1151 LCA in a Binary Tree(30 point(s))

本文介绍了一种解决二叉树中两个节点最低公共祖先(LCA)问题的有效算法,并提供了完整的实现代码。通过中序和先序遍历序列构造二叉树,利用递归方法查找指定节点的最近公共祖先。

摘要生成于 C知道 ,由 DeepSeek-R1 满血版支持, 前往体验 >

1151 LCA in a Binary Tree(30 point(s))

The lowest common ancestor (LCA) of two nodes U and V in a tree is the deepest node that has both U and V as descendants.

Given any two nodes in a binary tree, you are supposed to find their LCA.

Input Specification:
Each input file contains one test case. For each case, the first line gives two positive integers: M (≤ 1,000), the number of pairs of nodes to be tested; and N (≤ 10,000), the number of keys in the binary tree, respectively. In each of the following two lines, N distinct integers are given as the inorder and preorder traversal sequences of the binary tree, respectively. It is guaranteed that the binary tree can be uniquely determined by the input sequences. Then M lines follow, each contains a pair of integer keys U and V. All the keys are in the range of int.

Output Specification:
For each given pair of U and V, print in a line LCA of U and V is A. if the LCA is found and A is the key. But if A is one of U and V, print X is an ancestor of Y. where X is A and Y is the other node. If U or V is not found in the binary tree, print in a line ERROR: U is not found. or ERROR: V is not found. or ERROR: U and V are not found..

Sample Input:

6 8
7 2 3 4 6 5 1 8
5 3 7 2 6 4 8 1
2 6
8 1
7 9
12 -3
0 8
99 99

Sample Output:

LCA of 2 and 6 is 3.
8 is an ancestor of 1.
ERROR: 9 is not found.
ERROR: 12 and -3 are not found.
ERROR: 0 is not found.
ERROR: 99 and 99 are not found.

//AC code
/*
  1:根据中序,先序建树 
  2: 用 findnode( )查看待查询节点是否存在
  3:若待查询节点是存在,用 LCA( )查找最近公共祖先 
 其中LCA有三种: 
    u,v都在左子树或右子树,或者u,v分别在左子树和右子树,
 因此可采取如下步骤:
    (1)::判断当前遍历的节点是否为空,为空返回null,
    (2)::节点数据域是否等于u,是否等于p,是的话返回当前节点。
    (3)::之后判断left 和right是否为空, 若都不为空 ,则当前root为祖先指针,
        若其中一个为空,则返回另一边,为答案。
  4:格式输出 
*/ 
#include<cstdio>
#include<queue>
#include<map>
#include<algorithm>
using namespace std;
const int maxn=10010;
struct node{
    int data;
    node *lchild,*rchild;
};

int pre[maxn],in[maxn];
int n,k,u,v;

node *creat(int prel,int prer,int inl,int inr){
    if(prel>prer){
        return NULL;
    }
    node *root=new node;
    root->data=pre[prel]; 
    int k;
    for( k=inl;k<=inr;k++){
        if(in[k]==pre[prel])
        break;
    }  
    int leftnum=k-inl; 
    root->lchild =creat(prel+1,prel+leftnum,inl,k-1); //下标要写对哦
    root->rchild =creat(prel+leftnum+1,prer,k+1,inr);
    return root;
}

bool findnode(int u){ //查找节点 
    for(int i=0;i<n;i++){
        if(u==pre[i])
         return true;
    }
    return false;
}

node *LCA(node *root, int u, int v) { //查找两节点最近祖先 
        if (root == NULL) return NULL;
        if (root->data== u || root->data== v) return root;
        node *left =LCA(root->lchild,u,v);
        node *right = LCA(root->rchild,u,v);
        if (left && right ) return root; //u,v分别位于左右子树的情况
        return left == NULL ? right : left;
}

