C++基础语法梳理：算法丨查找算法（全）

Posted 2021-10-22 一起学编程

本期是C++基础语法分享的第十七节，今天给大家来梳理一下查找算法！

顺序查找

int SequentialSearch(vector<int>& v, int k) {
	for (int i = 0; i < v.size(); ++i)
		if (v[i] == k)
			return i;
	return -1;
}


/* The following is a Sentinel Search Algorithm which only performs 
    just one test in each loop iteration thereby reducing time complexity */

int BetterSequentialSearch(vector<int>& v, int k) {
    int last = v[v.size()-1];
    v[v.size()-1] = k;
    int i = 0;
	while (v[i]!= k)
        	i++;
    v[v.size()-1] = last;
    if(i < v.size()-1 || v[v.size()-1] == k)
        return i;
    return -1;
}

 二分查找（折半查找）

// 非递归

int BinarySearch(vector<int> v, int value , int low, int high) {
	if (v.size() <= 0) {
		return -1;
	}
	while (low <= high) {
		int mid = low + (high - low) / 2;
		if (v[mid] == value) {
			return mid;
		}
		else if (v[mid] > value) {
			high = mid - 1;
		}
		else {
			low = mid + 1;
		}
	}

	return -1;
}

// 递归
int BinarySearch2(vector<int> v, int value, int low, int high)
{
	if (low > high)
		return -1;
	int mid = low + (high - low) / 2;
	if (v[mid] == value)
		return mid;
	else if (v[mid] > value)
		return BinarySearch2(v, value, low, mid - 1);
	else
		return BinarySearch2(v, value, mid + 1, high);
}

插值查找

int InsertionSearch(int a[], int value, int low, int high)
{
    int mid = low+(value-a[low])/(a[high]-a[low])*(high-low);
    if(a[mid]==value)
        return mid;
    if(a[mid]>value)
        return InsertionSearch(a, value, low, mid-1);
    if(a[mid]<value)
        return InsertionSearch(a, value, mid+1, high);
}

斐波拉契算法

#include "stdafx.h"
#include <memory>
#include  <iostream>
using namespace std;

const int max_size=20;//斐波那契数组的长度

/*构造一个斐波那契数组*/ 
void Fibonacci(int * F)
{
    F[0]=0;
    F[1]=1;
    for(int i=2;i<max_size;++i)
        F[i]=F[i-1]+F[i-2];
}

/*定义斐波那契查找法*/  
int FibonacciSearch(int *a, int n, int key)  //a为要查找的数组,n为要查找的数组长度,key为要查找的关键字
{
  int low=0;
  int high=n-1;
  
  int F[max_size];
  Fibonacci(F);//构造一个斐波那契数组F 

  int k=0;
  while(n>F[k]-1)//计算n位于斐波那契数列的位置
      ++k;

  int  * temp;//将数组a扩展到F[k]-1的长度
  temp=new int [F[k]-1];
  memcpy(temp,a,n*sizeof(int));

  for(int i=n;i<F[k]-1;++i)
     temp[i]=a[n-1];
  
  while(low<=high)
  {
    int mid=low+F[k-1]-1;
    if(key<temp[mid])
    {
      high=mid-1;
      k-=1;
    }
    else if(key>temp[mid])
    {
     low=mid+1;
     k-=2;
    }
    else
    {
       if(mid<n)
           return mid; //若相等则说明mid即为查找到的位置
       else
           return n-1; //若mid>=n则说明是扩展的数值,返回n-1
    }
  }  
  delete [] temp;
  return -1;
}

int main()
{
    int a[] = {0,16,24,35,47,59,62,73,88,99};
    int key=100;
    int index=FibonacciSearch(a,sizeof(a)/sizeof(int),key);
    cout<<key<<" is located at:"<<index;
    return 0;
}

哈希查找

#include<stdio.h>
#include<stdlib.h>

#define SUCCESS 1
#define UNSUCCESS 0
#define OVERFLOW -1
#define OK 1
#define ERROR -1
#define MAXNUM 9999		// 用于初始化哈希表的记录 key

typedef int Status;
typedef int KeyType;

// 哈希表中的记录类型
typedef struct {
	KeyType key;
}RcdType;

// 哈希表类型
typedef struct {
	RcdType *rcd;
	int size;
	int count;
	int *tag;
}HashTable;

// 哈希表每次重建增长后的大小
int hashsize[] = { 11, 31, 61, 127, 251, 503 };
int index = 0;

