knn之構造kd樹和最近鄰求取c++實現
阿新 • • 發佈：2019-01-04
這份程式碼測試樣例為
6
7 2
2 3
5 4
4 7
9 6
8 1
8 2
這樣，通過中位數來選取根節點(這樣的方法其實在一定程度上是有很大問題的，因為根節點的選取方法不同，會導致整棵樹的結構不同，這裡由於資料的關係，不能構成完全二叉樹，所以在對於特殊的樣例來說是會出錯的，比如說(10,10)這個測試樣例，根本無法找到包含他的子節點（區域），所以會導致出錯))。
以上程式碼，經過測試，除了(10,10)這種類似的特殊資料會出錯，別的基本正確，程式碼寫的很亂。。。。#include<iostream> #include<algorithm> #include<cstring> #include<vector> #include<cmath> #include<queue> using namespace std; struct node{ pair<int,int>x; int dim; node*left; node*right; node*father; node(pair<int,int>p=make_pair(0,0),int dim=0,node*left=0,node*right=0,node*father=0) :dim(dim),left(left),right(right),father(father) { x=p; } }; bool cmp1(node*a,node* b) { return a->x.first<b->x.first; } bool cmp2(node*a,node*b) { return a->x.second<b->x.second; } vector<node*>vec; node* buildtree(vector<node*>temp,int cnt) { if(temp.size()==0) return 0; else if(temp.size()==1) return temp[0]; else{ if(cnt==1) sort(temp.begin(),temp.end(),cmp1); else sort(temp.begin(),temp.end(),cmp2); int mid=temp.size()/2; vector<node*>p; for(int i=0;i<mid;i++) { p.push_back(temp[i]); } vector<node*>q; for(int i=mid+1;i<temp.size();i++) { q.push_back(temp[i]); } node*left=buildtree(p,(cnt+1)%2); node*right=buildtree(q,(cnt+1)%2); node*fat=new node(make_pair(temp[mid]->x.first,temp[mid]->x.second),cnt,left,right,0); if(left!=0) left->father=fat; if(right!=0) right->father=fat; //cout<<fat->x.first<<" "<<fat->x.second<<endl; return fat; } } void traverse(node*root) { if(root==0) { } else { cout<<root->x.first<<" "<<root->x.second<<endl; traverse(root->left); traverse(root->right); } } node*find_first_belong(node*key,node*root) { node*temp=root; while(true) //遍歷找到其歸屬的葉節點 { if(temp->left==0&&temp->right==0) { break; } else { int dim=temp->dim;//選擇維度比較 if(dim==1)//選擇x1比較 { if(key->x.first<=temp->x.first) temp=temp->left; else temp=temp->right; } else //選擇x2比較 { if(key->x.second<=temp->x.second) temp=temp->left; else temp=temp->right; } } } return temp; } double distance(node*a,node*b) { double ax1=a->x.first; double ax2=a->x.second; double bx1=b->x.first; double bx2=b->x.second; return sqrt(pow(ax1-bx1,2)+pow(ax2-bx2,2)); } node*query(node*key,node*root,double mindis) //這裡就是最不明白的一點，當另一區域跟圓相交，書上說是遞迴進行最近鄰搜尋， //沒搞懂到底怎麼遞迴搜尋，所以這裡就直接用了很簡單的遍歷比較，希望以後能搞懂 { node*rec=root; double mind=mindis; queue<node*>q; q.push(root); while(!q.empty()) { node*temp=q.front(); double dis=distance(key,temp); if(dis<mind) { mind=dis; rec=temp; } q.pop(); if(temp->left!=0) q.push(temp->left); if(temp->right) q.push(temp->right); } return rec; } node*find_nearest(node*key,node*belong) { node *nearest=belong; double mindis=distance(key,belong); //cout<<mindis<<" mindis"<<endl; while(true) { //cout<<belong->x.first<<" "<<belong->x.second<<endl; node*fat=belong->father; if(fat==0) break; int fdim=fat->dim; if(distance(fat,key)<mindis) { mindis=distance(fat,key); nearest=fat; } if(fdim==1) //判斷圓是否與x1=fat->x.first相交 { int fx1=fat->x.first; int kx1=key->x.first; if(abs(fx1-kx1)<mindis) { node*res=query(key,fat->right,mindis); if(res!=0&&distance(res,key)<mindis) { nearest=res; mindis=distance(res,key); } } } else //反之 { int fx2=fat->x.second; int kx2=key->x.second; if(abs(fx2-kx2)<mindis) { node*res=query(key,fat->right,mindis); if(res!=0&&distance(res,key)<mindis) { nearest=res; mindis=distance(res,key); } } } belong=fat; if(belong==0) break; } return nearest; } node*search(node*key,node*root) { node* belong=find_first_belong(key,root); //cout<<belong->x.first<<" "<<belong->x.second<<endl; node* nearest=find_nearest(key,belong); } int main() { int n; cin>>n; for(int i=0;i<n;i++) { int x,y; cin>>x>>y; node* temp=new node(make_pair(x,y)); vec.push_back(temp); } node*root=buildtree(vec,1); //traverse(root); int x,y; cin>>x>>y; node *key=new node(make_pair(x,y)); node*near=search(key,root); cout<<near->x.first<<" "<<near->x.second<<endl; }
這裡還有一個很大的問題在於，我不知道一旦判定了圓和其他區域相交之後該怎麼進行遞迴搜尋，所以這裡直接用了遍歷。。。。
總算搞懂了什麼遞迴搜尋：
下面的是第二個版本：
