区间树上的重叠区间查找算法

2023年10月24日 272次阅读来源: 查找算法

要求：对实验二的红黑树进行扩展，构造1000个节点的区间树，在区间树上查找具有最小低端点的重叠区间

思想：

1.对红黑树节点的扩展：每个节点结构如下：

typedef structnode{
    timeval itimeval;  //时间区间
    int key;            //关键字：区间中的低端节点值
    int max;
//Max(pnode->left->max,pnode->right->max,pnode->itimeval.high);
    struct node * left;
    struct node * right;
    struct node * parent;
    enum rb_color  color; 
}TimeValNode,*TimeValTree;

2.对红黑树旋转算法的修改

旋转节点后修改相应节点的max值。

3.对红黑树插入算法的修改

插入的节点肯定在最底端(不考虑NIL节点),这个会破坏max的值在红黑树中定义的性质，因此需要自底向上的调整从树根到该插入节点的路径上所有节点的max值。

head.h:

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

enum rb_color {RED,BLACK};

typedef struct timeval{
	int low;
	int high;
}timeval;

typedef struct node{
	timeval itimeval;
	int key;
	int max;
	struct node * left;
	struct node * right;
	struct node * parent;
	enum rb_color  color;  
}TimeValNode,*TimeValTree;

TimeValTree NIL;
void Init();
TimeValTree  Creat_Node(TimeValTree*,timeval);
void Left_Rotate(TimeValTree*,TimeValTree);
void Right_Rotate(TimeValTree*,TimeValTree);
void RB_Insert(TimeValTree*,TimeValTree);
void RB_Insert_Fixup(TimeValTree*,TimeValTree);
void Inorder(TimeValTree );
void Preorder(TimeValTree );
int  height(TimeValTree );
TimeValTree InterVal_Search(TimeValTree,timeval);

lab.c文件：

#include "head.h"


void Init(){
	NIL = (TimeValTree)malloc(sizeof(TimeValNode));
	NIL->key = 0;
	NIL->itimeval.low = 0;
	NIL->itimeval.high = 0;
	NIL->max = 0;
	NIL->left= NULL;
	NIL->parent = NULL;
	NIL->right = NULL;
	NIL->color = BLACK;
}

int GetMax(int a,int b,int c){
  return (a=a>b?a:b)>c?a:c;
}


TimeValTree Creat_Node(TimeValTree *pnode,timeval itimeval){
	if(((*pnode) = (TimeValTree)malloc(sizeof(TimeValNode)))!=NULL){
		(*pnode)->itimeval.high = itimeval.high;
		(*pnode)->itimeval.low = itimeval.low;
		(*pnode)->key = itimeval.low;
		(*pnode)->max = itimeval.high;
		(*pnode)->left = NIL;
		(*pnode)->right = NIL;
		(*pnode)->parent = NIL;
		(*pnode)->color = RED;
		return *pnode;
	}
	else return NULL;
}


void Left_Rotate(TimeValTree * T,TimeValTree pnode){
	
	TimeValTree temp = pnode->right;
	pnode->right = temp->left;
	if(temp->left!=NIL)
		temp->left->parent = pnode;
	temp->parent = pnode->parent;
	if(pnode->parent==NIL)
		*T = temp;
	else if(pnode->parent->left==pnode)
		pnode->parent->left = temp;
	else
		pnode->parent->right = temp;
	temp->left = pnode;
	pnode->parent = temp;
	temp->max =pnode->max;
	pnode->max=GetMax(pnode->left->max,temp->left->max,pnode->itimeval.high);
}


void Right_Rotate(TimeValTree * T,TimeValTree pnode){
	
	TimeValTree temp = pnode->left;
	pnode->left = temp->right;
	if(temp->right!=NIL)
		temp->right->parent = pnode;
	temp->parent = pnode->parent;
	if(pnode->parent==NIL)
		*T = temp;
	else if(pnode->parent->left==pnode)
		pnode->parent->left = temp;
	else
		pnode->parent->right = temp;
	temp->right = pnode;
	pnode->parent = temp;
	temp->max =pnode->max;
	pnode->max=GetMax(pnode->right->max,temp->right->max,pnode->itimeval.high);
}



