洛谷P2553 [AHOI2001]多项式乘法

板子题，处理一下输入输出即可

Code:

#include <map>
#include <set>
#include <array>
#include <queue>
#include <stack>
#include <cmath>
#include <vector>
#include <cstdio>
#include <cstring>
#include <sstream>
#include <iostream>
#include <stdlib.h>
#include <algorithm>
#include <unordered_map>

using namespace std;

typedef long long ll;
typedef pair<int, int> PII;

#define sd(a) scanf("%d", &a)
#define sdd(a, b) scanf("%d%d", &a, &b)
#define slld(a) scanf("%lld", &a)
#define slldd(a, b) scanf("%lld%lld", &a, &b)

const int N = 100;//3e6 + 10;
const int M = 1e6 + 20;
const int mod = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const double PI = acos(-1.0);

int n, m;
ll ans[N];
int rev[N];

struct Complex{
    double x, y;

    Complex(double _x = 0.0, double _y = 0.0){
        x = _x, y = _y;
    }

    Complex operator + (const Complex & b){
        return Complex(x + b.x, y + b.y);
    }

    Complex operator - (const Complex &b){
        return Complex(x - b.x, y - b.y);
    }

    Complex operator * (const Complex &b){
        return Complex(x * b.x - y * b.y, x * b.y + y * b.x);
    }
};

void change(Complex y[], int len){
    
    for(int i = 0; i < len; i ++){
        rev[i] = rev[i >> 1] >> 1;
        if(i & 1) rev[i] |= (len >> 1);
    }

    for(int i = 0; i < len; i ++){
        if(i < rev[i]) swap(y[i], y[rev[i]]);
    }
}

void fft(Complex y[], int len, int on){
    change(y, len);

    for(int h = 2; h <= len; h <<= 1){
        Complex wn(cos(2 * PI / h), sin(2 * PI * on / h));

        for(int j = 0; j < len; j += h){
            Complex w(1, 0);

            for(int k = j; k < j + h / 2; k ++){
                Complex u = y[k];
                Complex t = w * y[k + h / 2];

                y[k] = u + t;
                y[k + h / 2] = u - t;
                w = w * wn;

            }
        }
    }
    if(on == -1){
        for(int i = 0; i < len; i ++){
            y[i].x /= len;
        }
    }
}

Complex x1[N], x2[N];
int a[N], b[N];

void solve()
{
    string s;
    while(cin >> s){
        int i = 1;
        n = 0, m = 0;
        while(s[i] != ')'){
            int x = 0;
            while(s[i] != 'a' && s[i] != ')' && s[i] != '+'){
                x = x * 10 + s[i] - '0';
                i ++;
            }
            n ++;
            if(s[i] != ')' && s[i] != '+'){
                i += 2;
                int y = 0;
                while(s[i] != '+' && s[i] != ')'){
                    y = y * 10 + s[i] - '0';
                    i ++;
                }
                a[y] = x;
            }
            else a[0] = x;
            if(s[i] == '+') i ++;
        }
        i += 3;
        while(s[i] != ')'){
            int x = 0;
            while(s[i] != 'a' && s[i] != ')' && s[i] != '+'){
                x = x * 10 + s[i] - '0';
                i ++;
            }
            m ++;
            if(s[i] != ')' && s[i] != '+'){
                i += 2;
                int y = 0;
                while(s[i] != '+' && s[i] != ')'){
                    y = y * 10 + s[i] - '0';
                    i ++;
                } 
                b[y] = x;
            }
            else{
                b[0] = x;
            }
            if(s[i] == '+') i ++;
        }

        n --, m --;

        int len = 1;
        while(len <= n + m + 1) len <<= 1;

        for(int i = 0; i <= n; i ++) x1[i] = Complex(a[i], 0);

        for(int i = 0; i <= m; i ++) x2[i] = Complex(b[i], 0);

        for(int i = n + 1; i < len; i ++) x1[i] = Complex(0, 0);

        for(int i = m + 1; i < len; i ++) x2[i] = Complex(0, 0);

        fft(x1, len, 1);
        fft(x2, len, 1);

        for(int i = 0; i < len ; i ++) x1[i] = x1[i] * x2[i];

        fft(x1, len, -1);

        for(int i = n + m; i >= 1; i --){
            cout << (int)(x1[i].x + 0.5) << "a^" << i << "+";
        }
        cout << (int)(x1[0].x + 0.5) << "\n";

    }

}

int main()
{
#ifdef ONLINE_JUDGE
#else
    freopen("/home/jungu/code/in.txt", "r", stdin);
    // freopen("/home/jungu/桌面/11.21/2/in9.txt", "r", stdin);
#endif
    ios::sync_with_stdio(false);
    cin.tie(0), cout.tie(0);

    int T = 1;
    // sd(T);
    // cin >> T;
    while (T--)
    {
        solve();
    }

    return 0;
}