Day13 备战CCF-CSP练习

Day 13

题目描述

题目分析

大模拟，用栈储存每一个多项式，最后根据导数的加法原则依次求导相加，注意取模。

C++代码

#pragma GCC optimize(3, "Ofast", "inline")
#include <bits/stdc++.h>
#define int long longusing namespace std;
const int N = 100010, MOD = 1e9 + 7;
string oper;
int n, m;
stack<vector<pair<map<string, int>, int>>> heap;
map<string, int> num;
map<string, int> p;bool is_num(string x)
{for (auto s : x)if (!isdigit(s) && s != '-')return false;return true;
}int qmi(int a, int b)
{int res = 1;while (b){if (b & 1)res = res * a % MOD;a = a * a % MOD;b >>= 1;}return res % MOD;
}int to_num(string x)
{int res = 0, flag = 1;for (auto s : x){if (s == '-')flag = -1;elseres = res * 10 + s - '0';}return res * flag;
}void calc(string op)
{auto a = heap.top();heap.pop();auto b = heap.top();heap.pop();if (op == "+"){for (auto it : b)a.push_back(it);heap.push(a);}else if (op == "-"){for (auto it : a)b.push_back({it.first, -1ll * it.second});heap.push(b);}else{vector<pair<map<string, int>, int>> t;for (auto itb : b){for (auto ita : a){pair<map<string, int>, int> tmp;for (auto [k, v] : itb.first){tmp.first[k] = itb.first[k] + ita.first[k];}tmp.second = ita.second * itb.second % MOD;t.push_back(tmp);}}heap.push(t);}
}signed main()
{ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);cin >> n >> m;for (int i = 1; i <= n; i++){string s = "x" + to_string(i);p[s] = 0;}getline(cin, oper);getline(cin, oper);for (int i = 0; i < oper.size(); i++){string x = "";while (oper[i] != ' ' && i < oper.size())x += oper[i++];if (x == "+" || x == "-" || x == "*")calc(x);else if (is_num(x)){vector<pair<map<string, int>, int>> c;c.push_back({p, to_num(x)});heap.push(c);}else{auto t = p;t[x]++;vector<pair<map<string, int>, int>> c;c.push_back({t, 1});heap.push(c);}}// auto t = heap.top();// for (auto [y, c] : t)// {//     for (auto [k, v] : y)//         cerr << k << ' ' << v << endl;//     cerr << "c " << c << '\n';// }while (m--){int id;cin >> id;string x = "x" + to_string(id);for (int i = 1; i <= n; i++){string x2 = "x" + to_string(i);int number;cin >> number;num[x2] = number;}// for (auto [y, c] : num)// {//     cerr << y << ' ' << c << '\n';// }int res = 0;for (auto t : heap.top()){auto it = t.first;int c = t.second;if (c == 0)continue;int k = c;for (auto y : it){string w = y.first;int mi = y.second;// cout << w << ' ' << num[w] << ' ' << mi << '\n';if (x == w){if (mi == 0){k = 0ll;break;}else{k = k * qmi(num[w], mi - 1) % MOD;k = k * mi % MOD;}}else{k = k * qmi(num[w], mi) % MOD;}// cout << k << '\n';}res = (res + k) % MOD;}cout << (res % MOD + MOD) % MOD << '\n';}return 0;
}