数据结构与算法(0)-四则运算

最新推荐文章于 2023-01-29 16:11:44 发布

转载最新推荐文章于 2023-01-29 16:11:44 发布 · 110 阅读

0 ·

CC 4.0 BY-SA版权

原文链接：http://www.cnblogs.com/willingtosmile/p/10471532.html

文章标签：

#数据结构与算法

本文深入探讨了大数四则运算的实现方法，包括加法、减法、乘法和除法，通过逆序存储和逐位计算的方式，解决了传统整型无法处理大数运算的问题。文章提供了详细的代码实现，适合对数据结构和算法感兴趣的读者。

数据结构算法(0)--大数运算

总结并记录学习数据结构过程中遇到的问题及算法.

一些常见算法：

Note:

大数四则运算.

加法

#include <iostream>
#include<string>
#include<stdio.h>
using namespace std;

#define MAXSIZE 1000
int num1[MAXSIZE], num2[MAXSIZE];

void sum(char a[], char b[])
{
    int len1 = strlen(a);
    int len2 = strlen(b);
    int i, j;

    int lensum = len1 > len2 ? len1 : len2;  //总计算长度
    lensum++;
    for (i = len1 - 1, j = 0; i >= 0; --i)    //逆序存储
    {
        num1[j++] = a[i] - '0';
    }
    for (i = len2 - 1, j = 0; i >= 0; --i)
    {
        num2[j++] = b[i] - '0';
    }
    for (i = 0; i < lensum; ++i)
    {
        int temp = num1[i] + num2[i];
        num1[i] = temp % 10;
        num1[i + 1] += temp / 10;
    }
    for (i = lensum - 1; i >= 0 && num1[i] == 0; --i);  //去除前置0
    
    if (i >= 0)
    {
        for (; i >= 0; --i)
            cout << num1[i];
    }
    else
        cout << 0;
    cout << endl;
}

int main()
{
    
    char a[MAXSIZE], b[MAXSIZE];
    int i, j;
    cin >> a >> b;
    sum(a, b);
    system("pause");
}

减法

#include <iostream>
#include<string>
#include<stdio.h>
using namespace std;

#define MAXSIZE 1000
int num1[MAXSIZE], num2[MAXSIZE];
bool myStrcmp(const char str1[], const char str2[])
{ 
    if (strlen(str1) > strlen(str2)) 
        return true; 
    if (strlen(str1) == strlen(str2))
            return strcmp(str1, str2) >= 0; 
    return false; 
}
void sum(char a[], char b[])
{
    int len1 = strlen(a);
    int len2 = strlen(b);
    int i, j;

    int lensum = len1 > len2 ? len1 : len2;  //总计算长度
    lensum++;
    for (i = len1 - 1, j = 0; i >= 0; --i)    //逆序存储
    {
        num1[j++] = a[i] - '0';
    }
    for (i = len2 - 1, j = 0; i >= 0; --i)
    {
        num2[j++] = b[i] - '0';
    }
    for (i = 0; i < lensum; ++i)
    {
        num1[i] -= num2[i];
        if (num1[i] < 0)
        {
            num1[i] += 10;
            num1[i + 1]--;
        }
    }
    for (i = lensum - 1; i >= 0 && num1[i] == 0; --i);  //去除前置0
    
    if (i >= 0)
    {
        for (; i >= 0; --i)
            cout << num1[i];
    }
    else
        cout << 0;
    cout << endl;
}

int main()
{
    
    char a[MAXSIZE], b[MAXSIZE];
    int i, j;
    cin >> a >> b;
    bool sign = myStrcmp(a, b);
    if (sign)
    {
        sum(a, b);
    }
    else
    {
        cout << '-';
        sum(b, a);
    }
    system("pause");
}

乘法

#include <iostream>
#include<string>
#include<stdio.h>
using namespace std;

#define MAXSIZE 1000
int num1[MAXSIZE], num2[MAXSIZE], num3[MAXSIZE*3];

void sum(char a[], char b[])
{
    int len1 = strlen(a);
    int len2 = strlen(b);
    int i, j;

    int lensum = len1 + len2 +1;  //总计算长度
    for (i = len1 - 1, j = 0; i >= 0; --i)    //逆序存储
    {
        num1[j++] = a[i] - '0';
    }
    for (i = len2 - 1, j = 0; i >= 0; --i)
    {
        num2[j++] = b[i] - '0';
    }
    for (i = 0; i < len1; ++i)   //计算
    {
        for (j = 0; j < len2; ++j)
        {
            num3[i + j] += num1[i] * num2[j];
        }
    }
    for (i = 0; i < lensum; ++i)   //处理进位
    {
        if (num3[i] >= 10)
        {
            num3[i + 1] += num3[i] / 10;
            num3[i] %= 10;
        }
    }
    for (i = lensum - 1; i >= 0 && num3[i] == 0; --i);  //去除前置0
    if (i >= 0)
    {
        for (; i >= 0; --i)
            cout << num3[i];
    }
    else
        cout << 0;
    cout << endl;
}

int main()
{
    
    char a[MAXSIZE], b[MAXSIZE];
    int i, j;
    cin >> a >> b;
    sum(a, b);
    system("pause");
}

除法

#include <iostream>
#include<string>
#include<stdio.h>
using namespace std;

#define MAXSIZE 5000
char a[MAXSIZE], b[MAXSIZE];
int result[MAXSIZE];

void sub(char a[], char b[])  //正序相减
{
    int i=0, j;
    int len2 = strlen(b);
    while (true)
    {
        if (a[i] == 0)
            ++i;
        else
        {
            j = i;
            break;
        }
    }
    for (; i < len2; ++i)
    {
        a[i] = a[i] - b[i] + '0';
    }
    for (i = len2 - 1; i > j; --i)
    {
        if (a[i] < '0')
        {
            a[i] += 10;
            a[i - 1]--;
        }
    }
}

int main()
{
    int i = 0, j, pos;
    cin >> a >> b;
    int len1 = strlen(a);
    int len2 = strlen(b);
    if (len1 < len2 || (len1 == len2 && strcmp(a, b) < 0))
    {
        cout << i << " ";
        for (i = 0; i < len1; ++i)
            cout << a[i];
        cout << endl;
    }
    else
    {
        pos = 0;    //商的位数
        while (true)
        {
            result[pos] = 0;
            while (strcmp(a, b) >= 0)    //循环进行减法运算
            {
                sub(a,b);
                result[pos]++;
            }
            ++pos;
            if (len1 == len2)
                break;
            for (i = len2 - 1; i >= 0; --i)
                b[i + 1] = b[i];
            b[0] = '0';    //在除数前面补0，进行减法运算
            ++len2;
            b[len2] = '\0';
        }
        i = 0;
        while (result[i] == 0)   //去除商的前面0
            ++i;
        for (; i < pos; ++i)
            cout << result[i];
        j = 0;   //余数
        while (a[j] == '0')
            ++j;
        if (j == len1)
            cout << " " << 0 << endl;
        else
        {
            cout << " ";
            for (; j < len1; ++j)
                cout << a[j] - '0';
            cout << endl;
        }
    }
    system("pause");
}

转载于:https://www.cnblogs.com/willingtosmile/p/10471532.html