Primary Arithmetic

本文介绍了一种计算多位数相加时进位次数的方法,并提供了一个C++实现示例。该方法对于评估数学教育中加法练习题难度有所帮助。

FJNU.1531
PKU.2562

Description
Children are taught to add multi-digit numbers from right-to-left one digit at a time. Many find the "carry" operation - in which a 1 is carried from one digit position to be added to the next - to be a significant challenge. Your job is to count the number of carry operations for each of a set of addition problems so that educators may assess their difficulty.

Input
Each line of input contains two unsigned integers less than 10 digits. The last line of input contains 0 0.

Output
For each line of input except the last you should compute and print the number of carry operations that would result from adding the two numbers, in the format shown below.

Sample Input
123 456
555 555
123 594
0 0

Sample Output
No carry operation.
3 carry operations.
1 carry operation.

Source
23 September, 2000 - Waterloo

My Program

#include<iostream>
#define N 10
using namespace std;

int main()
{
    
int c[N+1],d[N+1];
    
int m,n,i,k;
    
long a,b;
    
while(cin>>a>>b)
    
{
        
for(i=0;i<=N;i++)
            c[i]
=d[i]=0;
        
if(a==0&&b==0)
            
break;
        m
=n=N;k=0;
        
while(a>0)
        
{
            c[m]
=a%10;
            a
/=10;
            m
--;
        }

        
while(b>0)
        
{
            d[n]
=b%10;
            b
/=10;
            n
--;
        }

        
for(i=N;i>0;i--)
        
{
            d[i]
+=c[i];
            
if(d[i]>=10)
            
{
                k
++;
                d[i
-1]++;
                d[i]
%=10;
            }

        }

        
if(k==0)
            cout
<<"No carry operation."<<endl;
        
else
            
if(k==1)
                cout
<<"1 carry operation."<<endl;
            
else
                cout
<<k<<" carry operations."<<endl;
    }

    
return 0;
}

YOYO's Note: 
计算有多少次进位,虽然它只是10位,我还是用了数组 = = ||
不知道有没有其他更简单的方法……?或许直接加了比较是否会好些?懒得去试了……
注意输出时0、单数、复数的格式。

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