hdu4249 A Famous Equation

A Famous Equation

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 38    Accepted Submission(s): 18

Problem Description

Mr. B writes an addition equation such as 123+321=444 on the blackboard after class. Mr. G removes some of the digits and makes it look like “1?3+??1=44?”. Here “?” denotes removed digits. After Mr. B realizes some digits are missing, he wants to recover them. Unfortunately, there may be more than one way to complete the equation. For example “1?3+??1=44?” can be completed to “123+321=444” , “143+301=444” and many other possible solutions. Your job is to determine the number of different possible solutions.

 

Input

Each test case describes a single line with an equation like a+b=c which contains exactly one plus sign “+” and one equal sign “=” with some question mark “?” represent missing digits. You may assume a, b and c are non-negative integers, and the length of each number is no more than 9. In the other words, the equation will contain three integers less than 1,000,000,000.

 

Output

For each test case, display a single line with its case number and the number of possible solutions to recover the equation.

 

Sample Input

   
   
   
   

    
    
    
    7+1?=1?
?1+?1=22
   
   
   
   

 

Sample Output

   
   
   
   

    
    
    
    Case 1: 3
Case 2: 1


    
    
    
    
 
     
 
      Hint 
     
 There are three solutions for the first case: 7+10=17, 7+11=18, 7+12=19 There is only one solution for the second case: 11+11=22 Note that 01+21=22 is not a valid solution because extra leading zeros are not allowed. 
    
    
    
    
     
   
   
   
   

 

Source

Fudan Local Programming Contest 2012

 

呃，动态规划题。

模拟高精度加法，从低位扫到高位。

dp[i][0]表示前i位满足条件且没进位的方法数，dp[i][1]表示前i位满足条件且进1的方法数。

暴力枚举每一位的数字，然后往前递推即可。

代码很难看，还是勉为其难的贴一下吧……orz，主要是前导0那部分处理的太搓了……

#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;

char str[105];
int a[15];
int b[15];
int c[15];
long long dp[10][2];

int main()
{
    int i,j,n,tag,t,aup,bup,cup,cnt=1,x,y,z,p,q,r;
    while(scanf("%s",str)!=EOF)
    {
        memset(dp,0,sizeof(dp));
        n=strlen(str);
        tag=0;
        aup=bup=cup=0;
        for (i=n-1;i>=0;i--)
        {
            if (str[i]=='=' || str[i]=='+') tag++;
            else
            {
                t=str[i]=='?'?-1:(str[i]-'0');
                if (tag==0) c[cup++]=t;
                if (tag==1) b[bup++]=t;
                if (tag==2) a[aup++]=t;
            }
        }
        if (cup<max(aup,bup))
        {
            printf("Case %d: 0\n",cnt++);
            continue;
        }
        for (i=aup;i<=cup;i++)
        {
            a[i]=0;
        }
        for (i=bup;i<=cup;i++)
        {
            b[i]=0;
        }
        for (i=0;i<cup;i++)
        {
            for (x=0;x<=9;x++)
            {
                if (i==aup-1 && aup!=1 && x==0 && a[i]==-1) continue;
                if (a[i]!=-1 && x>=1) continue;
                for (y=0;y<=9;y++)
                {
                    if (i==bup-1 && bup!=1 && y==0 && b[i]==-1) continue;
                    if (b[i]!=-1 && y>=1) continue;
                    for (z=0;z<=9;z++)
                    {
                        if (i==cup-1 && cup!=1 && z==0 && c[i]==-1) continue;
                        if (c[i]!=-1 && z>=1) continue;
                        p=a[i]==-1?x:a[i];
                        q=b[i]==-1?y:b[i];
                        r=c[i]==-1?z:c[i];
                        if (p+q==r)
                        {
                            if (i==0) dp[i][0]++;
                            else dp[i][0]+=dp[i-1][0];
                        }
                        if (p+q==10+r)
                        {
                            if (i==0) dp[i][1]++;
                            else dp[i][1]+=dp[i-1][0];
                        }
                        if (p+q+1==r && i!=0)
                        {
                            dp[i][0]+=dp[i-1][1];
                        }
                        if (p+q+1==r+10 && i!=0)
                        {
                            dp[i][1]+=dp[i-1][1];
                        }
                    }
                }
            }
         }
        printf("Case %d: %I64d\n",cnt++,dp[cup-1][0]);
    }
    return 0;
}