[C++知识库]大整数运算

大整数的存储

整数的高位存在数组的高位，整数的低位存在数组的低位
A + B

#include<iostream>
#include<cstring>
using namespace std;
struct bign{
	int d[1000];
	int len;
	bign(){
		memset(d, 0, sizeof(d));
		len = 0;
	}
};
bign change(char str[]){
	bign a;
	a.len = strlen(str);
	for(int i = 0; i < a.len; i++){
		a.d[i] = str[a.len - 1 - i] - '0';
	} 
	return a;
} 
bign add(bign a, bign b){
	bign c;
	int carry = 0;
	for (int i = 0; i < a.len || i < b.len; i++){
		int temp = a.d[i] + b.d[i] + carry;
		c.d[c.len++] = temp % 10; 
		carry = temp / 10;
	} 
	if(carry != 0) c.d[c.len++] = carry;
	return c; 
} 
void show(bign c){
	for (int i = c.len - 1; i >= 0; i--){
		cout << c.d[i];
	}
}
int main(){
	char str1[1000], str2[1000];
	cin >> str1 >> str2;
	bign a = change(str1);
	bign b = change(str2);
	show(add(a, b));
	return 0;
}

加法中的进位

struct bign{
	int d[1000];
	int len;
	bign(){
		memset(d, 0, sizeof(d));
		len = 0;
	}
};
bign add(bign a, bign b){
	bign c;
	int carry = 0;
	for(int i = 0; i < a.len || i < b.len; i++)
	{
		int temp = a.d[i] + b.d[i] + carry;
		c.d[c.len++] = temp % 10;
		carry = temp / 10;
	}
	if(carry != 0) c.d[c.len++] = carry;//循环完仍有进位，直接加到最高位
	return c;
}

A-B

bign sub(bign a, bign b){
	bign c;
	for (int i = 0; i < a.len || i < b.len; i++){
		if(a.d[i] < b.d[i]){//向上借一位
			a.d[i + 1]--;
			a.d[i] += 10;
		}
		c.d[c.len++] = a.d[i] - b.d[i];
	}
	while(c.len - 1 >= 1 && c.d[c.len--] == 0{
		c.len--;
	}
	return c;
}

A * B

bign add(bign a, bign b){
	bign c;
	int carry = 0;
	for(int i = 0; i < a.len || i < b.len; i++)
	{
		int temp = a.d[i] * b.d[i] + carry;
		c.d[c.len++] = temp % 10;
		carry = temp / 10;
	}
	while(carry != 0) //乘法有可能不止进一位
	{
		c.d[c.len++] =  carry % 10;
		carry /= 10;
	}
	return c;
}