二叉树/树笔记
PART1：建树
1.直接一个数组建树，子节点为当前下标*2以及当前下标*2+1，适用于完全二叉树
2.struct 法（数组大小取决于节点个数
struct node{ int fa,l,r,depth; }
3.链表法（待补充）
struct node { bool have_v; int v; node *l,*r; node():have_v(false),l(NULL),r(NULL){}//结构体初始化 }*root;
PART2：树的遍历（这里用struct法演示)
1.对完全二叉树的三种递归遍历
#pragma GCC optimize(2) #pragma GCC optimize(1) #include<bits/stdc++.h> typedef long long ll; typedef unsigned long long ull; const ull base=131; #define MAX 100009 #define PI 3.141592653589793 using namespace std; int n; inline void preorder(int i){ printf("%d ",i); if(i+i<=n) preorder(2*i); if(i+i+1<=n) preorder(2*i+1); } inline void inorder(int i){ if(i+i<=n) inorder(i+i); printf("%d ",i); if(i+i+1<=n) inorder(i+i+1); } inline void postorder(int i){ if(i+i<=n) postorder(2*i); if(2*i+1<=n) postorder(i+i+1); printf("%d ",i); } int main() { scanf("%d",&n); preorder(1);cout<<"\n"; inorder(1);cout<<"\n"; postorder(1);cout<<"\n"; }
2.对非完全二叉树的遍历
#pragma GCC optimize(2) #pragma GCC optimize(1) #include<bits/stdc++.h> typedef long long ll; typedef unsigned long long ull; const ull base=131; #define MAX 100009 #define PI 3.141592653589793 using namespace std; int n; struct node{ int fa,l,r; }tree[MAX]; inline void preorder(int i){ printf("%d ",i); if(tree[i].l) preorder(tree[i].l); if(tree[i].r) preorder(tree[i].r); } inline void inorder(int i){ if(tree[i].l) inorder(tree[i].l); printf("%d ",i); if(tree[i].r) inorder(tree[i].r); } inline void postorder(int i){ if(tree[i].l) postorder(tree[i].l); if(tree[i].r) postorder(tree[i].r); printf("%d ",i); } int main() { cin>>n; for(int i =1;i<=n;i++) { int x,y;cin>>x>>y; if(x){ tree[i].l=x; tree[x].fa=i; } if(y){ tree[i].r=y; tree[y].fa=i; } } preorder(1);cout<<"\n"; inorder(1);cout<<"\n"; postorder(1);cout<<"\n"; }
3.dfs和bfs找节点公共祖先
链接二叉树的最近公共祖先 - 题目 - Daimayuan Online Judge
dfs
#pragma GCC optimize(2) #pragma GCC optimize(1) #include<bits/stdc++.h> typedef long long ll; typedef unsigned long long ull; const ull base=131; #define MAX 2009 #define PI 3.141592653589793 using namespace std; struct node{ int fa,l,r; }tree[MAX]; int n,a[MAX],b[MAX]; int main() { cin>>n; for(int i=1;i<=n;i++){ int x,y;cin>>x>>y; if(x){ tree[i].l=x;tree[x].fa=i; } if(y){ tree[i].r=y;tree[y].fa=i; } } int u,v;cin>>u>>v; int l1=0; while(u!=1) { a[++l1]=u,u=tree[u].fa; } a[++l1]=1; int l2=0; while(v!=1) { b[++l2]=v,v=tree[v].fa; } b[++l2]=1; int x=0; for(int i=l1,j=l2;i&&j;--i,--j){ if(a[i]==b[j]) x=a[i]; else break; } cout<<x<<endl; }
bfs赋值深度版本
#pragma GCC optimize(2) #pragma GCC optimize(1) #include<bits/stdc++.h> typedef long long ll; typedef unsigned long long ull; const ull base=131; #define MAX 2009 #define PI 3.141592653589793 using namespace std; struct node{ int fa,l,r,depth; }tree[MAX]; int n,a[MAX]; int main() { cin>>n; for(int i=1;i<=n;i++){ int x,y;cin>>x>>y; if(x){ tree[i].l=x;tree[x].fa=i; } if(y){ tree[i].r=y;tree[y].fa=i; } } int front=1,rear=1; a[1]=1,tree[1].depth=1; while(front<=rear){ int p=a[front];front++; if(tree[p].l) a[++rear]=tree[p].l,tree[tree[p].l].depth=tree[p].depth+1; if(tree[p].r) a[++rear]=tree[p].r,tree[tree[p].r].depth=tree[p].depth+1; } int u,v;cin>>u>>v; if(tree[u].depth<tree[v].depth) swap(u,v); int cha=tree[u].depth-tree[v].depth; for(int i=1;i<=cha;i++) u=tree[u].fa; while(u!=v) u=tree[u].fa,v=tree[v].fa; cout<<u<<endl; }
UVA - 122 Trees on the level
Trees on the level - UVA 122 - Virtual Judge (csgrandeur.cn)
指针建树加bfs层次遍历
#pragma GCC optimize(2) #pragma GCC optimize(1) #include<bits/stdc++.h> typedef long long ll; typedef unsigned long long ull; const ull base=131; #define MAX 277 #define PI 3.141592653589793 using namespace std; struct node { bool have_v; int v; node *l,*r; node():have_v(false),l(NULL),r(NULL){}//结构体初始化 }*root; bool failed; node* newnode(){ return new node();} void addnode(int v,char* s){ int n=strlen(s); node* u=root; for(int i=0;i<n;i++) { if(s[i]=='L'){ if(u->l==NULL) u->l=newnode();u=u->l;} else if(s[i]=='R'){ if(u->r==NULL) u->r=newnode();u=u->r;} } if(u->have_v) failed=true; u->v=v; u->have_v=true; } inline void remove_tree(node* u){//释放节点 if(u==NULL) return; remove_tree(u->l); remove_tree(u->r); delete u; } bool read_input() { char s[400]; failed=false; int v; root=newnode();// for(;;) { if(scanf("%s", s) != 1) {//读入EOF return false; } if(strcmp(s,"()") == 0) {//结束读入 break; } sscanf(&s[1],"%d",&v);//读入第一个数字 addnode(v,strchr(s,',')+1);//读入从第一个逗号右边读入的数据 } return true; } bool bfs(vector<int>& ans){ queue<node*>q; ans.clear(); q.push(root); while(!q.empty()){ node* u=q.front();q.pop(); if(!u->have_v) return false; ans.push_back(u->v); if(u->l!=NULL) q.push(u->l); if(u->r!=NULL) q.push(u->r); } return true; } int main(){ vector<int> ans; while(read_input()){ if(!bfs(ans)){ failed=true; } if(failed) cout<<"not complete\n"; else{ for(int i=0;i<ans.size()-1;i++) cout<<ans[i]<<' '; cout<<ans[ans.size()-1]<<"\n"; } } }