然而還是沒有解決(10,10)的情況，明天再說！！！！#include<iostream> #include<algorithm> #include<cstring> #include<vector> #include<cmath> #include<queue> using namespace std; struct node{ pair<int,int>x; int dim; node*left; node*right; node*father; node(pair<int,int>p=make_pair(0,0),int dim=0,node*left=0,node*right=0,node*father=0) :dim(dim),left(left),right(right),father(father) { x=p; } }; bool cmp1(node*a,node* b) { return a->x.first<b->x.first; } bool cmp2(node*a,node*b) { return a->x.second<b->x.second; } vector<node*>vec; node* buildtree(vector<node*>temp,int cnt) { if(temp.size()==0) return 0; else if(temp.size()==1) return temp[0]; else{ if(cnt==1) sort(temp.begin(),temp.end(),cmp1); else sort(temp.begin(),temp.end(),cmp2); int mid=temp.size()/2; vector<node*>p; for(int i=0;i<mid;i++) { p.push_back(temp[i]); } vector<node*>q; for(int i=mid+1;i<temp.size();i++) { q.push_back(temp[i]); } node*left=buildtree(p,(cnt+1)%2); node*right=buildtree(q,(cnt+1)%2); node*fat=new node(make_pair(temp[mid]->x.first,temp[mid]->x.second),cnt,left,right,0); if(left!=0) left->father=fat; if(right!=0) right->father=fat; //cout<<fat->x.first<<" "<<fat->x.second<<endl; return fat; } } void traverse(node*root) { if(root==0) { } else { cout<<root->x.first<<" "<<root->x.second<<endl; traverse(root->left); traverse(root->right); } } node*find_first_belong(node*key,node*root) { node*temp=root; while(true) //遍歷找到其歸屬的葉節點 { if(temp->left==0&&temp->right==0) { break; } else { int dim=temp->dim;//選擇維度比較 if(dim==1)//選擇x1比較 { if(key->x.first<=temp->x.first) temp=temp->left; else temp=temp->right; } else //選擇x2比較 { if(key->x.second<=temp->x.second) temp=temp->left; else temp=temp->right; } } } return temp; } double distance(node*a,node*b) { double ax1=a->x.first; double ax2=a->x.second; double bx1=b->x.first; double bx2=b->x.second; return sqrt(pow(ax1-bx1,2)+pow(ax2-bx2,2)); } node*query(node*key,node*root,double mindis)//沒有用的函式 { node*rec=root; double mind=mindis; queue<node*>q; q.push(root); while(!q.empty()) { node*temp=q.front(); double dis=distance(key,temp); if(dis<mind) { mind=dis; rec=temp; } q.pop(); if(temp->left!=0) q.push(temp->left); if(temp->right) q.push(temp->right); } return rec; } node*find_nearest(node*key,node*belong,node*root) { node *nearest=belong; double mindis=distance(key,belong); //cout<<belong->x.first<<" belong "<<belong->x.second<<endl; //cout<<mindis<<" mindis"<<endl; while(true) { //cout<<belong->x.first<<" "<<belong->x.second<<endl; node*fat=belong->father; if(fat==0||fat==root->father) break; node*other=new node(); //相比第一個這裡還更加對了，因為這裡還考慮到了萬一歸屬的葉節點不是左節點的情況 if(fat->left==belong) { other=fat->right; } else other=fat->left; //cout<<fat->x.first<<" "<<" fat "<<fat->x.second<<endl; int fdim=fat->dim; if(distance(fat,key)<mindis) { mindis=distance(fat,key); nearest=fat; } if(fdim==1) //判斷圓是否與x1=fat->x.first相交 { int fx1=fat->x.first; int kx1=key->x.first; if(abs(fx1-kx1)<mindis) { node*tm=find_first_belong(key,other); node*res=find_nearest(key,tm,other); //傳說中的遞迴搜尋在這裡，利用他之前的函式 if(res!=0&&distance(res,key)<mindis) { nearest=res; mindis=distance(res,key); } } //cout<<fx1<<" xxxx "<<kx1<<" "<<mindis<<endl; } else //反之 { int fx2=fat->x.second; int kx2=key->x.second; if(abs(fx2-kx2)<mindis) { node*tm=find_first_belong(key,other); //cout<<tm->x.first<<" **** "<<tm->x.second<<endl; //cout<<other->x.first<<" other "<<other->x.second<<endl; node*res=find_nearest(key,tm,other); if(res!=0&&distance(res,key)<mindis) { nearest=res; mindis=distance(res,key); //cout<<mindis<<" mindis"<<endl; } } } belong=fat; if(belong==0) break; } return nearest; } node*search(node*key,node*root) { node* belong=find_first_belong(key,root); //cout<<belong->x.first<<" "<<belong->x.second<<endl; node* nearest=find_nearest(key,belong,root); return nearest; } int main() { int n; cin>>n; for(int i=0;i<n;i++) { int x,y; cin>>x>>y; node* temp=new node(make_pair(x,y)); vec.push_back(temp); } node*root=buildtree(vec,1); //traverse(root); int x,y; cin>>x>>y; node *key=new node(make_pair(x,y)); node*near=search(key,root); cout<<"the nearest point is "<<near->x.first<<" "<<near->x.second<<endl; }