HDU 3460 Ancient Printer(思维题或字典树)

Ancient Printer

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/65536 K (Java/Others)
Total Submission(s): 1477    Accepted Submission(s): 735

Problem Description

The contest is beginning! While preparing the contest, iSea wanted to print the teams' names separately on a single paper.
Unfortunately, what iSea could find was only an ancient printer: so ancient that you can't believe it, it only had three kinds of operations:

● 'a'-'z': twenty-six letters you can type
● 'Del': delete the last letter if it exists
● 'Print': print the word you have typed in the printer

The printer was empty in the beginning, iSea must use the three operations to print all the teams' name, not necessarily in the order in the input. Each time, he can type letters at the end of printer, or delete the last letter, or print the current word. After printing, the letters are stilling in the printer, you may delete some letters to print the next one, but you needn't delete the last word's letters.
iSea wanted to minimize the total number of operations, help him, please.

 

Input

There are several test cases in the input.

Each test case begin with one integer N (1 ≤ N ≤ 10000), indicating the number of team names.
Then N strings follow, each string only contains lowercases, not empty, and its length is no more than 50.

The input terminates by end of file marker.

 

Output

For each test case, output one integer, indicating minimum number of operations.

 

Sample Input

  

   2
freeradiant
freeopen
  

 

Sample Output

  

   21

   

    

     Hint
    
The sample's operation is:
f-r-e-e-o-p-e-n-Print-Del-Del-Del-Del-r-a-d-i-a-n-t-Print
   
    
  

 

Author

iSea @ WHU

 

Source

2010 ACM-ICPC Multi-University Training Contest（3）——Host by WHU 

一 字符串排序

最小操作数=第一个字符串+相邻字符串不同的部分+最后一个和最大长度的那个互换（因为最后一个不用删除，所以用最大的那个）+n（print数）

#include<iostream>
#include<string.h>
#include<algorithm>
#include<stdio.h>
using namespace std;
string w[10005];
int calc(string a, string b) {
	int i;
	for (i = 0; i < a.length() && i < b.length() && a[i] == b[i]; i++)
		;
	return a.length() - i + b.length() - i;
}
int main() {
	int n, i;
	while (scanf("%d", &n) != EOF) {
		for (i = 0; i < n; i++)
			cin >> w[i];
		sort(w, w + n);
		int sum = w[0].length() + 1;
		int MAX = w[0].length();
		for (i = 1; i < n; i++) {
			sum += calc(w[i], w[i - 1]) + 1;
			if (w[i].length() > MAX)
				MAX = w[i].length();
		}
		printf("%d\n", sum + w[n - 1].length() - MAX);
	}
	return 0;
}

二 字典树

题意要求的是打印单词的最少操作数

只有三个操作：

输入，删除，还有打印，前缀就不需要重复输入，想到了字典树，这道题目也就好做了

要 求最少的操作数，所以首先要归类，所有拥有相同前缀的单词，放在一块输入，题目还说，最后一次打印不需要删除

理论上是像上面说的，但实际我们在计算最少操作数时，可以这样算，首先假设所有的单词都需要重新打印还有删除，所以总操作数是单词总长度*2

接下来，计算出前缀，可以这样想，只需计算出每一个节点被哪些单词共有，如题目中的样例，“freeradiant”，“freeopen”，f 被俩个节点共有，所以省了一步删除还有一步输入，所以就是（2-1）*2；

最后再找 出最长的一个单词的长度max，很容易理解，最后一行不用删除，那最后一行肯定是越长越好，

根据这三个数值，可以发现，最少的操作=总操作数-总共可以省掉的操作数-多删除掉的最后一行的长度(max)

在代码实现上，额，125ms，不是很快，还是用到了栈还有字典树

#include<iostream>
#include<stack>
#include<string>
using namespace std;
struct node
{
    node *next[26];
    int v;//记录有多少个单词经过该节点，或者说，有多少单词拥有到该节点为止的前缀
    int lev;//层数，好像用处不是很大
};
node *root;
void insert(char *s)//插入操作
{
    node *p=root;
    for(;*s!='\0';s++)
    {
        int d=*s-'a';
        if(p->next[d]!=NULL)
        {
            p=p->next[d];
            p->v++;
        }
        else
        {
            p->next[d]=new node();
            p=p->next[d];    
            p->v++;
        }
    }
}
int find()//遍历整棵树
{
    node *p=root,*cur=root,*nex;
    int sum=0;
    stack<node*> nd;
    cur->lev=0;
    nd.push(cur);
    while(!nd.empty())
    {
        cur=nd.top();
        nd.pop();
        if(cur->lev>0)//根节点不计算
        {
          sum+=(cur->v-1)*2;
        }
        for(int i=0;i<26;i++)
        {
            nex=cur->next[i];
            if(nex!=NULL&&nex->v>1)//单词数大于一，表示有可以省掉的操作，才有必要进行计算，
            {
                nex->lev=cur->lev+1;
                nd.push(nex);//压入栈
            }
        }
    }
    return sum;
}
void del(node *p)//释放空间
{
    for(int i=0;i<26;i++)
    {
        if(p->next[i]!=NULL)
            del(p->next[i]);
    }
    delete(p);
}
int main()
{
    int sum,i,j,n,max,len;
    char str[55];
    while(scanf("%d",&n)!=EOF)
    {
        sum=max=0;
        root=new node();
        for(i=0;i<n;i++)
        {
            scanf("%s",str);
            insert(str);
            len=strlen(str);
            if(len>max)//找出最长的单词
                max=len;
            sum+=len;//计算单词总长度
        }
        j=find();
        sum=sum*2-j-max+n;
        cout<<sum<<endl;
        del(root);
    }
}