大整数的加减乘除运算

客官°小女子只卖身不卖艺 2023-08-17 17:46 119阅读 0赞

**大整数乘法（不考虑负数）**

#include<iostream>
    #include<string>
    using namespace std;
    int main()
    {
        char str1[100];
        cin >> str1;
        char str2[100];
        cin >> str2;
        int a[100] = { 0 }, b[100] = { 0 }, result[10000] = { 0 };
        int len_a, len_b, len_r;
        len_a = strlen(str1);
        len_b = strlen(str2);
        //将字符串逆序存储
        for (int i = 0; i < len_a; i++)
        {
    	a[len_a - i - 1] = a[i] - '0';
        }
        for (int i = 0; i < len_b; i++)
        {
            b[len_b - i - 1] = b[i] - '0';
        }
        //计算，将结果存于c中
        for (int i = 0; i < len_b; i++)
        {
            for (int j = 0; j < len_a; j++)
            {
    	    result[i + j] += a[j] * a[i];
    	    result[i + j + 1] += result[i + j] / 10;		//处理进位
    	    result[i + j] %= 10;
            }
        }
        len_r = len_a + len_b;
        //删除结果集中高位的前缀0 
        while (result[len_r - 1] == 0 && len_r > 1)
        {
    	len_r--;
        }
        //将结果逆序输出
        for (int i = len_r - 1; i >= 0; i--)
        {
    	cout << result[i];
        }
        cout << endl;
        return 0;
    }

![20191002150210283.png][]

**大整数加法**

#include <iostream>
    using namespace std;
    #define MAXD 100
    int main()
    {
        char str1[MAXD], str2[MAXD]; 
        int a[MAXD], b[MAXD];
        memset(str1, 0, sizeof(str1));
        memset(str1, 0, sizeof(str2));
        memset(a, 0, sizeof(a));
        memset(b, 0, sizeof(b));//将这些数组清零
        cin >> str1;
        cin >> str2;
        int len1, len2, i, j;
        len1 = strlen(str1);
        len2 = strlen(str2);
        j = 0;
        int max = len1>len2 ? len1 : len2;
        //将字符串反转并且转换为数字保存到数组里面
        for (i = len1 - 1; i >= 0; i--)
        {
    	a[j++] = str1[i] - '0';
        }
        j = 0;
        for (i = len2 - 1; i >= 0; i--)
        {
    	b[j++] = str2[i] - '0';
        }
        for (i = 0; i < max; i++)
        {
    	b[i] += a[i];	//相加
    	if (b[i] >= 10)
    	{
    	    b[i] -= 10;
    	    b[i + 1] += 1;	//产生进位
    	}
        }
        if (b[max] != 0)
        {
    	cout << b[max];
        }
        for (i = max - 1; i >= 0; i--)
        {
    	cout << b[i];
        }
        cout << endl;
        return 0;
    }

![20191002163846153.png][]

**大整数减法**

#include <iostream>
    #include <algorithm>
    using namespace std;
    int main()
    {
        int a[201] = { 0 }, b[201] = { 0 }, c[201] = { 0 };
        int len_a, len_b, maxlen;
        char str1[200];
        char str2[200];
        //输入两个大整数 
        cin >> str1;
        cin >> str2;
        //获取大整数的长度 
        len_a = strlen(str1);
        len_b = strlen(str2);
        //大整数逆序存储 
        for (int i = 0; i < len_a; i++)
        {
    	a[i] = str1[len_a - i - 1] - '0';
        }
        for (int i = 0; i < len_b; i++)
        {
    	b[i] = str2[len_b - i - 1] - '0';
        }
        //去除大整数的前导0
        while (a[len_a - 1] == 0 && len_a > 1)
        {
    	len_a;
        }
        while (b[len_b - 1] == 0 && len_b > 1)
        {
    	len_b--;
        }
        maxlen = max(len_a, len_b);
        //若a<b，输出一个负号，并交换a和b，始终确保a存放较大数 
        if (len_a < len_b)
        {
    	cout << '-';
    	swap(a, b);
    	swap(len_a, len_b);
        }
        if (len_a == len_b)
        {
    	for (int i = len_a - 1, j = len_b - 1; i >= 0; i--)
    	{
    	    if (a[i] == b[i])
                {
    		continue;
    	    }
    	    else if (a[i]>b[i])
    	    {
    		break;
    	    }
    	    else
    	    {
    	    	cout << '-';
    		swap(a, b);
    		swap(len_a, len_b);
    		break;
    	    }
    	}
        }
        //计算a-b
        for (int i = 0; i < maxlen; i++)
        {
    	if (a[i]<b[i])
    	{
    	    a[i] += 10;			//借位
    	    a[i + 1]--;
    	}
    	c[i] = a[i] - b[i];
        }
        //去除结果中的前导0
        while (c[maxlen - 1] == 0 && maxlen>1)
        {
    	maxlen--;
        }
        //输出结果 
        for (int i = maxlen - 1; i >= 0; i--)
        {
    	cout << c[i];
        }
        cout << endl;
        return 0;
    }

