1143. Lowest Common Ancestor (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.

A binary search tree (BST) is recursively defined as a binary tree which has the following properties:

The left subtree of a node contains only nodes with keys less than the node's key.
The right subtree of a node contains only nodes with keys greater than or equal to the node's key.
Both the left and right subtrees must also be binary search trees.

Given any two nodes in a BST, 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 (<= 1000), the number of pairs of nodes to be tested; and N (<= 10000), the number of keys in the BST, respectively. In the second line, N distinct integers are given as the preorder traversal sequence of the BST. 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 BST, 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

6 3 1 2 5 4 8 7

2 5

8 7

1 9

12 -3

0 8

99 99

Sample Output:

LCA of 2 and 5 is 3.

8 is an ancestor of 7.

ERROR: 9 is not found.

ERROR: 12 and -3 are not found.

ERROR: 0 is not found.

ERROR: 99 and 99 are not found.

建树有两种方法，一种是把前序遍历从小到大排序就是中序遍历，然后根据前中序遍历建树。注释部分。
另一种是直接用前序遍历建树。其实中序遍历就是助于判断左右子树，用前序遍历就可以单独判断左右子树的。
代码：

#include <iostream>

#include <cstdio>

#include <algorithm>

#include <map>

using namespace std;

struct tree

{

    int Data,Height;

    tree *Last,*Left,*Right;

}*head;

int q[],z[],m,n;

map<int,tree *> mp;

tree *createNode(int d,int h)

{

    tree *p = new tree();

    p -> Data = d;

    mp[d] = p;

    p -> Height = h;

    p -> Last = p -> Left = p -> Right = NULL;

    return p;

}

tree *createTree(int ql,int qr,int zl,int zr,int h)

{

    tree *p = createNode(q[ql],h);

    for(int i = zl;i <= zr;i ++)

    {

        if(z[i] == q[ql])

        {

            if(i > zl)p -> Left = createTree(ql + ,ql + i - zl,zl,i - ,h + ),p -> Left -> Last = p;

            if(i < zr)p -> Right = createTree(ql + i - zl + ,qr,i + ,zr,h + ),p -> Right -> Last = p;

            break;

        }

    }

    return p;

}

tree *createTre(int l,int r,int h)

{

    tree *p = createNode(q[l],h);

    for(int i = l + ;i <= r + ;i ++)

    {

        if(i == r +  || q[i] >= q[l])

        {

            if(i > l + )p -> Left = createTre(l + ,i - ,h + ),p -> Left -> Last = p;

            if(r >= i)p -> Right = createTre(i,r,h + ),p -> Right -> Last = p;

            return p;

        }

    }

}

void check(int a,int b)

{

    if(mp[a] == NULL && mp[b] == NULL)printf("ERROR: %d and %d are not found.\n",a,b);

    else if(mp[a] == NULL)printf("ERROR: %d is not found.\n",a);

    else if(mp[b] == NULL)printf("ERROR: %d is not found.\n",b);

    else

    {

        tree *t1 = mp[a],*t2 = mp[b];

        while(t1 -> Height != t2 -> Height)

        {

            if(t1 -> Height > t2 -> Height)t1 = t1 -> Last;

            else t2 = t2 -> Last;

        }

        if(t1 == t2)

        {

            printf("%d is an ancestor of %d.\n",t1 -> Data,a == t1 -> Data ? b : a);

            return;

        }

        t1 = t1 -> Last;

        t2 = t2 -> Last;

        while(t1 != t2)

        {

            t1 = t1 -> Last;

            t2 = t2 -> Last;

        }

        printf("LCA of %d and %d is %d.\n",a,b,t1 -> Data);

    }

}

int main()

{

    int a,b;

    scanf("%d%d",&m,&n);

    for(int i = ;i < n;i ++)

    {

        scanf("%d",&q[i]);

        //z[i] = q[i];

    }

    //sort(z,z + n);

//    head = createTree(0,n - 1,0,n - 1,0);

    head = createTre(,n - ,);

    for(int i = ;i < m;i ++)

    {

        scanf("%d%d",&a,&b);

        check(a,b);

    }

}

巴特西

1143. Lowest Common Ancestor (30)

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