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);
    }
}