数据结构与算法(0)-四则运算

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");
}