无限大整数相加算法的C语言源代码

忙里偷闲，终于完成了无限大整数相加算法的C语言代码,无限大整数相加算法的算法分析在这里。

500位的加法运行1000次，不打印结果的情况下耗时0.036秒，打印结果的情况下耗时16.285秒。

下面是源码：

#include <stdio.h>

#include <stdlib.h>

#include<string.h>

#include <time.h>



#define MAXNUM 1000000000000000000

/*

存储数据用的结构

long int型指针（Number）指向一个long int 数组，索引值最底的位，

为10进制数的最低18位。依次类推。

int型数值（Length）为数组的长度。

因为数组长度受int型最大值的限制，所以这个算法也不能真正实现“无限”。

*/

struct BigInt{

    long long* Number;

    int Length;

};



void PrintBigInt(BigInt* bigNumber);



long long pow(int x, int y);



BigInt* MakeBigIntFromString(char* bigIntString);



void DeleteBigInt(BigInt* bigNumber);



BigInt* Add2BigInt(BigInt* n1, BigInt* n2);



void main(){



    char* numberStr = "99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999\0";

    char* numberStr2 = "99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999\0";

    BigInt* bn = MakeBigIntFromString(numberStr);

    BigInt* bn2 = MakeBigIntFromString(numberStr2);

    double tstart, tend, tcost;

    tstart = clock();

    PrintBigInt(bn);

    PrintBigInt(bn2);

    for (int i = 0; i < 1000; i++){

        BigInt* result = Add2BigInt(bn, bn2);

        //PrintBigInt(result);

        DeleteBigInt(result);

    }

    DeleteBigInt(bn);

    DeleteBigInt(bn2);

    tend = clock();

    tcost = (double)(tend - tstart) / CLOCKS_PER_SEC;

    printf("%lf\n", tcost);

}



BigInt* Add2BigInt(BigInt* n1, BigInt* n2){



    int maxLength = n1->Length;

    if (maxLength < n2->Length){

        maxLength = n2->Length;

    }



    /*

    加法只可能产生1位的进位，所以，只需要创建一个和最大长度相同的。

    */

    BigInt* nOut = (BigInt*)malloc(sizeof(BigInt));

    nOut->Length = maxLength;

    nOut->Number = (long long*)malloc(sizeof(long long)* nOut->Length);

    for (int i = 0; i < nOut->Length; i++){

        nOut->Number[i] = 0;

    }

    for (int i = 0; i < nOut->Length; i++){

        if (n1->Length > i){

            nOut->Number[i] += n1->Number[i];

        }

        if (n2->Length > i){

            nOut->Number[i] += n2->Number[i];

        }



        /*

        处理进位。最高位不需要处理。

        */

        if (i != (nOut->Length - 1)){

            if (nOut->Number[i] >= MAXNUM){

                nOut->Number[i] -= MAXNUM;

                nOut->Number[i + 1] = 1;

            }

        }

    }



    return nOut;



}



/*

从高到低显示数值

不考虑单个long long数据超出18位的情况。

*/

void PrintBigInt(BigInt* bigNumber){

    if (bigNumber == NULL){

        return;

    }

    if (bigNumber->Length < 1){

        return;

    }

    int length = bigNumber->Length - 1;

    for (int i = length; i >= 0; i--){

        if (i != length){

            if (bigNumber->Number[i] == 0){

                printf("000000000000000000");

            }

            else{

                printf("%018lld", bigNumber->Number[i]);

            }

        }

        else{

            if ((*bigNumber).Number[i] != 0){

                printf("%lld", bigNumber->Number[i]);

            }

        }

    }

    printf("\n");



}



/*

把字符串表示的数值格式化为BigInt型的结构

字符串结束位置用\0表示。

*/

BigInt* MakeBigIntFromString(char* bigIntString){

    /*获取字符串长度*/

    int cLength = strlen(bigIntString);

    BigInt* outBigInt = (BigInt*)malloc(sizeof(BigInt));

    if (cLength % 18 != 0){

        outBigInt->Length = cLength / 18 + 1;

    }

    else{

        outBigInt->Length = cLength / 18;

    }

    if (outBigInt->Length == 0){

        outBigInt->Length == 1;

        outBigInt->Number = (long long *)malloc(sizeof(long long));

        outBigInt->Number[0] = 0;



        return outBigInt;

    }

    outBigInt->Number = (long long *)malloc(sizeof(long long)* outBigInt->Length);

    for (int i = 0; i < outBigInt->Length; i++){

        outBigInt->Number[i] = 0;

    }



    int powNum = 0;

    int numPos = 0;

    for (int i = cLength - 1; i >= 0; i--){

        powNum = (cLength - 1 - i) % 18;

        numPos = (cLength - 1 - i) / 18;

        outBigInt->Number[numPos] += (bigIntString[i] - 48) * pow(10, powNum);

    }



    return outBigInt;

}



/*

简单的幂函数

x y 都必须为正整数

*/

long long pow(int x, int y){

    if (x == 0 || x < 0 || y < 0){

        return 0;

    }

    if (x == 1 || y == 0){

        return 1;

    }

    long long outNum = x;



    for (int i = 1; i < y; i++){

        outNum = outNum * x;

    }



    return outNum;

}



void DeleteBigInt(BigInt* bigNumber){

    if (bigNumber != NULL){

        if (bigNumber->Number != NULL){

            free(bigNumber->Number);

        }

        free(bigNumber);

    }

}