POJ-1785-Binary Search Heap Construction(笛卡尔树)

Description

Read the statement of problem G for the definitions concerning trees. In the following we define the basic terminology of heaps. A heap is a tree whose internal nodes have each assigned a priority (a number) such that the priority of each internal node is less
than the priority of its parent. As a consequence, the root has the greatest priority in the tree, which is one of the reasons why heaps can be used for the implementation of priority queues and for sorting.

A binary tree in which each internal node has both a label and a priority, and which is both a binary search tree with respect to the labels and a heap with respect to the priorities, is called a treap. Your task is, given a set of label-priority-pairs, with
unique labels and unique priorities, to construct a treap containing this data.

Input

The input contains several test cases. Every test case starts with an integer n. You may assume that 1<=n<=50000. Then follow n pairs of strings and numbers l1/p1,...,ln/pn denoting the label and priority of each node. The strings are non-empty and composed
of lower-case letters, and the numbers are non-negative integers. The last test case is followed by a zero.

Output

For each test case output on a single line a treap that contains the specified nodes. A treap is printed as (< left sub-treap >< label >/< priority >< right sub-treap >). The sub-treaps are printed recursively, and omitted if leafs.

Sample Input

7 a/7 b/6 c/5 d/4 e/3 f/2 g/1

7 a/1 b/2 c/3 d/4 e/5 f/6 g/7

7 a/3 b/6 c/4 d/7 e/2 f/5 g/1

0

Sample Output

(a/7(b/6(c/5(d/4(e/3(f/2(g/1)))))))

(((((((a/1)b/2)c/3)d/4)e/5)f/6)g/7)

(((a/3)b/6(c/4))d/7((e/2)f/5(g/1)))

Source

Ulm Local 2004

思路：先按字符串排下序，建笛卡尔树，递归输出。

#include <cstdio>

#include <cstring>

#include <algorithm>

using namespace std;

struct S{

int id,val;

int parent,l,r;

}node[50005];

int stk[50005],top;

char s[50005][20];

bool cmp(struct S a,struct S b)

{

    if(strcmp(s[a.id],s[b.id])<0) return 1;

    return 0;

}

int build(int n)

{

    int i;

    top=0;

    stk[top]=0;

    for(i=1;i<n;i++)

    {

        while(top>=0 && node[stk[top]].val<node[i].val) top--;//注意。这里让小于当前值的出栈

        if(top>-1)

        {

            node[i].parent=stk[top];

            node[node[stk[top]].r].parent=i;

            node[i].l=node[stk[top]].r;

            node[stk[top]].r=i;

        }

        else

        {

            node[stk[0]].parent=i;

            node[i].l=stk[0];

        }

        stk[++top]=i;

    }

    return stk[0];//返回根节点

}

void dfs(int x)

{

    printf("(");//先输出左括号

    if(node[x].l!=-1) dfs(node[x].l);//假设有左子树。就先输出左子树

    printf("%s/%d",s[node[x].id],node[x].val);//输出自己

    if(node[x].r!=-1) dfs(node[x].r);//再输出右子树

    printf(")");//右括号

}

int main()

{

    int n,i,root;

    while(~scanf("%d",&n) && n)

    {

        for(i=0;i<n;i++)

        {

            scanf("%*[ ]%[a-z]/%d",s[i],&node[i].val);

            node[i].id=i;

            node[i].parent=node[i].l=node[i].r=-1;

        }

        sort(node,node+n,cmp);//按字符串字典序排序

        root=build(n);//建树

        dfs(root);//递归输出

        printf("\n");

    }

}

巴特西

POJ-1785-Binary Search Heap Construction(笛卡尔树)

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