Educational Codeforces Round 75

Posted 2021-03-25 dup4

目录

• Contest Info
• Solutions
  • A. Broken Keyboard
  • B. Binary Palindromes
  • C. Minimize The Integer
  • D. Salary Changing
  • E2. Voting (Hard Version)

Contest Info

---

Practice Link

Solved	A	B	C	D	E1	E2	F
6/7	O	O	O	O	O	O	-

• O 在比赛中通过
• ? 赛后通过
• ! 尝试了但是失败了
• - 没有尝试

Solutions

---

A. Broken Keyboard

题意：
有一个打字机，如果某个按键是好的，那么按下那个按键之后会在打字槽中追加一个该字符，如果是坏的则会追加两个。
现在给出打印槽中最后的结果，问有哪些按键能确定一定是好的。

思路：
将连续的相同字符取出来，如果长度为奇数，那么一定能确定该字符对应的按键是好的。

代码：

view code

#pragma GCC optimize("Ofast,unroll-loops,no-stack-protector,fast-math")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
#define fi first
#define se second
#define endl "
" 
using namespace std;
using db = double;
using ll = long long;
using ull = unsigned long long; 
using pII = pair <int, int>;
using pLL = pair <ll, ll>;
constexpr int mod = 1e9 + 7;
template <class T1, class T2> inline void chadd(T1 &x, T2 y) { x += y; while (x >= mod) x -= mod; while (x < 0) x += mod; } 
template <class T1, class T2> inline void chmax(T1 &x, T2 y) { if (x < y) x = y; }
template <class T1, class T2> inline void chmin(T1 &x, T2 y) { if (x > y) x = y; }
inline int rd() { int x; cin >> x; return x; }
template <class T> inline void rd(T &x) { cin >> x; }
template <class T> inline void rd(vector <T> &vec) { for (auto &it : vec) cin >> it; }  
#define dbg(x...) do { cout << "33[32;1m" << #x << " -> "; err(x); } while (0) 
void err() { cout << "33[39;0m" << endl; } 
template <class T, class... Ts> void err(const T& arg, const Ts&... args) { cout << arg << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A> 
void err(const T <t> &arg, const A&... args) { for (auto &v : arg) cout << v << ' '; err(args...); }
inline void pt() { cout << endl; } 
template <class T, class... Ts> void pt(const T& arg, const Ts&... args) { cout << arg << ' '; pt(args...); }
template <template<typename...> class T, typename t, typename... A> 
void pt(const T <t> &arg, const A&... args) { for (auto &v : arg) cout << v << ' '; pt(args...); }
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll qpow(ll base, ll n) { ll res = 1; while (n) { if (n & 1) res = res * base % mod; base = base * base % mod; n >>= 1; } return res; }
//head
constexpr int N = 1e5 + 10;
int n, cnt[30]; string s;
void run() {
    cin >> s;
    memset(cnt, -1, sizeof cnt);
    for (int i = 0, len = s.size(), num = 0; i <= len; ++i) {
        if (i == len) {
            if (num & 1) {
                cnt[s[i - 1] - 'a'] = 1;
            }
        } else if (i && s[i] != s[i - 1]) {
            if (num & 1) {
                cnt[s[i - 1] - 'a'] = 1; 
            }
            num = 0;
        }
        ++num;
    }
    for (int i = 0; i < 26; ++i) if (cnt[i] > 0) 
        cout << char(i + 'a');
    cout << endl;
    
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr); cout.tie(nullptr);
    cout << fixed << setprecision(20);
    int _T = rd();
    while (_T--) run();
    return 0;
}

