C - たくさんの数式 / Many Formulas
Time limit : 2sec / Memory limit : 256MB
Score : 300 points
Problem Statement
You are given a string S consisting of digits between 1
and 9
, inclusive. You can insert the letter +
into some of the positions (possibly none) between two letters in this string. Here, +
must not occur consecutively after insertion.
All strings that can be obtained in this way can be evaluated as formulas.
Evaluate all possible formulas, and print the sum of the results.
Constraints
- 1≤|S|≤10
- All letters in S are digits between
1
and9
, inclusive.
Input
The input is given from Standard Input in the following format:
S
Output
Print the sum of the evaluated value over all possible formulas.
Sample Input 1
Copy
125
Sample Output 1
Copy
176
There are 4 formulas that can be obtained: 125
, 1+25
, 12+5
and 1+2+5
. When each formula is evaluated,
- 125
- 1+25=26
- 12+5=17
- 1+2+5=8
Thus, the sum is 125+26+17+8=176.
Sample Input 2
Copy
9999999999
Sample Output 2
Copy
12656242944
#include <iostream>
#include <cstdio>
#include <string>
using namespace std;
long long toIntSum(string s)
{
long long sum=0,tmp=0;
for (int i=0;i<s.size();i++)
{
if(s[i]=='+')
{
sum+=tmp;
tmp=0;
}
else
tmp=tmp*10+s[i]-'0';
}
return sum+tmp;
}
int main ()
{
string str;
cin>>str;
int len =str.size()-1,a[11]={0};//加号最多=串长-1;a[i]==0表示i处没有加号,a[i]==1表示i处有加号.
long long sum=0;
while(true)
{
string s;
for (int i=0;i<len;i++)
{
a[i+1]+=a[i]/2;
a[i]%=2;
}
if(a[len])
break;
for (int i=0;i<len;i++)//把加号和数字合成一个串
{
s+=str[i];
if(a[i])
s+="+";
}
s+=str[len];
sum+=toIntSum(s);
a[0]++;
}
cout<<sum;
return 0;
}