// 初始哈希表
Status InitHashTable(HashTable &H, int size) {
	int i;
	H.rcd = (RcdType *)malloc(sizeof(RcdType)*size);
	H.tag = (int *)malloc(sizeof(int)*size);
	if (NULL == H.rcd || NULL == H.tag) return OVERFLOW;
	KeyType maxNum = MAXNUM;
	for (i = 0; i < size; i++) {
		H.tag[i] = 0;
		H.rcd[i].key = maxNum;
	}
	H.size = size;
	H.count = 0;
	return OK;
}

// 哈希函数：除留余数法
int Hash(KeyType key, int m) {
	return (3 * key) % m;
}

// 处理哈希冲突：线性探测
void collision(int &p, int m) {
	p = (p + 1) % m;
}

// 在哈希表中查询
Status SearchHash(HashTable H, KeyType key, int &p, int &c) {
	p = Hash(key, H.size);
	int h = p;
	c = 0;
	while ((1 == H.tag[p] && H.rcd[p].key != key) || -1 == H.tag[p]) {
		collision(p, H.size);  c++;
	}

	if (1 == H.tag[p] && key == H.rcd[p].key) return SUCCESS;
	else return UNSUCCESS;
}

//打印哈希表
void printHash(HashTable H)
{
	int  i;
	printf("key : ");
	for (i = 0; i < H.size; i++)
		printf("%3d ", H.rcd[i].key);
	printf("\\n");
	printf("tag : ");
	for (i = 0; i < H.size; i++)
		printf("%3d ", H.tag[i]);
	printf("\\n\\n");
}

// 函数声明：插入哈希表
Status InsertHash(HashTable &H, KeyType key);

// 重建哈希表
Status recreateHash(HashTable &H) {
	RcdType *orcd;
	int *otag, osize, i;
	orcd = H.rcd;
	otag = H.tag;
	osize = H.size;

	InitHashTable(H, hashsize[index++]);
	//把所有元素，按照新哈希函数放到新表中
	for (i = 0; i < osize; i++) {
		if (1 == otag[i]) {
			InsertHash(H, orcd[i].key);
		}
	}
	return OK;
}

// 插入哈希表
Status InsertHash(HashTable &H, KeyType key) {
	int p, c;
	if (UNSUCCESS == SearchHash(H, key, p, c)) { //没有相同key
		if (c*1.0 / H.size < 0.5) { //冲突次数未达到上线
			//插入代码
			H.rcd[p].key = key;
			H.tag[p] = 1;
			H.count++;
			return SUCCESS;
		}
		else recreateHash(H); //重构哈希表 
	}
	return UNSUCCESS;
}

// 删除哈希表
Status DeleteHash(HashTable &H, KeyType key) {
	int p, c;
	if (SUCCESS == SearchHash(H, key, p, c)) {
		//删除代码
		H.tag[p] = -1;
		H.count--;
		return SUCCESS;
	}
	else return UNSUCCESS;
}

int main()
{
	printf("-----哈希表-----\\n");
	HashTable H;
	int i;
	int size = 11;
	KeyType array[8] = { 22, 41, 53, 46, 30, 13, 12, 67 };
	KeyType key;

	//初始化哈希表
	printf("初始化哈希表\\n");
	if (SUCCESS == InitHashTable(H, hashsize[index++])) printf("初始化成功\\n");

	//插入哈希表
	printf("插入哈希表\\n");
	for (i = 0; i <= 7; i++) {
		key = array[i];
		InsertHash(H, key);
		printHash(H);
	}

	//删除哈希表
	printf("删除哈希表中key为12的元素\\n");
	int p, c;
	if (SUCCESS == DeleteHash(H, 12)) {
		printf("删除成功，此时哈希表为：\\n");
		printHash(H);
	}

	//查询哈希表
	printf("查询哈希表中key为67的元素\\n");
	if (SUCCESS == SearchHash(H, 67, p, c)) printf("查询成功\\n");

	//再次插入，测试哈希表的重建
	printf("再次插入，测试哈希表的重建：\\n");
	KeyType array1[8] = { 27, 47, 57, 47, 37, 17, 93, 67 };
	for (i = 0; i <= 7; i++) {
		key = array1[i];
		InsertHash(H, key);
		printHash(H);
	}

	getchar();
	return 0;
}

二叉查找树（二叉搜索查找）

/*
二叉搜索树的查找算法:
在二叉搜索树b中查找x的过程为：
1. 若b是空树，则搜索失败，否则：
2. 若x等于b的根节点的数据域之值，则查找成功；否则：
3. 若x小于b的根节点的数据域之值，则搜索左子树；否则：
4. 查找右子树。 
*/

