Educational Codeforces Round 88 (Rated for Div. 2)

传送门

视频题解。
这场题目质量还可以，只是E太水了。。
AB贪心+模拟就不用多说了，C其实是个标准的三分，但要注意一下如果有多个极值点的情况要选最小的一个，在代码实践中加个=就行。D题利用好权值范围不超过60这个性质，维护最优集合，可以证明这个最优集合最大为60，然后就随便做的，但注意要判断相等的情况（一开始没考虑这里fst了）。E题水题，通过样例可以发现构造思路，证明也很容易。

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A. Berland Poker

/*
 * Author:  heyuhhh
 * Created Time:  2020/5/28 22:36:35
 */
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#include <functional>
#include <numeric>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#define Local
#ifdef Local
  #define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
  void err() { std::cout << std::endl; }
  template<typename T, typename...Args>
  void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
  template <template<typename...> class T, typename t, typename... A> 
  void err(const T <t> &arg, const A&... args) {
  for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
  #define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 1e5 + 5;
 
void run() {
    int n, m, k; cin >> n >> m >> k;
    int has = n / k;
    if (m <= has) {
        cout << m << '\n';
    } else {
        int ans = max(0, has - (m - has + k - 2) / (k - 1));   
        cout << ans << '\n';
    }
}
 
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    cout << fixed << setprecision(20);
    int T; cin >> T; while(T--)
    run();
    return 0;
}

B. New Theatre Square

/*
 * Author:  heyuhhh
 * Created Time:  2020/5/28 22:41:15
 */
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#include <functional>
#include <numeric>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#define Local
#ifdef Local
  #define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
  void err() { std::cout << std::endl; }
  template<typename T, typename...Args>
  void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
  template <template<typename...> class T, typename t, typename... A> 
  void err(const T <t> &arg, const A&... args) {
  for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
  #define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 1e5 + 5;
 
void run() {
    int n, m, x, y;
    cin >> n >> m >> x >> y;
    y = min(y, 2 * x);
    vector <string> s(n);
    ll ans = 0;
    for (int i = 0; i < n; i++) {
        cin >> s[i];
        for (int j = 1; j < m; j++) {
            if (s[i][j - 1] == '.' && s[i][j] == '.') {
                ans += y; 
                s[i][j - 1] = s[i][j] = '*';
                ++j;
            }
        }
        for (int j = 0; j < m; j++) {
            if (s[i][j] == '.') ans += x;
        }
    }
    cout << ans << '\n';
}
 
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    cout << fixed << setprecision(20);
    int T; cin >> T; while(T--)
    run();
    return 0;
}

C. Mixing Water

/*
 * Author:  heyuhhh
 * Created Time:  2020/5/28 22:56:00
 */
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#include <functional>
#include <numeric>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#define Local
#ifdef Local
  #define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
  void err() { std::cout << std::endl; }
  template<typename T, typename...Args>
  void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
  template <template<typename...> class T, typename t, typename... A> 
  void err(const T <t> &arg, const A&... args) {
  for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
  #define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 1e5 + 5;
const double eps = 1e-6;
 
void run() {
    int h, c, t; cin >> h >> c >> t;
    if (h + c >= 2 * t) {
        cout << 2 << '\n';
        return;
    }
    auto f = [&] (ll x, ll y) {
        return fabs((double)t - 1.0 * (x * h + y * c) / (x + y));
    };
    ll l = 0, r = INF, lmid, rmid;
    while (l < r) {
        lmid = l + ((r - l) / 3);   
        rmid = r - ((r - l) / 3);
        if (f(lmid + 1, lmid) <= f(rmid + 1, rmid)) {
            r = rmid - 1;
        } else {
            l = lmid + 1;
        }
    }   
    ll ans = 2 * l + 1;
    //if (l > 10000000) {
        //ans = ll(1.0 * (h - t) / (2 * t - h - c) + 0.5);
        //ans = 2ll * ans + 1;
    //}
    cout << ans << '\n';
}
 
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    int T; cin >> T; while(T--)
    run();
    return 0;
}

D. Yet Another Yet Another Task

/*
 * Author:  heyuhhh
 * Created Time:  2020/5/28 23:50:13
 */
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#include <functional>
#include <numeric>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#define Local
#ifdef Local
  #define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
  void err() { std::cout << std::endl; }
  template<typename T, typename...Args>
  void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
  template <template<typename...> class T, typename t, typename... A> 
  void err(const T <t> &arg, const A&... args) {
  for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
  #define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 1e5 + 5;
 
int a[N];
 
int f[N][21];
 
int n;
 
void Get_st(){
    for(int j=1;j<=20;j++)
        for(int i=1;i<=n;i++)
            if(i+(1<<(j-1))<=n) f[i][j]=max(f[i][j-1],f[i+(1<<(j-1))][j-1]);
}
int Get_max(int l,int r){
    int k=0;
    while(1<<(k+1)<=r-l+1) k++;
    return max(f[l][k],f[r-(1<<k)+1][k]);
} 
 
void run() {
    cin >> n;
    for (int i = 1; i <= n; i++) {
        cin >> a[i];
        f[i][0] = a[i];
    }
    Get_st();
    set <pii> s;
    s.insert(MP(0, 0));
    int ans = -INF;
    int sum = 0;
    for (int i = 1; i <= n; i++) {
        sum += a[i];
        for (auto it : s) {
            int res = sum - it.fi - Get_max(it.se + 1, i);
            ans = max(ans, res);
        }
        auto it = s.lower_bound(MP(sum, 0));
        if (it != s.end() && it -> fi == sum) {
            s.erase(it);
        }
        s.insert(MP(sum, i));
        if (sz(s) > 60) {
            auto it = s.end(); --it;
            s.erase(it);
        }
    }
    cout << ans << '\n';
}
 
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    cout << fixed << setprecision(20);
    run();
    return 0;
}

E. Modular Stability

/*
 * Author:  heyuhhh
 * Created Time:  2020/5/29 0:15:24
 */
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#include <functional>
#include <numeric>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#define Local
#ifdef Local
  #define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
  void err() { std::cout << std::endl; }
  template<typename T, typename...Args>
  void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
  template <template<typename...> class T, typename t, typename... A> 
  void err(const T <t> &arg, const A&... args) {
  for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
  #define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 1e5 + 5, MOD = 998244353;
int qpow(ll a, ll b) {
    ll res = 1;
    while (b) {
        if (b & 1) res = res * a % MOD;
        a = a * a % MOD;
        b >>= 1;
    }
    return res;   
}
 
 
void run() {
    int n, k; cin >> n >> k;
    if (n < k) {
        cout << 0 << '\n';
        return;
    }
    vector <int> fac(n + 1), inv(n + 1);
    fac[0] = 1;
    for (int i = 1; i <= n; i++) fac[i] = 1ll * fac[i - 1] * i % MOD;
    inv[n] = qpow(fac[n], MOD - 2);
    for (int i = n - 1; i >= 0; i--) inv[i] = 1ll * inv[i + 1] * (i + 1) % MOD;
    auto C = [&] (int n, int m) {
        return 1ll * fac[n] * inv[m] % MOD * inv[n - m] % MOD;  
    };
    int ans = 0;
    for (int i = 1; i <= n; i++) {
        int cnt = n / i - 1;
        if (1 + cnt >= k) {
            ans = (ans + C(cnt, k - 1)) % MOD;
        }
    }
    cout << ans << '\n';
}
 
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    cout << fixed << setprecision(20);
    run();
    return 0;
}