两个最接近的数之间的差值-红黑树-快速排序

#include<iostream>#include <ctime>#include <limits>using namespace std;typedef struct rb_node{//带父节点的红黑树int value;rb_node *left,*right,*parent;bool rb;//rb=0表示结点,rb=1表示红结点int min,max,min_gap;//计算红黑树中两个最接近的数的差值}rb_node,*pRBNode;pRBNode nil;//所有结点的公共黑色结点，类似于NULLint four_min(int a,int b,int c,int d){int num1=a>b?b:a;int num2 = num1>c?c:num1;return num2>d?d:num2;}void binary_tree_left_rotation(pRBNode &pn,pRBNode y)//二叉搜索树左旋{pRBNode x=y->right;y->right=x->left;if(x->left!=nil){x->left->parent=y;}x->parent=y->parent;if(y->parent==nil){pn=x;}else if(y==y->parent->left){y->parent->left=x;}else{y->parent->right=x;}x->left=y;y->parent=x;if(y->left!=nil){//调整y结点的值y->min=y->left->min;}else{y->min=y->value;}if(y->right!=nil){y->max=y->right->max;}else{y->max=y->value;}y->min_gap=four_min(abs(y->left->min_gap),abs(y->right->min_gap),abs(y->value-y->left->max),abs(y->right->min-y->value));if(x->left!=nil){//调整x结点的值x->min=x->left->min;}else{x->min=x->value;}if(x->right!=nil){x->max=x->right->max;}else{x->max=x->value;}x->min_gap=four_min(abs(x->left->min_gap),abs(x->right->min_gap),abs(x->value-x->left->max),abs(x->right->min-x->value));}void binary_tree_right_rotation(pRBNode &pn,pRBNode x)//二叉搜索树右旋{pRBNode y=x->left;x->left=y->right;if(y->right!=nil){y->right->parent=x;}y->parent=x->parent;if(x->parent==nil){pn=y;}else if(x==x->parent->left){x->parent->left=y;}else{x->parent->right=y;}y->right=x;x->parent=y;if(x->left!=nil){//调整x结点的值x->min=x->left->min;}else{x->min=x->value;}if(x->right!=nil){x->max=x->right->max;}else{x->max=x->value;}x->min_gap=four_min(abs(x->left->min_gap),abs(x->right->min_gap),abs(x->value-x->left->max),abs(x->right->min-x->value));if(y->left!=nil){//调整y结点的值y->min=y->left->min;}else{y->min=y->value;}if(y->right!=nil){y->max=y->right->max;}else{y->max=y->value;}y->min_gap=four_min(abs(y->left->min_gap),abs(y->right->min_gap),abs(y->value-y->left->max),abs(y->right->min-y->value));}void rb_tree_insert_fixup(pRBNode &pn,pRBNode pz)//红黑结点修复{while(pz->parent->rb){//子结点父结点均为红结点pRBNode y;if(pz->parent==pz->parent->parent->left){//当前结点的父结点是当前结点父结点的父节点的左子树y=pz->parent->parent->right;if(y->rb){//堂叔为红结点,case onepz->parent->rb=0;pz->parent->parent->rb=1;y->rb=0;pz=pz->parent->parent;}else{if(pz==pz->parent->right){//case twopz=pz->parent;binary_tree_left_rotation(pn,pz);}pz->parent->rb=0;//case threepz->parent->parent->rb=1;binary_tree_right_rotation(pn,pz->parent->parent);}}else{//当前结点的父结点是当前结点父结点的父节点的右子树y=pz->parent->parent->left;if(y->rb){//堂叔结点是红色pz->parent->rb=0;pz->parent->parent->rb=1;y->rb=0;pz=pz->parent->parent;}else{if(pz==pz->parent->left){//case twopz=pz->parent;binary_tree_right_rotation(pn,pz);}pz->parent->rb=0;//case threepz->parent->parent->rb=1;binary_tree_left_rotation(pn,pz->parent->parent);}}pn->rb=0;}}void binary_tree_insert(pRBNode &pn,pRBNode pz){pRBNode x=pn;pRBNode y=nil;while (x!=nil){y=x;if(pz->value<=x->value){x=x->left;}else{x=x->right;}}if(y==nil){pn=pz;pn->rb=0;}else if(pz->value<=y->value){y->left=pz;}else{y->right=pz;}pz->parent=y;pRBNode ptm=pz;int left_gap,right_gap,c_left_gap,right_c_gap;while (y!