// 在根指针T所指二叉查找树中递归地查找其关键字等于key的数据元素，若查找成功，
// 则指针p指向該数据元素节点，并返回TRUE，否则指针指向查找路径上访问的最终
// 一个节点并返回FALSE，指针f指向T的双亲，其初始调用值为NULL
Status SearchBST(BiTree T, KeyType key, BiTree f, BiTree &p){

  if(!T) { //查找不成功
    p=f;
    return false;
  }
  else if (key == T->data.key) { //查找成功
    p=T;
    return true;
  }
  else if (key < T->data.key) //在左子树中继续查找
    return SearchBST(T->lchild, key, T, p);
  else //在右子树中继续查找
    return SearchBST(T->rchild, key, T, p);
}

红黑树

#define BLACK 1
#define RED 0
#include <iostream>

using namespace std;

class bst {
private:

	struct Node {
		int value;
		bool color;
		Node *leftTree, *rightTree, *parent;

		Node() : value(0), color(RED), leftTree(NULL), rightTree(NULL), parent(NULL) { }

		Node* grandparent() {
			if (parent == NULL) {
				return NULL;
			}
			return parent->parent;
		}

		Node* uncle() {
			if (grandparent() == NULL) {
				return NULL;
			}
			if (parent == grandparent()->rightTree)
				return grandparent()->leftTree;
			else
				return grandparent()->rightTree;
		}

		Node* sibling() {
			if (parent->leftTree == this)
				return parent->rightTree;
			else
				return parent->leftTree;
		}
	};

	void rotate_right(Node *p) {
		Node *gp = p->grandparent();
		Node *fa = p->parent;
		Node *y = p->rightTree;

		fa->leftTree = y;

		if (y != NIL)
			y->parent = fa;
		p->rightTree = fa;
		fa->parent = p;

		if (root == fa)
			root = p;
		p->parent = gp;

		if (gp != NULL) {
			if (gp->leftTree == fa)
				gp->leftTree = p;
			else
				gp->rightTree = p;
		}

	}

	void rotate_left(Node *p) {
		if (p->parent == NULL) {
			root = p;
			return;
		}
		Node *gp = p->grandparent();
		Node *fa = p->parent;
		Node *y = p->leftTree;

		fa->rightTree = y;

		if (y != NIL)
			y->parent = fa;
		p->leftTree = fa;
		fa->parent = p;

		if (root == fa)
			root = p;
		p->parent = gp;

		if (gp != NULL) {
			if (gp->leftTree == fa)
				gp->leftTree = p;
			else
				gp->rightTree = p;
		}
	}

	void inorder(Node *p) {
		if (p == NIL)
			return;

		if (p->leftTree)
			inorder(p->leftTree);

		cout << p->value << " ";

		if (p->rightTree)
			inorder(p->rightTree);
	}

	string outputColor(bool color) {
		return color ? "BLACK" : "RED";
	}

	Node* getSmallestChild(Node *p) {
		if (p->leftTree == NIL)
			return p;
		return getSmallestChild(p->leftTree);
	}

	bool delete_child(Node *p, int data) {
		if (p->value > data) {
			if (p->leftTree == NIL) {
				return false;
			}
			return delete_child(p->leftTree, data);
		}
		else if (p->value < data) {
			if (p->rightTree == NIL) {
				return false;
			}
			return delete_child(p->rightTree, data);
		}
		else if (p->value == data) {
			if (p->rightTree == NIL) {
				delete_one_child(p);
				return true;
			}
			Node *smallest = getSmallestChild(p->rightTree);
			swap(p->value, smallest->value);
			delete_one_child(smallest);

			return true;
		}
		else {
			return false;
		}
	}

	void delete_one_child(Node *p) {
		Node *child = p->leftTree == NIL ? p->rightTree : p->leftTree;
		if (p->parent == NULL && p->leftTree == NIL && p->rightTree == NIL) {
			p = NULL;
			root = p;
			return;
		}

		if (p->parent == NULL) {
			delete  p;
			child->parent = NULL;
			root = child;
			root->color = BLACK;
			return;
		}

		if (p->parent->leftTree == p) {
			p->parent->leftTree = child;
		}
		else {
			p->parent->rightTree = child;
		}
		child->parent = p->parent;

		if (p->color == BLACK) {
			if (child->color == RED) {
				child->color = BLACK;
			}
			else
				delete_case(child);
		}