void RB_Insert(TimeValTree *T,TimeValTree pnode){
	
	TimeValTree ptemp = *T,qtemp = NIL;
	//if(pnode==NULL) {printf("pnode is null\n");return;}
	while(ptemp!=NIL){
		qtemp = ptemp;
		if(pnode->key < ptemp->key)
			ptemp = ptemp->left;
		else
			ptemp = ptemp->right;
	}
	pnode->parent = qtemp;
	if(qtemp == NIL)
		*T = pnode;
	else if (pnode->key > qtemp->key)
		qtemp->right = pnode;
	else
		qtemp->left = pnode;
	pnode->left = NIL;
	pnode->right = NIL;
	pnode->color = RED;
	RB_Insert_Fixup(T,pnode);
	while(pnode!=NIL){
		pnode->max = GetMax(pnode->left->max,pnode->right->max,pnode->itimeval.high);
		pnode = pnode->parent;
	}
}

void RB_Insert_Fixup(TimeValTree* T,TimeValTree pnode){
	
	TimeValTree ptemp = NULL;
	while(pnode->parent->color==RED){

		if(pnode->parent==pnode->parent->parent->left){
			ptemp = pnode->parent->parent->right;
			if(ptemp->color==RED){
				pnode->parent->color = BLACK;
				pnode->parent->parent->color = RED;
				ptemp->color = BLACK;
				pnode = pnode->parent ->parent ;
			}
			else{
				if(pnode->parent->right==pnode){  //case2:
					pnode = pnode->parent ;
					Left_Rotate(T,pnode);
				}
				pnode->parent->color = BLACK;
				pnode->parent->parent->color = RED; 
				Right_Rotate(T,pnode->parent->parent);
			}
		}//if
		else{
			ptemp = pnode->parent->parent->left;
			if(ptemp->color==RED){
				pnode->parent->color = BLACK;
				pnode->parent->parent->color = RED;
				ptemp->color = BLACK;
				pnode = pnode->parent ->parent ;
			}
			else{
				if(pnode->parent->left==pnode){  //case2:
					pnode = pnode->parent ;
					Right_Rotate(T,pnode);
				}
				pnode->parent->color = BLACK;
				pnode->parent->parent->color = RED; 
				Left_Rotate(T,pnode->parent->parent);
			}
		}//else
	}//while
	(*T)->color = BLACK;
}


void Inorder(TimeValTree T){
	if(T!=NIL){
		Inorder(T->left);
	    printf("timeval:%d---%d\tmax:%d\tcolor:%s\n",T->itimeval.low,T->itimeval.high,T->max,T->color?"BLACK":"RED");
		Inorder(T->right);
	}
}

void Preorder(TimeValTree T){
	if(T!=NIL){
		printf("timeval:%d---%d\tmax:%d\tcolor:%s\n",T->itimeval.low,T->itimeval.high,T->max,T->color?"BLACK":"RED");
		Preorder(T->left);
		Preorder(T->right);
	}
}

int  height(TimeValTree T){
	int left,right;
	if(T==NIL) return 0;
	left = height(T->left);
	right = height(T->right);
	return left>right?left+1:right+1;
}

int IsOverlap(timeval itimeval_1,timeval itimeval_2 ){
	if(itimeval_1.low<=itimeval_2.high && itimeval_1.high>=itimeval_2.low)
		return 1;
	return 0;
}

/*
TimeValTree InterVal_Search(TimeValTree T,timeval itimeval){
	TimeValTree pnode;
	if(T->max<itimeval.low || T==NIL ) return NIL;
	if(T->left!=NIL && T->left->max>=itimeval.low){
		pnode = InterVal_Search(T->left,itimeval);
		if(pnode!=NIL)
			return pnode;
		else if(IsOverlap(T->itimeval,itimeval))
			return T;
		else 
			return NIL;
	}
	else if(IsOverlap(T->itimeval,itimeval))
		return T;
	else
		return InterVal_Search(T->right,itimeval);
}
*/


