ZOJ3829——Known Notation（贪心，模拟）

Known Notation

---

Time Limit: 2 Seconds      Memory Limit: 65536 KB

---

Do you know reverse Polish notation (RPN)? It is a known notation in the area of mathematics and computer science. It is also known as postfix notation since every operator in an expression follows all of its operands. Bob is a student in Marjar University. He is learning RPN recent days.

To clarify the syntax of RPN for those who haven't learnt it before, we will offer some examples here. For instance, to add 3 and 4, one would write "3 4 +" rather than "3 + 4". If there are multiple operations, the operator is given immediately after its second operand. The arithmetic expression written "3 - 4 + 5" in conventional notation would be written "3 4 - 5 +" in RPN: 4 is first subtracted from 3, and then 5 added to it. Another infix expression "5 + ((1 + 2) × 4) - 3" can be written down like this in RPN: "5 1 2 + 4 × + 3 -". An advantage of RPN is that it obviates the need for parentheses that are required by infix.

In this problem, we will use the asterisk "*" as the only operator and digits from "1" to "9" (without "0") as components of operands.

You are given an expression in reverse Polish notation. Unfortunately, all space characters are missing. That means the expression are concatenated into several long numeric sequence which are separated by asterisks. So you cannot distinguish the numbers from the given string.

You task is to check whether the given string can represent a valid RPN expression. If the given string cannot represent any valid RPN, please find out the minimal number of operations to make it valid. There are two types of operation to adjust the given string:

1. Insert. You can insert a non-zero digit or an asterisk anywhere. For example, if you insert a "1" at the beginning of "2*3*4", the string becomes "12*3*4".
2. Swap. You can swap any two characters in the string. For example, if you swap the last two characters of "12*3*4", the string becomes "12*34*".

The strings "2*3*4" and "12*3*4" cannot represent any valid RPN, but the string "12*34*" can represent a valid RPN which is "1 2 * 34 *".

Input

There are multiple test cases. The first line of input contains an integer T indicating the number of test cases. For each test case:

There is a non-empty string consists of asterisks and non-zero digits. The length of the string will not exceed 1000.

Output

For each test case, output the minimal number of operations to make the given string able to represent a valid RPN.

Sample Input

3
1*1
11*234**
*

Sample Output

1
0
2

---

Author: CHEN, Cong

首先有这样几个性质。

1.m个 * 至少需要 m+1 个数字，如果 数字数量n<m+1 那么至少要添加 m+1-n 个 数字。

2.一个序列的任意前缀都满足条件n>=m+1，则该序列合法。

3.连续的n个数字后接m个* (n>=m+1)， 一定合法。

所以可以依据贪心的思想，数字尽量往前放，*尽量往后放一定是正确的。

首先可以确定最少添加的数字数量，并且把数字放到最前面。

然后扫描一遍序列，依据性质2，将不合法的*与结尾的数字交换，交换的代价一定是小于添加元素的。

#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <iostream>
#define INF 0x7fffffff
using namespace std;

typedef long long LL;
const int N = 1e5 + 10;

int main()
{
    int T;
    char s[2005];
    scanf("%d",&T);
    while(T--)
    {
        scanf("%s",&s);
        int len=strlen(s);
        int op=0,num=0;
        for(int i=0; i<len; i++)
        {
            if(s[i]=='*') op++;
            else num++;
        }

        int k=max(0, op+1-num);
        int ans=k;
        
        int cnt_op=0, cnt_num=k;
        int last=len-1;
        while(last && s[last]=='*') last--;
        
        for(int i=0; i<len; i++)
        {
            if(s[i]=='*') cnt_op++;
            else cnt_num++;

            if(cnt_op+1>cnt_num)
            {
                swap(s[i], s[last]);
                while(last && s[last]=='*') last--;
                cnt_op--;
                cnt_num++;
                ans++;
            }
        }

        printf("%d\n",ans);
    }

    return 0;
}