大数加减优化

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一、大数加减的代码

大数相加

vector<int> add(vector<int> &A, vector<int> &B)
{
    if (A.size() < B.size()) return add(B, A);
    vector<int> C;
    int t = 0;
    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(t);
    return C;
}

大数相减

// C = A - B, 满足A >= B, A >= 0, B >= 0
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;
}

二、大数加减编程题

AcWing 791. 高精度加法

#include<bits/stdc++.h>
using namespace std;

vector<int> add(vector<int> &A, vector<int> &B)
{
    if (A.size() < B.size()) return add(B, A);
    vector<int> C;
    int t = 0;
    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(t);
    return C;
}
int main()
{
	string a,b;
	cin>>a>>b;
	vector<int> A;
	vector<int> 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--) printf("%d",C[i]);

	return 0;
}

AcWing 792. 高精度减法

#include<bits/stdc++.h>
using namespace std;

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

	return 0;
}

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