PAT甲级2018秋7-4 1151 LCA in a Binary Tree (30分)

今天药忘吃喽~ 2023-02-24 14:24 98阅读 0赞

[算法笔记总目录][Link 1]  
[关键英语单词解释][Link 2]  
[1151 LCA in a Binary Tree (30分)][1151 LCA in a Binary Tree _30]  
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.

**代码一：**  
给定二叉树的先序和中序遍历，求两个结点的最近公共祖先。

#include<bits/stdc++.h>
    using namespace std;
    const int maxn = 10010;
    int in[maxn];
    int pre[maxn];
    struct node{ 
        int val;
        node *left,*right;
    };
    unordered_map<int,node*>mp;
    node* create(int preL,int preR,int inL,int inR){ 
        if(inL>inR) return NULL;
        node* now = new node;
        now->val = pre[preL];
        int i;
        for(i=inL;i<=inR;i++){ 
            if(in[i]==pre[preL]) break;
        }
        int numLeft=i-inL;
        now->left=create(preL+1,preL+numLeft,inL,i-1);
        now->right=create(preL+numLeft+1,preR,i+1,inR);
        mp[now->val]=now;
        return now;
    }
    
    node* lca(node* root,node* a,node* b){ 
        if(root == NULL)    return NULL;
        if(root==a || root==b)  return root;
        node* L = lca(root->left,a,b);
        node* R = lca(root->right,a,b);
        if(L==NULL) return R;
        if(R==NULL) return L;
        return root;
    }
    
    int main()
    { 
        int m,n;
        scanf("%d %d",&m,&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 = create(0,n-1,0,n-1);
        for(int i=0;i<m;i++){ 
            int a,b;
            scanf("%d %d",&a,&b);
            if(!mp[a] && !mp[b]) printf("ERROR: %d and %d are not found.\n",a,b);
            else if(!mp[a]) printf("ERROR: %d is not found.\n",a);
            else if(!mp[b]) printf("ERROR: %d is not found.\n",b);
            else{ 
                node* res = lca(root,mp[a],mp[b]);
                if(res->val==a)
                    printf("%d is an ancestor of %d.\n",a,b);
                else if(res->val==b)
                    printf("%d is an ancestor of %d.\n",b,a);
                else
                    printf("LCA of %d and %d is %d.\n",a,b,res->val);
            }
        }
        return 0;
    }

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzIxNDgwNjA3_size_16_color_FFFFFF_t_70]  
[代码二来自柳诺][Link 3]  
题目大意：给出中序序列和先序序列，再给出两个点，求这两个点的最近公共祖先～

分析：不用建树～已知某个树的根结点，若a和b在根结点的左边，则a和b的最近公共祖先在当前子树根结点的左子树寻找，如果a和b在当前子树根结点的两边，在当前子树的根结点就是a和b的最近公共祖先，如果a和b在当前子树根结点的右边，则a和b的最近公共祖先就在当前子树的右子树寻找。中序加先序可以唯一确定一棵树，在不构建树的情况下，在每一层的递归中，可以得到树的根结点，在此时并入lca算法可以确定两个结点的公共祖先～

#include <iostream>
    #include <vector>
    #include <map>
    using namespace std;
    map<int, int> pos;
    vector<int> in, pre;
    void lca(int inl, int inr, int preRoot, int a, int b) { 
        if (inl > inr) return;
        int inRoot = pos[pre[preRoot]], aIn = pos[a], bIn = pos[b];
        if (aIn < inRoot && bIn < inRoot)
            lca(inl, inRoot-1, preRoot+1, a, b);
        else if ((aIn < inRoot && bIn > inRoot) || (aIn > inRoot && bIn < inRoot))
            printf("LCA of %d and %d is %d.\n", a, b, in[inRoot]);
        else if (aIn > inRoot && bIn > inRoot)
            lca(inRoot+1, inr, preRoot+1+(inRoot-inl), a, b);
        else if (aIn == inRoot)
                printf("%d is an ancestor of %d.\n", a, b);
        else if (bIn == inRoot)
                printf("%d is an ancestor of %d.\n", b, a);
    }
    int main() { 
        int m, n, a, b;
        scanf("%d %d", &m, &n);
        in.resize(n + 1), pre.resize(n + 1);
        for (int i = 1; i <= n; i++) { 
            scanf("%d", &in[i]);
            pos[in[i]] = i;
        }
        for (int i = 1; i <= n; i++) scanf("%d", &pre[i]);
        for (int i = 0; i < m; i++) { 
            scanf("%d %d", &a, &b);
            if (pos[a] == 0 && pos[b] == 0)
                printf("ERROR: %d and %d are not found.\n", a, b);
            else if (pos[a] == 0 || pos[b] == 0)
                printf("ERROR: %d is not found.\n", pos[a] == 0 ? a : b);
            else
                lca(1, n, 1, a, b);
        }
        return 0;
    }

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzIxNDgwNjA3_size_16_color_FFFFFF_t_70 1]

[Link 1]: https://blog.csdn.net/qq_21480607/article/details/106660085
[Link 2]: https://blog.csdn.net/qq_21480607/article/details/106987591
[1151 LCA in a Binary Tree _30]: https://pintia.cn/problem-sets/994805342720868352/problems/1038430130011897856
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzIxNDgwNjA3_size_16_color_FFFFFF_t_70]: /images/20230209/9dadb564c08b446ca1e3925f01604447.png
[Link 3]: https://blog.csdn.net/liuchuo/article/details/82560863
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzIxNDgwNjA3_size_16_color_FFFFFF_t_70 1]: /images/20230209/a2c17719bf824c1cb83864384e3df0e6.png