int main(){
    scanf("%d %d",&k,&n);
    for(int i=0;i<n;i++)
        scanf("%d",&in[i]);
    for(int i=0;i<n;i++)
        scanf("%d",&pre[i]);
    node *root=creat(0,n-1,0,n-1); // 尴尬,刚开始中序,先序顺序输反了,调了半天bug 
    for(int i=0;i<k;i++){
        scanf("%d %d",&u,&v);
        if(findnode(u)==false && findnode(v)==false)
           printf("ERROR: %d and %d are not found.\n", u, v);
        else if (findnode(u)==false || findnode(v)==false)
            printf("ERROR: %d is not found.\n", findnode(u)==false ? u : v);
        else {
            node *temp=LCA(root,u,v);
            if(temp->data==u || temp->data==v){
               printf("%d is an ancestor of %d.\n",temp->data==u? u:v,temp->data==u? v:u);
            }else{
                printf("LCA of %d and %d is %d.\n",u,v,temp->data);
            }
        }
    }
    return 0;
}
//#pragma GCC optimize(2,3,“Ofast”,“inline”, “-ffast-math”) //#pragma GCC target(“avx,sse2,sse3,sse4,mmx”) #include #include #include #include #include #include #include #include #include<unordered_map> #include #include #include #include #include #include #include #define fi first #define se second #define pb push_back #define y1 hsduaishxu #define mkp make_pair using namespace std; typedef long long ll; typedef long double ld; typedef unsigned long long ull; typedef pair<int,int> pii; typedef pair<ll,int> pli; typedef pair<int,ll> pil; typedef pair<ll,ll> pll; typedef unsigned int uint; typedef vector vpii; typedef int128 i128; const int maxn=1000005; const ll mod=1000000007; inline int Min(int x,int y){return x<y?x:y;} inline int Max(int x,int y){return x>y?x:y;} inline ll Min(ll x,ll y){return x<y?x:y;} inline ll Max(ll x,ll y){return x>y?x:y;} inline void ad(int &x,int y,int z){x=y+z;if(x>=mod) x-=mod;} inline void ad(ll &x,ll y,ll z){x=y+z;if(x>=mod) x-=mod;} inline void ad(int &x,int y){x+=y;if(x>=mod) x-=mod;} inline void ad(int &x,ll y){x+=y;if(x>=mod) x-=mod;} inline void ad(ll &x,ll y){x+=y;if(x>=mod) x-=mod;} inline void siu(int &x,int y,int z){x=y-z;if(x<0) x+=mod;} inline void siu(int &x,int y){x-=y;if(x<0) x+=mod;} inline void siu(ll &x,ll y){x-=y;if(x<0) x+=mod;} inline ll myabs(ll x){return x<0?-x:x;} inline void tmn(int &x,int y){if(y<x) x=y;} inline void tmx(int &x,int y){if(y>x) x=y;} inline void tmn(ll &x,ll y){if(y<x) x=y;} inline void tmx(ll &x,ll y){if(y>x) x=y;} ll qpow(ll aa,ll bb){ll res=1;while(bb){if(bb&1) res=resaa%mod;aa=aaaa%mod;bb>>=1;}return res;} ll qpow(ll aa,ll bb,ll md){ll res=1;while(bb){if(bb&1) res=(i128)resaa%md;aa=(i128)aaaa%md;bb>>=1;}return res;} inline ll Inv(ll x,ll md){return qpow(x,md-2,md);} inline ll Inv(ll x){return qpow(x,mod-2);} int ,; int n,k; int p[maxn],q[maxn]; ll ans; vector g[maxn],h[maxn]; int r1,r2; int siz[maxn],dfn[maxn],dfscnt; void dfs(int u) { siz[u]=1;dfn[u]=dfscnt; for(auto v:g[u]) dfs(v),siz[u]+=siz[v]; } struct bit { int c[maxn]; void clr() { for(int i=1;i<=n;i) c[i]=0; } int lowbit(int x){return x&(-x);} void ad(int x,int k){while(x<=n){c[x]+=k;x+=lowbit(x);}} int qry(int x){int res=0;while(x>=1){res+=c[x];x-=lowbit(x);}return