i = 0; i < n; i++) {
		r[i] = b[i];
	}
}//时间复杂度为O(n)，空间复杂度为O(n)，空间复杂度可以优化为O(p)

int get_median(int *a,int *b,int n) {//2.2-11 寻找中位数
	int i = 0, j = 0;
	int k;
	while (i + j != n-2) {
		if (a[i] <= b[j]) {
			i++;
			k = a[i];
		}
		else if (a[i] > b[j]) {
			j++;
			k = b[j];
		}
	}
	return k;
}//时间复杂度为O(n)，空间复杂度为O(1)

int get_median_2(int *a, int *b, int n) {//2.2-11 寻找中位数(优解)
	int s1 = 0, d1 = n - 1, m1, s2 = 0, d2 = n - 1, m2;
	//分别表示序列A和B的首位数、末位数、中位数
	while (s1 != d1 || s2 != d2) {
		m1 = (s1 + d1) / 2;
		m2 = (s2 + d2) / 2;
		if (a[m1] == b[m2])
			return a[m1];
		if (a[m1] < b[m2]) {
			if ((s1 + d1) % 2 == 0) {
				s1 = m1; 
				d2 = m2;
			}
			else {
				s1 = m1 + 1;
				d2 = m2;
			}
		}
		else {
			if ((s2+ d2) % 2 == 0) {
				d1 = m1;
				s2 = m2;
			}
			else {
				d1 = m1;
				s2 = m2+1;
			}
		}
	}
	return a[s1] < b[s2] ? a[s1]:b[s2];
}//时间复杂度为O(log2n)，空间复杂度为O(1)

int get_main_element(int *a,int n) {//2.2-12 寻找主元素
	int c;//候选主元素
	for (int i = 0; i < n; i++) {
		if (a[i] == a[i + 1]) {
			c = a[i];
			break;
		}
	}
	for (int i = n / 2; i < n; i++) {
		if (a[i] == c && a[i]==a[i+1])
			return c;
	}
	return -1;
}

void quick_sort(int s[], int l, int r)
{
	if (l < r)
	{
		//Swap(s[l], s[(l + r) / 2]); //将中间的这个数和第一个数交换 参见注1
		int i = l, j = r, x = s[l];
		while (i < j)
		{
			while (i < j && s[j] >= x) // 从右向左找第一个小于x的数
				j--;
			if (i < j)
				s[i++] = s[j];

			while (i < j && s[i] < x) // 从左向右找第一个大于等于x的数
				i++;
			if (i < j)
				s[j--] = s[i];
		}
		s[i] = x;
		quick_sort(s, l, i - 1); // 递归调用 
		quick_sort(s, i + 1, r);
	}
}

int get_min_int(int *a, int n) {//2.12-13 寻找最小正整数
	quick_sort(a,0, n-1);
	bool have1 = true;
	for (int i = 0; i < n; i++) {
		if (a[i] <= 0)
			continue;
		else if (have1 == true && a[i] > 1)
			return 1;//只限首个大于0的数大于1时，返回1
		else if (a[i] + 1 != a[i + 1] && a[i] != a[i+1])
			return a[i] + 1;
		else
			have1 = false;
	}
	return -1;
}//时间复杂度为0(nlogn)，空间复杂度为O(1)

int get_min_int_2(int *a, int n) {//2.12-13 寻找最小正整数，空间换时间
	int i, *b;
	b = (int *)malloc(sizeof(int)*n);
	memset(b, 0, sizeof(int)*n);
	for (int i = 0; i < n; i++) {
		if (a[i] > 0)b[a[i] - 1] = 1;
	}
	for (i = 0; i < n; i++)
		if (b[i] == 0)
			break;
	return i + 1;
}//时间复杂度为0(n)，空间复杂度为O(n)

int main()
{
	SqList L;
	InitList(&L);//初始化
	SqList L2;
	InitList(&L2);
	for (int i = 0; i < 10; i++) //向线性表插入10个元素
	{
		//ListInsert(&L, i + 1, i*i-8*i);
		//ListInsert(&L, i + 1, i*i - 4 * i + 4);
		//ListInsert(&L, i + 1, 2+i);
		ListInsert(&L, i + 1, i*i+1);
		//ListInsert(&L2, i + 1, i-2);
	}
	//printList(L);
	//printList(L2);

	//2.2-1 删除最小元素
	//int num;
	//if (delMin(&L, &num)) {
	//	printf("return:%d\n", num);
	//	printList(L);
	//}
	//else
	//	printf("linear list is empty");

	//2.2-2 线性表倒置
	//reverse(&L);

	//2.2-3 删除所有x
	//del_x_3(&L,1);

	//2.2-4 删除s-t元素
	//del_s_t_1(&L, 3, 5);

	//2.2-5 删除s-t元素
	//del_s_t_2(&L, 0, 20);

	//2.2-6 删除重复元素
	//del_repeated(&L);

	//2.2-7 有序表合并
	//SqList L3;
	//InitList(&L3);
	//list_merge(L, L2, L3);
	//printList(L3);

	//2.2-8 顺序表位置互换
	//DataType a[10] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
	//reverse(a, 4, 6);
	//for (int i = 0; i < 10; i++) {
	//	printf("%d ", a[i]);
	//}

	//2.2-9 查找x
	//search_x(&L, 26);

	//2.2-10 循环左移P个位置
	//DataType a[10] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
	//moving(a, 6, 10);
	//for (int i = 0; i < 10; i++) {
	//	printf("%d ", a[i]);
	//}

	//2.2-11 寻找中位数
	//DataType a[9] = { 1, 3, 5, 7, 9, 11, 13, 15, 17 };
	//DataType b[9] = { 2, 4, 6,8, 10, 12, 14, 16, 18 };
	//printf("%d\n",get_median(a,b,9));
	//printf("%d", get_median_2(a, b, 9));

	//2.2-12 寻找主元素
	//int a[9] = { 1, 3, 3, 7, 9, 11, 3, 3, 17 };
	//int b[9] = { 1, 3, 3, 7, 9, 11, 3, 15, 17 };
	//printf("%d\n",get_main_element(a,9));
	//printf("%d\n", get_main_element(b, 9));

	//2.12-13 寻找最小正整数
	int a[9] = { 9, 3, 3, 4, 1, 2, 5, 6, 7 };
	int b[9] = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
	printf("%d\n",get_min_int_2(a, 9));
	printf("%d\n", get_min_int_2(b, 9));
	//for (int i = 0; i < 9; i++) {
	//	printf("%d ", a[i]);
	//}

	//printf("%d\n", get_main_element(a, 9));
	//printf("%d\n", get_main_element(b, 9));

	//printList(L);
	printf("\n");
	system("pause");
	return 0;
}