高精度加法

#include <iostream>
#include <vector>
#include <cstring>
using namespace std;

vector<int> add(vector<int> &A, vector<int> &B) {
	vector<int> C;
	int t = 0;
	if (A.size() < B.size())
		return add(B, A);
	for (int i = 0; i < A.size(); i ++ ) {
		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;
	cin >> a >> b;

	vector<int> A, B;
	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');

	vector<int> C = add(A, B);

	for (int i = C.size() - 1; i >= 0; i -- )
		cout << C[i];

	return 0;
}
 

高精度減法

#include <iostream>
#include <vector>
#include <cstring>
using namespace std;

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;
}

vector<int> sub(vector<int> &A, vector<int> &B) {
	vector<int> C;
	for (int i = 0, t = 0; i < A.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;
	}
	while (C.size() > 1 && C.back() == 0)
		C.pop_back();
	return C;
}

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

	vector<int> A, B;
	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');

	vector<int> C;
	if (cmp(A, B))
		C = sub(A, B);
	else {
		C = sub(B, A);
		cout << '-';
	}
	for (int i = C.size() - 1; i >= 0; i -- )
		cout << C[i];

	return 0;
}
 

高精度乘法(高精度乘低精度)

#include <iostream>
#include <vector>
#include <cstring>
using namespace std;

vector<int> mul(vector<int> &A,	int b) {
	vector<int> C;
	for (int i = 0, t = 0; i < A.size() || t; i ++ ) {
		if (i < A.size())
			t += A[i] * b;
		C.push_back(t % 10);
		t /= 10;
	}
	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');

	vector<int> C;
	C = mul(A, b);
	for (int i = C.size() - 1; i >= 0; i -- )
		cout << C[i];

	return 0;
}
 

高精度乘法(高精度乘高精度)

(暴力是O(n^2)的，還有一個FFT的演算法讓時間費用更低，但是奈何本蒟蒻實在是不會啊~QAQ)

#include<bits/stdc++.h>
using namespace std;
const int N = 1e5+10,M= 2e5+10;
int a[M],b[M],l1,l2;
char s[N];
void print(int a[])
{
    int k=M-1;
    while(k && !a[k]) k--;
    for(int i=k;i>=0;i--) cout<<a[i];
}
void mul(int a[],int b[])
{
    int t=0,temp[M];
    memset(temp,0,sizeof temp);
    for(int i=0;i<l1;i++)
        for(int j=0;j<l2;j++)
            temp[i+j]+=a[i]*b[j];

    for(int i=0;i<l1+l2;i++)
    {
        t+=temp[i];
        temp[i]=t%10;
        t/=10;
    }

    memcpy(a,temp,sizeof temp);
}
int main()
{
    scanf("%s",s);
    l1=strlen(s);
    for(int i=0;i<l1;i++) a[l1-i-1]=s[i]-'0';

    scanf("%s",s);
    l2=strlen(s);
    for(int i=0;i<l2;i++) b[l2-i-1]=s[i]-'0';

    mul(a,b);
    print(a);
    return 0;
}

高精度除法(高精度除以低精度)

#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;
vector<int> div(vector<int> &A, int b)
{
    vector<int> C;
    int t = 0;
    for(int i = A.size() - 1; i >= 0; i -- )
    {
        t = t * 10 + A[i];
        C.push_back(t / b);
        t %= 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');
    vector<int> C;
    C = div(A,b);
    for(int i = 0; i < C.size(); i ++ )
        cout << C[i];
    return 0;
}