res;} }T1,T2; int F[maxn],st[maxn],tp,sz[maxn],son[maxn]; vector e[maxn]; void dfs1(int u) { st[tp]=u;e[u].clear(); if(tp>k) F[u]=st[tp-k]; else F[u]=0; if(F[u]) e[F[u]].push_back(u); sz[u]=1;son[u]=0; for(auto v:h[u]) { dfs1(v); if(sz[v]>sz[son[u]]) son[u]=v; sz[u]+=sz[v]; } tp–; } void ins(int x,int k) { T1.ad(dfn[x],k);T1.ad(dfn[x]+siz[x],-k); T2.ad(dfn[x],k); } int qry(int x) { return T1.qry(dfn[x])+T2.qry(dfn[x]+siz[x]-1)-T2.qry(dfn[x]-1); } void dfs3(int u,int ty) { for(auto v:e[u]) { if(ty1) ans+=qry(v); else if(ty3) ins(v,-1); else if(ty==2) ins(v,1); } for(auto v:h[u]) dfs3(v,ty); } void dfs2(int u,int ty) { for(auto v:h[u]) if(v!=son[u]) dfs2(v,0); if(son[u]) { dfs2(son[u],1); for(auto v:h[u]) if(v!=son[u]) dfs3(v,1),dfs3(v,2); } for(auto v:e[u]) ins(v,1); if(!ty) dfs3(u,3); } void cal() { dfscnt=0;dfs(r1); T1.clr();T2.clr(); tp=0;dfs1(r2); dfs2(r2,0); } void solve() { cin>>n>>k; for(int i=1;i<=n;i) cin>>p[i]; for(int i=1;i<=n;i++) cin>>q[i]; for(int i=1;i<=n;i++) { if(!p[i]) r1=i; else g[p[i]].push_back(i); if(!q[i]) r2=i; else h[q[i]].push_back(i); } cal(); for(int i=1;i<=n;i++) swap(p[i],q[i]),swap(g[i],h[i]);swap(r1,r2); cal(); cout<<ans<<“\n”; } signed main() { freopen(“D.in”,“r”,stdin); freopen(“D.out”,“w”,stdout); ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); =1; //cin>>; while(–) { solve(); } return 0; } //by cristiano ronaldo dos santos aveiro #include <bits/stdc++.h> using namespace std; typedef long long ll; #define rep(i,s,t) for(register ll i = s;i <= t;++i) #define per(i,t,s) for(register ll i = t;i >= s;–i) const ll N = 1e6 + 5; ll n; ll k; ll rt1; ll rt2; ll top; ll idx; ll ans; ll p[N] = {}; ll q[N] = {}; ll fa[N] = {}; ll st[N] = {}; ll sz[N] = {}; ll siz[N] = {}; ll dfn[N] = {}; ll son[N] = {}; vector g[N]; vector g1[N]; vector g2[N]; class binary_indexed_tree { private: ll t[N] = {}; public: inline void init() { memset(t,0,sizeof(t)); } inline ll lowbit(ll x) { return x & (-x); } inline void upd(ll x,ll k) { while(x <= n) { t[x] += k; x += lowbit(x); } } inline ll qry(ll x) { ll ans = 0; while(x) { ans += t[x]; x -= lowbit(x); } return ans; } }; binary_indexed_tree t1; binary_indexed_tree t2; inline ll read() { ll x = 0; ll y = 1; char c = getchar(); while(c < ‘0’ || c > ‘9’) { if(c == ‘-’) y = -y; c = getchar(); } while(c >= ‘0’ && c <= ‘9’) { x = (x << 3) + (x << 1) + (c ^ ‘0’); c = getchar(); } return x * y; } inline void write(ll x) { if(x < 0) { putchar(‘-’); write(-x); return; } if(x > 9) write(x / 10); putchar(x % 10 + ‘0’); } inline void dfs(ll u) { siz[u] = 1; dfn[u] = ++idx; for(register auto v : g1[u]) { dfs(v); siz[u] += siz[v]; } } inline void dfs1(ll u) { st[++top] = u; g[u].clear(); if(top > k) fa[u] = st[top - k]; else fa[u] = 0; if(fa[u]) g[fa[u]].push_back(u); sz[u] = 1; son[u] = 0; for(auto v : g2[u]) { dfs1(v); if(sz[v] > sz[son[u]]) son[u] = v; sz[u] += sz[v]; } top–; } inline void ins(ll x,ll k) { t1.upd(dfn[x],k); t1.upd(dfn[x] + siz[x],-k); t2.upd(dfn[x],k); } inline ll query(ll x) { return t1.qry(dfn[x]) + t2.qry(dfn[x] + siz[x] - 