【2019沈阳网络赛】G、Special necklace——自闭的物理题

这道题让我差点怀疑自己高考没考过物理

题意中

指的是在三角形中电阻为 2a2a2a 而不是边上的电阻为 2a2a2a

实际上每条边的电阻R为

1R+12R=2a\frac{1}{R} + \frac{1}{2R} = 2aR1​+2R1​=2a

可以求得R=3aR = 3aR=3a

所以可以得到递推公式

an+1=1111an+43+3+13a_{n+1} = \frac{1}{ \frac{1}{ \frac{1}{ \frac{1}{a_{n}} + \frac{4}{3}} + 3} + \frac{1}{3}}an+1​=an​1​+34​1​+31​+31​1​

通过python打表

res = 5 / 3

print('%.20f' % res)

for i in range(20):

    res = 1 / ((1 / (1 / (1 / res + 4 / 3) + 3)) + 1 / 3)

    print('%.20f' % res)

得到

这是 a=1a = 1a=1 的情况，最后乘上 a 就行

很明显了，直接打表就行，借助一下字符串流

#include <bits/stdc++.h>

using namespace std;

vector<double> res;

void init() {

    res.push_back(1.66666666666666674068);

    res.push_back(1.61904761904761906877);

    res.push_back(1.61805555555555535818);

    res.push_back(1.61803444782168193150);

    res.push_back(1.61803399852180329610);

    res.push_back(1.61803398895790206957);

    res.push_back(1.61803398875432269399);

    res.push_back(1.61803398874998927148);

    res.push_back(1.61803398874989712297);

    res.push_back(1.61803398874989468048);

    res.push_back(1.61803398874989468048);

    res.push_back(1.61803398874989468048);

    res.push_back(1.61803398874989468048);

    res.push_back(1.61803398874989468048);

    res.push_back(1.61803398874989468048);

}

void solve() {

    int t;

    cin >> t;

    init();

    while (t--) {

        string str;

        double a;

        cin >> str >> a;

        if (str.length() > 2) {

            cout << fixed << setprecision(10) << res.back() * a << endl;

            continue;

        }

        stringstream ss(str);

        int n;

        ss >> n;

        if (n > res.size() - 1) {

            cout << fixed << setprecision(10) << res.back() * a << endl;

        } else {

            cout << fixed << setprecision(10) << res[n - 1] * a << endl;

        }

    }

}

int main() {

    ios_base::sync_with_stdio(false);

    cin.tie(0);

    cout.tie(0);

#ifdef ACM_LOCAL

    freopen("in.txt", "r", stdin);

    freopen("out.txt", "w", stdout);

    long long test_index_for_debug = 1;

    char acm_local_for_debug;

    while (cin >> acm_local_for_debug) {

        cin.putback(acm_local_for_debug);

        if (test_index_for_debug > 20) {

            throw runtime_error("Check the stdin!!!");

        }

        auto start_clock_for_debug = clock();

        solve();

        auto end_clock_for_debug = clock();

        cout << "Test " << test_index_for_debug << " successful" << endl;

        cerr << "Test " << test_index_for_debug++ << " Run Time: "

             << double(end_clock_for_debug - start_clock_for_debug) / CLOCKS_PER_SEC << "s" << endl;

        cout << "--------------------------------------------------" << endl;

    }

#else

    solve();

#endif

    return 0;

}