注意:转入的vector为倒序的,如计算34982,vector应该从后往前存储:28943
高精度加法addition:
便于记忆的图片:
//高精度加法addition
// C = A + B, A >= 0, B >= 0
V add(V &A, V &B)
{
//保证A的位数比B的位数多
if (A.size() < B.size()) return add(B, A);
V 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;
}
高精度减法subtraction:
便于记忆的图片:
//高精度减法subtraction
// C = A - B, 满足A >= B, A >= 0, B >= 0
V sub(V &A, V &B)
{
V 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;
}
高精度乘法multiplication:
便于记忆的图片:
//高精度乘法multiplication
// C = A * b, A >= 0, b > 0
V mul(V a, int b)
{
V 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;
}
高精度除法division:
便于记忆的图片:
//高精度除法division
// A / b = C ... r, A >= 0, b > 0
V div(V a, int b)
{
vector<int> C;
int r = 0;
//从前往后除,存储的顺序是正的
for (int i = a.size() - 1; i >= 0; i -- )
{
r = r * 10 + a[i];
C.push_back(r / b);
r %= b;
}
//反转后是为了把一开始除的时候存储的 ‘0’放到末尾,便于删除
reverse(C.begin(), C.end());
//除去末尾 ‘0’,此时结果为倒序
while (C.size() > 1 && C.back() == 0) C.pop_back();
//倒序输出
return C;
}
高精度比较大小:
//高精度比较
bool cmp(V a, V b)
{
//若两个数字长度不同,a小,则返回true
if(a.size() != b.size()) return a.size() < b.size();
//若长度相同,反转一下,直接比较,vector自动比较
reverse(a.begin(), a.end());
reverse(b.begin(), b.end());
//vector 按照字典序比较
return a < b;
}
高精度倒序输出:
//高精度倒序输出
void out(V res)
{
for(int i = res.size() - 1; i >= 0; i--) cout<<res[i];
cout<<endl;
}
完整版:
#include <cstdio>
#include <queue>
#include <stack>
#include <cstdio>
#include <string>
#include <iostream>
#include <algorithm>
using namespace std;
typedef vector<int> V;
//高精度加法addition
// C = A + B, A >= 0, B >= 0
V add(V &A, V &B)
{
if (A.size() < B.size()) return add(B, A);
V 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;
}
//高精度减法subtraction
// C = A - B, 满足A >= B, A >= 0, B >= 0
V sub(V &A, V &B)
{
V 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;
}
//高精度乘法multiplication
// C = A * b, A >= 0, b > 0
V mul(V a, int b)
{
V 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;
}
//高精度除法division
// A / b = C ... r, A >= 0, b > 0
V div(V a, int b)
{
vector<int> C;
int r = 0;
//从前往后除,存储的顺序是正的
for (int i = a.size() - 1; i >= 0; i -- )
{
r = r * 10 + a[i];
C.push_back(r / b);
r %= b;
}
//反转后是为了把一开始除的时候存储的 ‘0’放到末尾,便于删除
reverse(C.begin(), C.end());
//除去末尾 ‘0’,此时结果为倒序
while (C.size() > 1 && C.back() == 0) C.pop_back();
//倒序输出
return C;
}
//高精度比较
bool cmp(V a, V b)
{
//若两个数字长度不同,a小,则返回true
if(a.size() != b.size()) return a.size() < b.size();
//若长度相同,反转一下,直接比较,vector自动比较
reverse(a.begin(), a.end());
reverse(b.begin(), b.end());
//vector 按照字典序比较
return a < b;
}
//高精度倒序输出
void out(V res)
{
for(int i = res.size() - 1; i >= 0; i--) cout<<res[i];
cout<<endl;
}
int main()
{
return 0;
}