		delete p;
	}

	void delete_case(Node *p) {
		if (p->parent == NULL) {
			p->color = BLACK;
			return;
		}
		if (p->sibling()->color == RED) {
			p->parent->color = RED;
			p->sibling()->color = BLACK;
			if (p == p->parent->leftTree)
				rotate_left(p->sibling());
			else
				rotate_right(p->sibling());
		}
		if (p->parent->color == BLACK && p->sibling()->color == BLACK
			&& p->sibling()->leftTree->color == BLACK && p->sibling()->rightTree->color == BLACK) {
			p->sibling()->color = RED;
			delete_case(p->parent);
		}
		else if (p->parent->color == RED && p->sibling()->color == BLACK
			&& p->sibling()->leftTree->color == BLACK && p->sibling()->rightTree->color == BLACK) {
			p->sibling()->color = RED;
			p->parent->color = BLACK;
		}
		else {
			if (p->sibling()->color == BLACK) {
				if (p == p->parent->leftTree && p->sibling()->leftTree->color == RED
					&& p->sibling()->rightTree->color == BLACK) {
					p->sibling()->color = RED;
					p->sibling()->leftTree->color = BLACK;
					rotate_right(p->sibling()->leftTree);
				}
				else if (p == p->parent->rightTree && p->sibling()->leftTree->color == BLACK
					&& p->sibling()->rightTree->color == RED) {
					p->sibling()->color = RED;
					p->sibling()->rightTree->color = BLACK;
					rotate_left(p->sibling()->rightTree);
				}
			}
			p->sibling()->color = p->parent->color;
			p->parent->color = BLACK;
			if (p == p->parent->leftTree) {
				p->sibling()->rightTree->color = BLACK;
				rotate_left(p->sibling());
			}
			else {
				p->sibling()->leftTree->color = BLACK;
				rotate_right(p->sibling());
			}
		}
	}

	void insert(Node *p, int data) {
		if (p->value >= data) {
			if (p->leftTree != NIL)
				insert(p->leftTree, data);
			else {
				Node *tmp = new Node();
				tmp->value = data;
				tmp->leftTree = tmp->rightTree = NIL;
				tmp->parent = p;
				p->leftTree = tmp;
				insert_case(tmp);
			}
		}
		else {
			if (p->rightTree != NIL)
				insert(p->rightTree, data);
			else {
				Node *tmp = new Node();
				tmp->value = data;
				tmp->leftTree = tmp->rightTree = NIL;
				tmp->parent = p;
				p->rightTree = tmp;
				insert_case(tmp);
			}
		}
	}

	void insert_case(Node *p) {
		if (p->parent == NULL) {
			root = p;
			p->color = BLACK;
			return;
		}
		if (p->parent->color == RED) {
			if (p->uncle()->color == RED) {
				p->parent->color = p->uncle()->color = BLACK;
				p->grandparent()->color = RED;
				insert_case(p->grandparent());
			}
			else {
				if (p->parent->rightTree == p && p->grandparent()->leftTree == p->parent) {
					rotate_left(p);
					rotate_right(p);
					p->color = BLACK;
					p->leftTree->color = p->rightTree->color = RED;
				}
				else if (p->parent->leftTree == p && p->grandparent()->rightTree == p->parent) {
					rotate_right(p);
					rotate_left(p);
					p->color = BLACK;
					p->leftTree->color = p->rightTree->color = RED;
				}
				else if (p->parent->leftTree == p && p->grandparent()->leftTree == p->parent) {
					p->parent->color = BLACK;
					p->grandparent()->color = RED;
					rotate_right(p->parent);
				}
				else if (p->parent->rightTree == p && p->grandparent()->rightTree == p->parent) {
					p->parent->color = BLACK;
					p->grandparent()->color = RED;
					rotate_left(p->parent);
				}
			}
		}
	}

	void DeleteTree(Node *p) {
		if (!p || p == NIL) {
			return;
		}
		DeleteTree(p->leftTree);
		DeleteTree(p->rightTree);
		delete p;
	}
public:

	bst() {
		NIL = new Node();
		NIL->color = BLACK;
		root = NULL;
	}

	~bst() {
		if (root)
			DeleteTree(root);
		delete NIL;
	}

	void inorder() {
		if (root == NULL)
			return;
		inorder(root);
		cout << endl;
	}

	void insert(int x) {
		if (root == NULL) {
			root = new Node();
			root->color = BLACK;
			root->leftTree = root->rightTree = NIL;
			root->value = x;
		}
		else {
			insert(root, x);
		}
	}

	bool delete_value(int data) {
		return delete_child(root, data);
	}
private:
	Node *root, *NIL;
};

int main()
{
	cout << "---【红黑树】---" << endl;
	// 创建红黑树
	bst tree;

	// 插入元素
	tree.insert(2);
	tree.insert(9);
	tree.insert(-10);
	tree.insert(0);
	tree.insert(33);
	tree.insert(-19);

	// 顺序打印红黑树
	cout << "插入元素后的红黑树：" << endl;
	tree.inorder();

	// 删除元素
	tree.delete_value(2);

	// 顺序打印红黑树
	cout << "删除元素 2 后的红黑树：" << endl;
	tree.inorder();

	// 析构
	tree.~bst();

	getchar();
	return 0;
}

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