=nil){//调整路径上的结点的min,max,min_gap值if(ptm==ptm->parent->left){//左子树的时候y->min=y->left->min;left_gap=y->left->min_gap;c_left_gap=y->value-y->left->max;if(y->right!=nil){//判断是否具有相应的结点right_gap=y->right->min_gap;right_c_gap=y->right->min-y->value;}else{right_gap=numeric_limits<int>::max();right_c_gap=numeric_limits<int>::max();}}else{//右子树的时候y->max=y->right->max;right_gap=y->right->min_gap;right_c_gap=y->right->min-y->value;if(y->left!=nil){left_gap=y->left->min_gap;c_left_gap=y->value-y->left->max;}else{left_gap=numeric_limits<int>::max();c_left_gap=numeric_limits<int>::max();}}y->min_gap=four_min(left_gap,c_left_gap,right_gap,right_c_gap);//获取最小的差值ptm=y;y=y->parent;}rb_tree_insert_fixup(pn,pz);//插入结点后可能会破坏红黑树的性质，}void build_binary_search_tree(pRBNode &pn,int n)//建立n个具有父节点的二叉搜索树{int value;pRBNode ptmp;//int a[10]={-2,-3,4,-3,-5,5,5,3,-3,0};for(int i=0;i<n;++i){value=rand()%10001-5000;ptmp=new rb_node;ptmp->left=nil;ptmp->right=nil;ptmp->parent=nil;ptmp->value=/*a[i]*/value;ptmp->rb=1;//红结点ptmp->min=value;ptmp->max=value;ptmp->min_gap=numeric_limits<int>::max();//初始为最大值//cout<<value/*a[i]*/<<"\t";binary_tree_insert(pn,ptmp);}//cout<<endl;}void InOrder(pRBNode pn)//中序遍历{if(pn!=nil){InOrder(pn->left);cout<<pn->value<<"\t";InOrder(pn->right);}}pRBNode binary_tree_search(pRBNode pn,int key)//二叉搜索树查找{pRBNode pp=pn;while (pp !=nil && key != pp->value){if(key<pp->value){pp=pp->left;}else{pp=pp->right;}}return pp;}pRBNode binary_tree_maximum(pRBNode pn)//最大值{while (pn!=nil && pn->right!=nil){pn=pn->right;}return pn;}pRBNode binary_tree_minimux(pRBNode pn)//最小值{while(pn!=nil && pn->left!=nil){pn=pn->left;}return pn;}pRBNode binary_tree_successor(pRBNode pz)//后继结点{if(pz->right!=nil){return binary_tree_minimux(pz->right);}pRBNode p=pz->parent;//父亲节点while(p!=nil && pz==p->right){pz=p;p=p->parent;}return p;}pRBNode binary_tree_predecessor(pRBNode pz){if(pz->left!=nil){return binary_tree_maximum(pz->left);}pRBNode p=pz->parent;while(p!=nil && pz==p->left){pz=p;p=p->parent;}return p;}int compare(const void *a,const void *b){return (*(int *)a- *(int *)b);}int minimum_gap(pRBNode pn,int n){int *a=new int[n];pRBNode pr=binary_tree_minimux(pn);for(int i=0;i<n;++i){a[i]=pr->value;pr=binary_tree_successor(pr);cout<<a[i]<<"\t";}cout<<endl;int *b=new int[n-1];for(int i=0;i<n-1;i++){b[i]=a[i+1]-a[i];cout<<b[i]<<"\t";}cout<<endl<<endl;delete []a;qsort(b,n-1,sizeof(int),compare);for(int i=0;i<n-1;i++){cout<<b[i]<<"\t";}cout<<endl;int result=b[0];delete []b;return result;}int main(){srand((unsigned)time(NULL));int n=100;nil=new rb_node;nil->left=nil;nil->right=nil;nil->rb=0;//黑色nil->parent=nil;nil->value=numeric_limits<int>::max();nil->min=numeric_limits<int>::max();nil->max=numeric_limits<int>::max();nil->min_gap=numeric_limits<int>::max();pRBNode pn=nil;build_binary_search_tree(pn,n);InOrder(pn);//中序排序cout<<endl;cout<<"minimum gap is : "<<minimum_gap(pn,n)<<"\t"<<pn->min_gap<<endl;}