进位&&大数字符串处理

Have Fun with Numbers

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Notice that the number 123456789 is a 9-digit number consisting exactly the numbers from 1 to 9, with no duplication. Double it we will obtain 246913578, which happens to be another 9-digit number consisting exactly the numbers from 1 to 9, only in a different permutation. Check to see the result if we double it again!

Now you are suppose to check if there are more numbers with this property. That is, double a given number with k digits, you are to tell if the resulting number consists of only a permutation of the digits in the original number.

Input Specification:

Each input contains one test case. Each case contains one positive integer with no more than 20 digits.

Output Specification:

For each test case, first print in a line "Yes" if doubling the input number gives a number that consists of only a permutation of the digits in the original number, or "No" if not. Then in the next line, print the doubled number.

Sample Input:

1234567899

 

Sample Output:

Yes
2469135798

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通过分析题目可知数的最大位为20位，就连最大的long long类型此时也会爆掉，因此要采用字符串来处理。
上代码：

#include<stdio.h>
#include<string.h>

int main(void){
    char num1[21],num2[21];
    scanf("%s",num1);
    char doublenum[21];
    char tmp;
    strcpy(num2,num1);
    int len=strlen(num2);
    //每位数字乘2后存储在数组num2中
    int carrybit=0;//储存每位数运算后的进位

    char midch;

　　　　//字符串处理的关键
    for(int i=len-1;i>=1;i--){
　　　　　　//根据人工列式计算的步骤给出算法
        midch=num2[i];
        num2[i]=((num2[i]-'0')*2+carrybit)%10+'0'; //先乘2再加上次运算产生的进位
        carrybit=((midch-'0')*2+carrybit)/10; //计算这一次的进位，注意不能再用num2[i],因为num2[i]已经改变  错误：carrybit=((num2[i]-'0')*2+carrybit)/10

　　} 
　　num2[0]=(num2[0]-'0')*2+carrybit+'0'; //最高位不用再进位，若最高位大于9，下面会给出处理

    if(num2[0]>'9'){//如果乘2后的数和原来的数位数不匹配，直接判定No
        printf("No\n");
        printf("%d%d",(num2[0]-'0')/10,(num2[0]-'0')%10);
        printf("%s",&num2[1]);
    }else{
        strcpy(doublenum,num2);
        
　　　　//冒泡排序num1 num2
        for(int i=0;i<len-1;i++){
            for(int j=0;j<len-i-1;j++)
             if(num2[j]>num2[j+1]){
                tmp=num2[j];
                num2[j]=num2[j+1];
                num2[j+1]=tmp;
            }
        }
        
        for(int i=0;i<len-1;i++){
            for(int j=0;j<len-i-1;j++)
            if(num1[j]>num1[j+1]){
                tmp=num1[j];
                num1[j]=num1[j+1];
                num1[j+1]=tmp;
            }
        }

        if(strcmp(num1,num2)==0){
            printf("Yes\n");
            printf("%s",doublenum);
        }else{
            printf("No\n");
            printf("%s",doublenum);
        }
    }

    return 0;
}

题目来源：

https://pintia.cn/problem-sets/17/problems/263