AtCoder Beginner Contest 045 C

C - たくさんの数式 / Many Formulas

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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 and 9, inclusive.

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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.

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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.

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Sample Input 2

Copy

9999999999

Sample Output 2

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12656242944
题意：把一个数用不同的切割方法 把每种切割后的数累加
题解：用二进制转化，用&符号判断切割的位置

#include<bits/stdc++.h>
using namespace std;
int main()
{
    string s;
    cin>>s;
    int n=s.size();
    int m=1<<(n-1);
    long long ans=0;
    for(int i=0;i<m;i++)
    {
        long long t=s[0]-'0';
        for(int j=0;j<n;j++)
        {
            if(j==n-1||i&1<<j)      //切的方法 
            {
                ans+=t;
                t=0;
                if(j==n-1)  break;
            }
            t*=10;
            t+=s[j+1]-'0';
        }
    }
    cout<<ans<<endl;
}