LevOJ平台.sln
高精度运算模板
描述
P1120 P1121 P1134 P1136 P1139 P1155 P2025 P2102 P2103
其中P1139 需要优化高精乘法，其他题目都可以套公式。
苯蒟蒻也没系统学过算法，群佬有更高级的算法一定要在评论区贴一下喵~
模板
// 高精度模板
#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <cmath>
using namespace std;int compare(string a, string b)
{while (a.size() > 1 && a[0] == '0')a.erase(0, 1);while (b.size() > 1 && b[0] == '0')b.erase(0, 1);if (a.size() > b.size())return 1;if (a.size() < b.size())return -1;for (size_t i = 0; i < a.size(); ++i){if (a[i] > b[i])return 1;if (a[i] < b[i])return -1;}return 0;
}// 将字符串逆序存储到数组中
vector<int> adjust(string x)
{vector<int> res;for (int i = x.size() - 1; i >= 0; i--)res.push_back(x[i] - '0');return res;
}// 大整数除二
string div2(const string &x)
{string res;int carry = 0;for (int i = 0; i < (int)x.size(); i++){int d = x[i] - '0' + carry;res += (d / 2) + '0';carry = (d % 2) * 10;}size_t pos = res.find_first_not_of('0');if (pos != string::npos)return res.substr(pos);elsereturn "0";
}// 高精度加法
string add(string a, string b, int scale)
{vector<int> A, B;vector<char> C;A = adjust(a);B = adjust(b);int carry = 0;for (int i = 0; i < (int)A.size() || i < (int)B.size(); i++){if (i < (int)A.size())carry += A[i];if (i < (int)B.size())carry += B[i];C.push_back((char)(carry % scale) + '0');carry /= scale;}if (carry)C.push_back((char)carry + '0');reverse(C.begin(), C.end());return string(C.begin(), C.end());
}// 高精度减法
string sub(string a, string b, int scale)
{vector<int> A, B;vector<char> C;A = adjust(a);B = adjust(b);if (compare(a, b) < 0){swap(A, B);C.push_back('-');}int borrow = 0;for (int i = 0; i < (int)A.size(); i++){int diff = A[i] - borrow;if (i < (int)B.size())diff -= B[i];if (diff < 0){diff += scale;borrow = 1;}elseborrow = 0;C.push_back('0' + diff);}while (C.size() > 1 && C.back() == '0')C.pop_back();if (C[0] == '-')reverse(C.begin() + 1, C.end());elsereverse(C.begin(), C.end());return string(C.begin(), C.end());
}// 高精度乘法
string mul(string a, string b, int scale)
{vector<int> A, B;vector<char> C;A = adjust(a);B = adjust(b);vector<int> res(A.size() + B.size(), 0);for (int i = 0; i < (int)A.size(); i++){for (int j = 0; j < (int)B.size(); j++){res[i + j] += A[i] * B[j];res[i + j + 1] += res[i + j] / scale;res[i + j] %= scale;}}for (int i = (int)res.size() - 1; i >= 0; i--)C.push_back((char)(res[i] % scale) + '0');reverse(C.begin(), C.end());while (C.size() > 1 && C.back() == '0')C.pop_back();reverse(C.begin(), C.end());return string(C.begin(), C.end());
}// 高精度阶乘
string fac(int n)
{string C;C.push_back('1');for (int i = 2; i <= n; i++){string temp = mul(C, to_string(i), 10);C = temp;}return C;
}// 高精度取模
string mod(string a, string b, int scale)
{vector<int> A, B;vector<char> C;A = adjust(a);B = adjust(b);while (compare(a, b) >= 0){a = sub(a, b, scale);}return a;
}// 高精度快速幂
string pow(string a, string b)
{string C = "1";while (!b.empty() && b != "0"){if ((b.back() - '0') % 2 == 1)C = mul(C, a, 10);a = mul(a, a, 10);b = div2(b);}return C;
}// 高精度浮点数加法
string fadd(string a, string b)
{string Ai = "0", Bi = "0", Af = "0", Bf = "0", Ci, Cf;size_t pos;pos = a.find('.');if (pos != string::npos){Ai = a.substr(0, pos);Af = a.substr(pos + 1, a.size() - pos - 1);}elseAi = a;pos = b.find('.');if (pos != string::npos){Bi = b.substr(0, pos);Bf = b.substr(pos + 1, b.size() - pos - 1);}elseBi = b;int m = max(Af.size(), Bf.size());Af.insert(Af.end(), m - Af.size(), '0');Bf.insert(Bf.end(), m - Bf.size(), '0');Cf = add(Af, Bf, 10);int carry = 0;if ((int)Cf.size() > m){carry = 1;Cf = Cf.substr(1);}Ci = add(Ai, Bi, 10);Ci = add(Ci, to_string(carry), 10);if (Ci.size() > 1 && Ci[0] == '0')Ci.erase(0, Ci.find_first_not_of('0'));while (Cf.size() > 1 && Cf.back() == '0')Cf.pop_back();return Ci + "." + Cf;
}// 高精度浮点数减法
string fsub(string a, string b)
{string Ai, Bi, Af = "0", Bf = "0", Ci, Cf;size_t pos;int neg = 0;pos = a.find('.');if (pos != string::npos){Ai = a.substr(0, pos);Af = a.substr(pos + 1, a.size() - pos - 1);}elseAi = a;pos = b.find('.');if (pos != string::npos){Bi = b.substr(0, pos);Bf = b.substr(pos + 1, b.size() - pos - 1);}elseBi = b;if (compare(Ai, Bi) < 0){swap(Ai, Bi);swap(Af, Bf);neg = 1;}int m = max(Af.size(), Bf.size());Af.insert(Af.end(), m - Af.size(), '0');Bf.insert(Bf.end(), m - Bf.size(), '0');Af.insert(Af.begin(), 1, '1');Cf = sub(Af, Bf, 10);int borrow = 1;if ((int)Cf.size() > m){borrow = 0;Cf = Cf.substr(1);}Ci = sub(Ai, Bi, 10);if (borrow)Ci = sub(Ci, to_string(borrow), 10);if (Ci.size() > 1 && Ci[0] == '0')Ci.erase(0, Ci.find_first_not_of('0'));while (Cf.size() > 1 && Cf.back() == '0')Cf.pop_back();if (neg)Ci = "-" + Ci;return Ci + "." + Cf;
}int main()
{string a, b;cin >> a >> b;string C = pow(a, b);cout << C << endl;return 0;
}
第四期完结！
看完了点个赞再走嘛
