POJ-1472（循环复杂度，递归分治 + 多项式）

最新推荐文章于 2023-08-15 00:42:53 发布

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最新推荐文章于 2023-08-15 00:42:53 发布

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该博客探讨了如何使用递归分治策略解决POJ-1472问题，重点在于理解多项式乘法和加法在算法中的应用。

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题目：http://poj.org/problem?id=1472

思想是分而治之，核心是递归算法，重点是多项式乘法和加法

#include <cstdlib>
#include <cstring>
#include <iostream>
#include <string>
#include <vector>
using namespace std;
#define MAX     10

class Polynomial{
private:
    struct Term{
        int co, exp;
        Term(int c, int e): co(c), exp(e){}
    };
    vector<Term> formula;//reverse of the normalized expression, each co > 0
private:
    void reset(int arr[MAX + 1]){
        formula.clear();
        for(int i = 0, n = MAX; i <= n; ++i){
            if(arr[i]) formula.push_back(Term(arr[i], i));
        }
    }
public:
    Polynomial(){
        formula.clear();
    }
    Polynomial(const string& s){
        formula.clear();
        if(s[0] == 'n') formula.push_back(Term(1, 1));
        else if(int n = atoi(s.c_str())) formula.push_back(Term(n, 0));
    }
    Polynomial& operator *= (const Polynomial& other){
        if(formula.empty()) return *this;
        if(other.formula.empty()){
            formula.clear();
            return *this;
        }
        
        int arr[MAX + 1];
        memset(arr, 0, sizeof(arr));
        const vector<Term>& v = other.formula;
        int i, n = v.size(), j, m = formula.size(), e, c;
        for(i = 0; i < n; ++i){
            e = v[i].exp;
            c = v[i].co;
            for(j = 0; j < m; ++j) arr[e + formula[j].exp] += c * formula[j].co;
        }
        reset(arr);
        return *this;
    }
    Polynomial& operator += (const Polynomial& other){
        if(other.formula.empty()) return *this;
        
        int arr[MAX + 1];
        memset(arr, 0, sizeof(arr));
        const vector<Term>& v = other.formula;
        int i, n;
        for(i = 0, n = v.size(); i < n; ++i)
            arr[v[i].exp] += v[i].co;
        for(i = 0, n = formula.size(); i < n; ++i)
            arr[formula[i].exp] += formula[i].co;
        reset(arr);
        return *this;
    }
    friend ostream& operator << (ostream& out, const Polynomial& poly){
        const vector<Term>& formula = poly.formula;
        if(formula.empty()){
            out<< "0";
            return out;
        }
        bool first = true;
        for(int i = formula.size() - 1; i >= 0; --i){
            if(first) first = false;
            else out << "+";
            if(formula[i].exp){
                if(formula[i].co != 1) out << formula[i].co << "*";
                out << "n";
                if(formula[i].exp > 1) out << '^' << formula[i].exp;
            }
            else out << formula[i].co;
        }
        return out;
    }
};

Polynomial analyseLoop(istream& in)
{
    string s;
    in >> s;
    Polynomial poly(s), move;
    while(in >> s, s != "END"){
        if(s == "OP"){
            in >> s;
            move += Polynomial(s);
        }
        else move += analyseLoop(in);
    }
    return poly *= move;
}
Polynomial analyseProgram(istream& in)
{
    string s;
    Polynomial poly;
    in >> s;
    while(in >> s, s != "END"){
        if(s == "LOOP") poly += analyseLoop(in);
        else{
            in >> s;
            poly += Polynomial(s);
        }
    }
    return poly;
}

int main()
{
    ios::sync_with_stdio(false);
    int t, test;
    cin >> test;
    for(t = 1; t <= test; ++t){
        cout << "Program #" << t << "\n";
        cout << "Runtime = " << analyseProgram(cin) << "\n\n";
    }
    return 0;
}

A了之后，感觉C++的函数重载特性简直酷毙了……