1) - t2.qry(dfn[x] - 1); } inline void dfs3(ll u,ll k) { for(auto v : g[u]) { if(k == 1) ans += query(v); else if(k == 2) ins(v,1); else if(k == 3) ins(v,-1); } for(auto v : g2[u]) dfs3(v,k); } inline void dfs2(ll u,ll k) { for(auto v : g2[u]) if(v != son[u]) dfs2(v,0); if(son[u]) { dfs2(son[u],1); for(auto v : g2[u]) { if(v != son[u]) { dfs3(v,1); dfs3(v,2); } } } for(register auto v : g[u]) ins(v,1); if(!k) dfs3(u,3); } int main() { freopen(“D.in”,“r”,stdin); freopen(“D.out”,“w”,stdout); n = read(); k = read(); rep(i,1,n) p[i] = read(); rep(i,1,n) q[i] = read(); rep(i,1,n) { if(!p[i]) rt1 = i; else g1[p[i]].push_back(i); if(!q[i]) rt2 = i; else g2[q[i]].push_back(i); } idx = 0; dfs(rt1); t1.init(); t2.init(); top = 0; dfs1(rt2); dfs2(rt2,0); rep(i,1,n) { swap(p[i],q[i]); swap(g1[i],g2[i]); swap(rt1,rt2); } idx = 0; dfs(rt1); t1.init(); t2.init(); top = 0; dfs1(rt2); dfs2(rt2,0); write(ans); fclose(stdin); fclose(stdout); return 0; }针对以下问题,上述两段代码的功能有什么不同,请指出并修正第二段代码,使得第二段代码功能与第一段代码功能完全等价小丁的树 题目描述 小丁拥有两棵均具有 n n 个顶点,编号集合为 { 1 , 2 , ⋯ &thinsp; , n } {1,2,⋯,n} 的有根树 T 1 , T 2 T 1 ​ ,T 2 ​ ,现在他需要计算这两棵树的相似程度。 为了计算,小丁定义了对于一棵树 T T 和 T T 上两个不同顶点 u , v u,v 的距离函数 d T ( u , v ) d T ​ (u,v),其定义为 u , v u,v 两个点距离成为祖先关系有多近,具体来说,对于所有在 T T 上为祖先关系的点对 ( u ′ , v ′ ) (u ′ ,v ′ ), dis ⁡ ( u , u ′ ) + dis ⁡ ( v , v ′ ) dis(u,u ′ )+dis(v,v ′ ) 的最小值即为 d T ( u , v ) d T ​ (u,v) 的值,其中 dis ⁡ ( u , v ) dis(u,v) 表示 u , v u,v 在树 T T 上的唯一简单路径包含的边数,即 u , v u,v 的距离。 点对 ( u ′ , v ′ ) (u ′ ,v ′ ) 为祖先关系,当且仅当 u ′ u ′ 是 v ′ v ′ 的祖先或 v ′ v ′ 是 u ′ u ′ 的祖先。(注意,每个点都是自己的祖先) 小丁心里还有一个参数 k k,如果节点对 ( u , v ) (u,v) 满足以下条件,称之为不相似的节点对: 1 ≤ u < v ≤ n 1≤u<v≤n " d T 1 ( u , v ) 0 d T 1 ​ ​ (u,v)=0 且 d T 2 ( u , v ) k d T 2 ​ ​ (u,v)>k“ 或 " d T 2 ( u , v ) 0 d T 2 ​ ​ (u,v)=0 且 d T 1 ( u , v ) k d T 1 ​ ​ (u,v)>k​“ 小丁认为,不相似的节点对越多, T 1 T 1 ​ 和 T 2 T 2 ​ 就越不相似,你能告诉他总共有多少不相似的节点对吗? 输入格式 第一行两个整数 n , k n,k,表示 T 1 T 1 ​ 和 T 2 T 2 ​ 的节点数和参数 k k。 第二行 n n 个正整数 p 1 , p 2 , ⋯ &thinsp; , p n p 1 ​ ,p 2 ​ ,⋯,p n ​ , T 1 T 1 ​ 中节点 i i 的父节点为 p i p i ​ ,特别的,若 p i 0 p i ​ =0,则 i i 是 T 1 T 1 ​ 的根。 第三行 n n 个正整数 q 1 , q 2 , ⋯ &thinsp; , q n q 1 ​ ,q 2 ​ ,⋯,q n ​ , T 2 T 2 ​ 中节点 i i 的父节点为 q i q i ​ ,特别的,若 q i 0 q i ​ =0,则 i i 是 T 2 T 2 ​ 的根。 输出格式 一行一个整数,表示不相似的节点对总数。 样例 1 输入 5 0 0 1 1 2 3 5 3 1 1 0 样例 1 输出 4 样例 1 解释 ( 2 , 3 ) , ( 2 , 4 ) , ( 2 , 5 ) , ( 4 , 5 ) (2,3),(2,4),(2,5),(4,5) 为不相似的节点对。 其余样例见下发文件。 数据规模与约定 对于所有数据, 1 ≤ n ≤ 2 × 10 5 , 0 ≤ k < n , 0 ≤ p i , q i ≤ n 1≤n≤2×10 5 ,0≤k<n,0≤p i ​ ,q i ​ ≤n,且由 p i , q i p i ​ ,q i ​ 形成的是一棵 n n 个节点的有根树。 本题采用捆绑评测,你只有通过了一个子任务中所有测试点才能得到该子任务的分数。 Subtask 1(10pts): 1 ≤ n ≤ 100 1≤n≤100。 Subtask 2(20pts): 1 ≤ n ≤ 3000 1≤n≤3000。 Subtask 3(20pts): k 0 k=0。 Subtask 4(10pts): 0 ≤ k ≤ 20 0≤k≤20。 Subtask 5(40pts):无特殊限制。
最新发布
07-25
评论 3
添加红包

请填写红包祝福语或标题

红包个数最小为10个

红包金额最低5元

当前余额3.43前往充值 >
需支付:10.00
成就一亿技术人!
领取后你会自动成为博主和红包主的粉丝 规则
hope_wisdom
发出的红包

打赏作者

ZCAIHUI_

你的鼓励将是我创作的最大动力

¥1 ¥2 ¥4 ¥6 ¥10 ¥20
扫码支付:¥1
获取中
扫码支付

您的余额不足,请更换扫码支付或充值

打赏作者

实付
使用余额支付
点击重新获取
扫码支付
钱包余额 0

抵扣说明:

1.余额是钱包充值的虚拟货币,按照1:1的比例进行支付金额的抵扣。
2.余额无法直接购买下载,可以购买VIP、付费专栏及课程。

余额充值