TimeValTree InterVal_Search(TimeValTree T,timeval itimeval){
	TimeValTree pnode;
	if(T->max<itimeval.low || T==NIL ) return NIL;
	if(T->left!=NIL && T->left->max>=itimeval.low){
		return  InterVal_Search(T->left,itimeval);
	
	}
	else if(IsOverlap(T->itimeval,itimeval))
		return T;
	else
		return InterVal_Search(T->right,itimeval);
}

main.c文件：

#include"head.h"

int main(){
	TimeValTree T ,pnode;
	int i,k1,k2;
	timeval itimeval;
	Init();
	T = NIL;
	pnode = NULL;
/*/...........................
	itimeval.low = 16;
		itimeval.high = 21; 
		if(Creat_Node(&pnode,itimeval)==NULL){
			printf("fail to creat node...\n");
			exit(1);
		}
		RB_Insert(&T,pnode);

		itimeval.low = 8;
		itimeval.high = 9; 
		if(Creat_Node(&pnode,itimeval)==NULL){
			printf("fail to creat node...\n");
			exit(1);
		}
		RB_Insert(&T,pnode);

		itimeval.low = 25;
		itimeval.high = 30; 
		if(Creat_Node(&pnode,itimeval)==NULL){
			printf("fail to creat node...\n");
			exit(1);
		}
		RB_Insert(&T,pnode);

		itimeval.low = 5;
		itimeval.high = 8; 
		if(Creat_Node(&pnode,itimeval)==NULL){
			printf("fail to creat node...\n");
			exit(1);
		}
		RB_Insert(&T,pnode);

		itimeval.low = 15;
		itimeval.high = 23; 
		if(Creat_Node(&pnode,itimeval)==NULL){
			printf("fail to creat node...\n");
			exit(1);
		}
		RB_Insert(&T,pnode);

		itimeval.low = 17;
		itimeval.high = 19; 
		if(Creat_Node(&pnode,itimeval)==NULL){
			printf("fail to creat node...\n");
			exit(1);
		}
		RB_Insert(&T,pnode);

		itimeval.low = 26;
		itimeval.high = 26; 
		if(Creat_Node(&pnode,itimeval)==NULL){
			printf("fail to creat node...\n");
			exit(1);
		}
		RB_Insert(&T,pnode);
		itimeval.low = 0;
		itimeval.high = 3; 
		if(Creat_Node(&pnode,itimeval)==NULL){
			printf("fail to creat node...\n");
			exit(1);
		}
		RB_Insert(&T,pnode);

		itimeval.low = 6;
		itimeval.high = 10; 
		if(Creat_Node(&pnode,itimeval)==NULL){
			printf("fail to creat node...\n");
			exit(1);
		}
		RB_Insert(&T,pnode);

		itimeval.low = 19;
		itimeval.high = 20; 
		if(Creat_Node(&pnode,itimeval)==NULL){
			printf("fail to creat node...\n");
			exit(1);
		}
		RB_Insert(&T,pnode);
		
//.......................................*/
	srand((unsigned)time(NULL));
	for(i = 0;i<1000;i++){
		itimeval.low=rand() % 2000;
		itimeval.high = itimeval.low + 30;
		if(Creat_Node(&pnode,itimeval)==NULL){
			printf("fail to creat node...\n");
			exit(1);
		}
		RB_Insert(&T,pnode);
	}
	
	//printf("InOrder:\n");
	//Inorder(T);
	//printf("\nPreOrder:\n");
	//Preorder(T);
	//printf("\nheight:%d\n",height(T));
	itimeval.low = 32;
	itimeval.high = 35;
	pnode = InterVal_Search(T,itimeval);
	if(pnode!=NIL)
		printf("timeval:%d---%d\tmax:%d\tcolor:%s\n",pnode->itimeval.low,pnode->itimeval.high,pnode->max,pnode->color?"BLACK":"RED");
	else 
		printf("no such timeval\n");
}

    原文作者：查找算法
    原文地址: https://blog.csdn.net/smileteo/article/details/18185523
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