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hdu3699 A hard Aoshu Problem 暴搜

2024-07-31 00:34:14   220人阅读

http://acm.hdu.edu.cn/showproblem.php?pid=3699

A hard Aoshu Problem

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 62768/32768 K (Java/Others)
Total Submission(s): 968    Accepted Submission(s): 490


Problem Description
Math Olympiad is called “Aoshu” in China. Aoshu is very popular in elementary schools. Nowadays, Aoshu is getting more and more difficult. Here is a classic Aoshu problem:


ABBDE __ ABCCC = BDBDE

In the equation above, a letter stands for a digit(0 – 9), and different letters stands for different digits. You can fill the blank with ‘+’, ‘-‘ , ‘×’ or ‘÷’. 

How to make the equation right? Here is a solution:


12245 + 12000 = 24245

In that solution, A = 1, B = 2, C = 0, D = 4, E = 5, and ‘+’ is filled in the blank.

When I was a kid, finding a solution is OK. But now, my daughter’s teacher tells her to find all solutions. That’s terrible. I doubt whether her teacher really knows how many solutions are there. So please write a program for me to solve this kind of problems.

 

Input
The first line of the input is an integer T( T <= 20) indicating the number of test cases.

Each test case is a line which is in the format below:


s1 s2 s3 

s1, s2 and s3 are all strings which are made up of capital letters. Those capital letters only include ‘A’,’B’,’C’,’D’ and ‘E’, so forget about ‘F’ to ‘Z’. The length of s1,s2 or s3 is no more than 8.

When you put a ‘=’ between s2 and s3, and put a operator( ‘+’,’-‘, ‘×’ or ‘÷’.) between s1 and s2, and replace every capital letter with a digit, you get a equation. 

You should figure out the number of solutions making the equation right.

Please note that same letters must be replaced by same digits, and different letters must be replaced by different digits. If a number in the equation is more than one digit, it must not have leading zero.

 

Output
For each test case, print an integer in a line. It represents the number of solutions.
 

Sample Input
2
A A A
BCD BCD B
 

Sample Output
5
72
 

Source
2010 Asia Fuzhou Regional Contest

题意很简单，都不知道咋描述。。

就是爆搜下，注意下前导0以及除法别直接除。。

/**
 * @author neko01
 */
//#pragma comment(linker, "/STACK:102400000,102400000")
#include <cstdio>
#include <cstring>
#include <string.h>
#include <iostream>
#include <algorithm>
#include <queue>
#include <vector>
#include <cmath>
#include <set>
#include <map>
using namespace std;
typedef long long LL;
#define min3(a,b,c) min(a,min(b,c))
#define max3(a,b,c) max(a,max(b,c))
#define pb push_back
#define mp(a,b) make_pair(a,b)
#define clr(a) memset(a,0,sizeof a)
#define clr1(a) memset(a,-1,sizeof a)
#define dbg(a) printf("%d\n",a)
typedef pair<int,int> pp;
const double eps=1e-8;
const double pi=acos(-1.0);
const int INF=0x7fffffff;
const LL inf=(((LL)1)<<61)+5;
map<char,int>mp;
char s[3][10];
int val[3][10];
int a[10];
bool vis[10];
int ans;
int gao(int x)
{
    int ans=0,len=strlen(s[x]);
    for(int i=0;i<len;i++)
        ans=ans*10+a[val[x][i]];
    return ans;
}
void dfs(int step)
{
    if(step==0)
    {
        if(a[val[0][0]]==0&&strlen(s[0])>1)
            return;
        if(a[val[1][0]]==0&&strlen(s[1])>1)
            return;
        if(a[val[2][0]]==0&&strlen(s[2])>1)
            return;
        int x=gao(0),y=gao(1),z=gao(2);
        if(x+y==z) ans++;
        if(x-y==z) ans++;
        if((LL)x*(LL)y==z) ans++;
        if(y!=0&&(LL)z*(LL)y==x) ans++;
        return;
    }
    for(int i=0;i<10;i++)
    {
        if(!vis[i])
        {
            vis[i]=true;
            a[step]=i;
            dfs(step-1);
            vis[i]=false;
        }
    }
}
int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        clr(vis);
        mp.clear();
        clr(val);
        int num=1;
        ans=0;
        for(int i=0;i<3;i++)
        {
            scanf("%s",s[i]);
            int len=strlen(s[i]);
            for(int j=0;j<len;j++)
            {
                if(mp[s[i][j]]==0)
                {
                    mp[s[i][j]]=num++;
                    val[i][j]=mp[s[i][j]];
                }
                else val[i][j]=mp[s[i][j]];
            }
        }
        dfs(num-1);
        printf("%d\n",ans);
    }
    return 0;
}



hdu3699 A hard Aoshu Problem 暴搜


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