【XJTU 2020暑期集训】Day16 - 2019 Multi-University Training Contest 5

D - equation

求出所有使绝对值号内表达式变号的 x 分界点并排序，然后对于分成的若干个区间去绝对值号解方程即可。

E - permutation 1

由于 K 较小，当 N 较大时，差值序列字典序第 K 小的排列一定形如 n,1,2,3\dots，所以不断地确定最终排列的前若干位，直到剩余的排列个数恰好大于等于 K，然后暴力枚举排列并排序即可。

Code

D - equation

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <vector>
#define MAX_N 100005
#define INF 0x3f3f3f3f
#define pii pair<int, int>
#define int long long

using namespace std;

int gcd(int a, int b) {
    return b ? gcd(b, a % b) : a;
}

struct Frac {
    int u, d;
    Frac() {}
    Frac(int _u, int _d) {
        int sgn = 1;
        if (_u < 0) {
            _u *= -1, sgn *= -1;
        }
        if (_d < 0) {
            _d *= -1, sgn *= -1;
        }
        int g = gcd(_u, _d);
        u = _u * sgn / g, d = _d / g;
    }
    friend ostream &operator<<(ostream &out, const Frac &a) {
        out << a.u << "/" << a.d;
        return out;
    }
    friend bool operator<(const Frac &a, const Frac &b) {
        return a.u * b.d < b.u * a.d;
    }
    friend bool operator>(const Frac &a, const Frac &b) {
        return a.u * b.d > b.u * a.d;
    }
    friend bool operator==(const Frac &a, const Frac &b) {
        return a.u * b.d == b.u * a.d;
    }
    friend bool operator<=(const Frac &a, const Frac &b) {
        return a.u * b.d <= b.u * a.d;
    }
};

int T, n, c;
int a[MAX_N];
int b[MAX_N];
int id[MAX_N];
Frac p[MAX_N];

int cmp(int a, int b) {
    return p[a] > p[b];
}

signed main() {
    ios::sync_with_stdio(false);
    cin >> T;
    while (T--) {
        cin >> n >> c;
        for (int i = 1; i <= n; i++) {
            cin >> a[i] >> b[i];
            b[i] = -b[i];
        }
        for (int i = 1; i <= n; i++) {
            p[i] = Frac(b[i], a[i]);
            id[i] = i;
        }
        sort(id + 1, id + 1 + n, cmp);
        vector<Frac> v;
        int sa = 0, sb = 0;
        for (int i = 1; i <= n; i++) {
            sa += a[i], sb += b[i];
        }
        if (!sa && !(c + sb)) {
            cout << "-1" << endl;
            continue;
        }
        if (sa) {
            Frac res(c + sb, sa);
            if (p[id[1]] <= res && res <= Frac(INF, 1)) {
                v.push_back(res);
            }
        }
        p[n + 1] = Frac(-INF, 1), id[n + 1] = n + 1;
        bool flag = false;
        for (int i = 1; i <= n; i++) {
            sa -= 2 * a[id[i]], sb -= 2 * b[id[i]];
            if (!sa && !(c + sb)) {
                flag = true;
                break;
            }
            if (sa) {
                Frac res(c + sb, sa);
                if (p[id[i + 1]] <= res && res <= p[id[i]]) {
                    v.push_back(res);
                }
            }
        }
        if (flag) {
            cout << "-1" << endl;
        } else {
            sort(v.begin(), v.end());
            v.erase(unique(v.begin(), v.end()), v.end());
            cout << (int)v.size();
            for (int i = 0; i < v.size(); i++) {
                cout << " " << v[i];
            }
            cout << endl;
        }
    }
}

E - permutation 1

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <vector>
#define MAX_N 25

using namespace std;

int T, n, K, cnt;
int p[MAX_N];
bool vis[MAX_N];

int getmin() {
    for (int i = 1; i <= n; i++) {
        if (!vis[i]) {
            vis[i] = true;
            return i;
        }
    }
    return -1;
}

int getfac(int x) {
    int ans = 1;
    for (int i = 2; i <= x; i++) {
        ans = ans * i;
        if (ans > K) {
            return ans;
        }
    }
    return ans;
}

bool cmp(const vector<int> &a, const vector<int> &b) {
    int ta, tb;
    if (cnt) {
        ta = a[0] - p[cnt], tb = b[0] - p[cnt];
        if (ta != tb) {
            return ta < tb;
        }
    }
    for (int i = 0; i < a.size() - 1; i++) {
        ta = a[i + 1] - a[i];
        tb = b[i + 1] - b[i];
        if (ta != tb) {
            return ta < tb;
        }
    }
    return false;
}

int main() {
    ios::sync_with_stdio(false);
    cin >> T;
    while (T--) {
        cin >> n >> K;
        for (int i = 1; i <= n; i++) {
            vis[i] = false;
        }
        int t = n;
        cnt = 0;
        if (getfac(t - 2) > K) {
            p[++cnt] = n, vis[n] = true, t--;
            p[++cnt] = 1, vis[1] = true, t--;
            while (getfac(t - 1) > K) {
                p[++cnt] = getmin(), t--;
            }
        }
        vector<int> v;
        for (int i = 1; i <= n; i++) {
            if (!vis[i]) {
                v.push_back(i);
            }
        }
        vector<vector<int> > vs;
        do {
            vs.push_back(v);
        } while (next_permutation(v.begin(), v.end()));
        sort(vs.begin(), vs.end(), cmp);
        for (int x : vs[K - 1]) {
            p[++cnt] = x;
        }
        cout << p[1];
        for (int i = 2; i <= n; i++) {
            cout << " " << p[i];
        }
        cout << endl;
    }
}