![20191002171539238.png][]

**大整数除法**

#include <iostream>
    #include <cstring>
    using namespace std;
    //去除前导0
    int DelZero(int x[], int len_x)
    {
        int i = len_x;
        while (x[i - 1] == 0 && i > 1)
        {
    	i--;
        }
        return i;
    }
    //逆序输出数组值 
    void Show(int x[], int len_x)
    {
        for (int i = len_x - 1; i >= 0; i--)
        {
    	cout << x[i];
        }
        cout << endl;
    }
    //若x>=y返回true，否则返回false 
    bool Compare(int x[], int y[], int len_x, int len_y)
    {
        if (len_x < len_y)
        {
    	return false;
        }
        if (len_x == len_y)
        {
    	for (int i = len_x - 1; i >= 0; i--)
    	{
    	    if (x[i] > y[i])
    	    {
    		return true;
    	    }
                if (x[i] < y[i])
    	    {
    		return false;
    	    }
    	}
    	return true;
        }
        return true;
    }
    //若x>=y,则x的高位减去y（只减一次）,返回值为x的新长度
    int sub(int x[], int y[], int z[], int len_x, int len_y)
    {
        int zLoc = len_x - len_y;    //商的位置 
        //若不够减，则商的位置后移一位 
        for (int i = 1; i <= len_y; i++)
        {
    	if (x[len_x - i] > y[len_y - i])
    	{
                break;
    	}
    	if (x[len_x - i] < y[len_y - i])
    	{
    	    zLoc--;
    	    break;
    	}
        }
        if (zLoc < 0)
        {
    	return len_x;
        }
        //当前被除数x的高位与除数y做一次减法运算 
        for (int i = zLoc, j = 0; i < len_x && j < len_y; i++, j++)
        {
    	while (x[i] < y[j])
    	{
    	    x[i + 1]--;
    	    x[i] += 10;
    	}
    	x[i] -= y[j];
        }
        //商的相应位置加一 
        z[zLoc]++;
        //计算当前被除数x的真实长度 
        while (x[len_x - 1] == 0)
        {
    	len_x--;
        }
        if (len_x <= 0)
        {
    	len_x = 1;
        }
        return len_x;
    }
    int main()
    {
        char str1[100], str2[100];
        cin >> str1;		//被除数
        cin >> str2;		//除数
        int a[100] = { 0 }, b[100] = { 0 }, c[100] = { 0 };
        int len_a = 0, len_b = 0, len_c = 1, maxlen = 0;
        int i;
        len_a = strlen(str1);
        len_b = strlen(str2);
        //被除数和除数分别逆序存放 
        for (i = 0; i < len_a; i++)
        {
    	a[i] = str1[len_a - 1 - i] - '0';
        }
        for (i = 0; i < len_b; i++)
        {
    	b[i] = str2[len_b - 1 - i] - '0';
        }
        //删除多余的0
        len_a = DelZero(a, len_a);
        len_b = DelZero(b, len_b);
        //通过从高位开始连续减去除数，计算商和余数 
        len_c = len_a - len_b + 1;
        while (Compare(a, b, len_a, len_b))
        {
    	len_a = sub(a, b, c, len_a, len_b);
        }
        //解决商的位数是0或负数的情况 
        if (len_c < 1)
        {
    	len_c = 1;
        }
        //去除商的前导0 
        len_c = DelZero(c, len_c);
        //输出商c 
        cout << "商是：";
        Show(c, len_c);
        //输出余数a 
        cout << "余数是：";
        Show(a, len_a);
        return 0;
    }

![20191002180034493.png][]

[20191002150210283.png]: /images/20230808/05863a3af840403e975de35e77c9b9a4.png
[20191002163846153.png]: /images/20230808/13b2a7020fff48a7842aa481d78156f3.png
[20191002171539238.png]: /images/20230808/39a0c3511111450aad4ec5898cea8548.png
[20191002180034493.png]: /images/20230808/6dcbbdf4d14c42bba1e42a045316d417.png