高精度

应用场景(常见)

应用场景

实现思路

大整数存储方式(C++)

大整数存储方式(C++)

计算过程

加法计算过程

加法计算过程

减法计算过程

减法计算过程

乘法计算过程

乘法计算过程

除法计算过程

乘法计算过程

代码模板

加法模板

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#include <iostream>
#include <vector>
#include <string>

using namespace std;

// C = A + B
vector<int> add(vector<int> &A, vector<int> &B)
{
	vector<int> C;
	int t = 0;
	for (int i = 0; i < A.size() || i < B.size(); i++)
	{
		if (i < A.size()) t += A[i];
		if (i < B.size()) t += B[i];
		C.push_back(t % 10);
		t /= 10;
	}
	if (t) C.push_back(1);
	return C;
}

int main()
{
	string a, b;
	vector<int> A,B;

	cin >> a >> b; // a = "123456"
	for (int i = a.size() - 1; i >= 0; i--) A.push_back(a[i] - '0');
	for (int i = b.size() - 1; i >= 0; i--) B.push_back(b[i] - '0');

	auto C = add(A, B);

	for (int i = C.size() - 1; i >= 0; i--) printf("%d", C[i]);
	system("pause");
	return 0;
}

减法模板

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#include <iostream>
#include <vector>
#include <string>

using namespace std;

// 判断是否有A >= B
bool cmp(vector<int> &A, vector<int> &B)
{
	if (A.size() != B.size()) return A.size() > B.size();
	for (int i = A.size() - 1; i >= 0; i--)
		if (A[i] != B[i])
			return A[i] > B[i];
	return true;
}

// C = A - B
vector<int> sub(vector<int> &A, vector<int> &B)
{
	vector<int> C;
	int t = 0;
	for (int i = 0; i < A.size() || i < B.size(); i++)
	{
		t = A[i] - t;
		if (i < B.size()) t -= B[i];
		C.push_back((t + 10) % 10);
		if (t < 0) t = 1;
		else t = 0;
	}
	// 去掉前导0,这个位置是逆序
	while (C.size() > 1 && C.back() == 0) C.pop_back();
	return C;
}

int main()
{
	string a, b;
	vector<int> A,B;

	cin >> a >> b; // a = "123456"
	for (int i = a.size() - 1; i >= 0; i--) A.push_back(a[i] - '0');
	for (int i = b.size() - 1; i >= 0; i--) B.push_back(b[i] - '0');

	if(cmp(A,B))
	{
		auto C = sub(A, B);
		for (int i = C.size() - 1; i >= 0; i--) printf("%d", C[i]);
	}
	else 
	{
		auto C = sub(B, A);

		printf("-");
		for (int i = C.size() - 1; i >= 0; i--) printf("%d", C[i]);
	}
	
	system("pause");
	return 0;
}

乘法模板

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#include <iostream>
#include <vector>
#include <string>

using namespace std;


// C = A * b
vector<int> mul(vector<int> &A, int b)
{
	vector<int> C;
	int t = 0;
	for (int i = 0; i < A.size() || t; i++)
	{
		if (i < A.size()) t += A[i] * b;
		C.push_back(t % 10);
		t /= 10;
	}
	return C;
}

int main()
{
	string a;
	int b;
	cin >> a >> b;

	vector<int> A;
	for (int i = a.size() - 1; i >= 0; i--) A.push_back(a[i] - '0');
	
	
	auto C = mul(A, b);
	
	for (int i = C.size() - 1; i >= 0; i--) printf("%d", C[i]);
	
	system("pause");
	return 0;
}

除法模板

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#include <iostream>
#include <vector>
#include <algorithm>
#include <string>

using namespace std;


// C...r = A / b 
vector<int> div(vector<int> &A, int b, int &r)
{
	vector<int> C;
	r = 0;
	for (int i = A.size() - 1; i >= 0; i--)
	{
		r = r * 10 + A[i];
		C.push_back(r / b);
		r %= b;
	}
	reverse(C.begin(),C.end());
	while (C.size() > 1 && C.back() == 0 )  C.pop_back();
	return C;
}

int main()
{
	string a;
	int b;
	cin >> a >> b;

	vector<int> A;
	for (int i = a.size() - 1; i >= 0; i--) A.push_back(a[i] - '0');
	
	int r;
	auto C = div(A, b, r);
	
	for (int i = C.size() - 1; i >= 0; i--) printf("%d", C[i]);
	cout << endl << r <<endl; 
	
	system("pause");
	return 0;
}