B. Binary Palindromes

题意：
给出(n)个(01)串，可以任意交换任意两个字符串的任意两个位置的字符，问最终最多能有多少回文串。

思路：
任意交换，只需要考虑(0)有多少个，(1)有多少个，然后根据原串长度贪心构造。

代码：

view code

#pragma GCC optimize("Ofast,unroll-loops,no-stack-protector,fast-math")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
#define fi first
#define se second
#define endl "
" 
using namespace std;
using db = double;
using ll = long long;
using ull = unsigned long long; 
using pII = pair <int, int>;
using pLL = pair <ll, ll>;
constexpr int mod = 1e9 + 7;
template <class T1, class T2> inline void chadd(T1 &x, T2 y) { x += y; while (x >= mod) x -= mod; while (x < 0) x += mod; } 
template <class T1, class T2> inline void chmax(T1 &x, T2 y) { if (x < y) x = y; }
template <class T1, class T2> inline void chmin(T1 &x, T2 y) { if (x > y) x = y; }
inline int rd() { int x; cin >> x; return x; }
template <class T> inline void rd(T &x) { cin >> x; }
template <class T> inline void rd(vector <T> &vec) { for (auto &it : vec) cin >> it; }  
#define dbg(x...) do { cout << "33[32;1m" << #x << " -> "; err(x); } while (0) 
void err() { cout << "33[39;0m" << endl; } 
template <class T, class... Ts> void err(const T& arg, const Ts&... args) { cout << arg << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A> 
void err(const T <t> &arg, const A&... args) { for (auto &v : arg) cout << v << ' '; err(args...); }
inline void pt() { cout << endl; } 
template <class T, class... Ts> void pt(const T& arg, const Ts&... args) { cout << arg << ' '; pt(args...); }
template <template<typename...> class T, typename t, typename... A> 
void pt(const T <t> &arg, const A&... args) { for (auto &v : arg) cout << v << ' '; pt(args...); }
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll qpow(ll base, ll n) { ll res = 1; while (n) { if (n & 1) res = res * base % mod; base = base * base % mod; n >>= 1; } return res; }
//head
constexpr int N = 1e5 + 10;
int n, cnt[2], len[110]; 
void run() {
    n = rd();
    cnt[0] = cnt[1] = 0;
    for (int i = 1; i <= n; ++i) {
        string s; cin >> s;
        len[i] = s.size();
        for (auto &c : s) ++cnt[c - '0'];
    }
    sort(len + 1, len + 1 + n);
    int res = 0;
    for (int i = 1; i <= n; ++i) {
        if (len[i] & 1) {
            if (cnt[0] & 1) {
                --cnt[0];
            } else if (cnt[1] & 1) {
                --cnt[1];
            } else if (cnt[0]) {
                --cnt[0];
            } else if (cnt[1]) {
                --cnt[1];
            } else {
                break;
            }
            --len[i];
        }
        if (len[i] > cnt[0]) {
            if (cnt[0] & 1) {
                len[i] = len[i] - cnt[0] + 1;
                cnt[0] = 1;
            } else {
                len[i] -= cnt[0];
                cnt[0] = 0;
            }
        } else {
            cnt[0] -= len[i];
            len[i] = 0;
        }
        if (len[i] > cnt[1]) {
            if (cnt[1] & 1) {
                len[i] = len[i] - cnt[1] + 1;
                cnt[1] = 1;
            } else {
                len[i] -= cnt[1];
                cnt[1] = 0;
            }
        } else {
            cnt[1] -= len[i];
            len[i] = 0;
        }
        if (len[i]) break;
        ++res;
    }
    pt(res);
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr); cout.tie(nullptr);
    cout << fixed << setprecision(20);
    int _T = rd();
    while (_T--) run();
    return 0;
}

C. Minimize The Integer

题意：
给出一个(n)位的整数，可能有前导(0)，现在可以任意交换两个相邻的并且奇偶性不同的数的位置，最终结果也可以存在前导(0)，问最终结果的最小值是多少。

思路：
显然，所有奇偶性相同的数的相对位置不变，那么将奇数取出来，偶数取出来，然后贪心取头即可。

代码：

view code

#pragma GCC optimize("Ofast,unroll-loops,no-stack-protector,fast-math")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
#define fi first
#define se second
#define endl "
" 
using namespace std;
using db = double;
using ll = long long;
using ull = unsigned long long; 
using pII = pair <int, int>;
using pLL = pair <ll, ll>;
constexpr int mod = 1e9 + 7;
template <class T1, class T2> inline void chadd(T1 &x, T2 y) { x += y; while (x >= mod) x -= mod; while (x < 0) x += mod; } 
template <class T1, class T2> inline void chmax(T1 &x, T2 y) { if (x < y) x = y; }
template <class T1, class T2> inline void chmin(T1 &x, T2 y) { if (x > y) x = y; }
inline int rd() { int x; cin >> x; return x; }
template <class T> inline void rd(T &x) { cin >> x; }
template <class T> inline void rd(vector <T> &vec) { for (auto &it : vec) cin >> it; }  
#define dbg(x...) do { cout << "33[32;1m" << #x << " -> "; err(x); } while (0) 
void err() { cout << "33[39;0m" << endl; } 
template <class T, class... Ts> void err(const T& arg, const Ts&... args) { cout << arg << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A> 
void err(const T <t> &arg, const A&... args) { for (auto &v : arg) cout << v << ' '; err(args...); }
inline void pt() { cout << endl; } 
template <class T, class... Ts> void pt(const T& arg, const Ts&... args) { cout << arg << ' '; pt(args...); }
template <template<typename...> class T, typename t, typename... A> 
void pt(const T <t> &arg, const A&... args) { for (auto &v : arg) cout << v << ' '; pt(args...); }
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll qpow(ll base, ll n) { ll res = 1; while (n) { if (n & 1) res = res * base % mod; base = base * base % mod; n >>= 1; } return res; }
//head
constexpr int N = 3e5 + 10;
int n; char s[N]; 
void out(vector <int> &vec) {
    cout << vec.back();
    vec.pop_back();
}
void run() {
    vector <int> vec[2];
    cin >> (s + 1);
    for (int i = 1; s[i]; ++i) {
        int num = s[i] - '0';
        vec[num & 1].push_back(num);
    }
    reverse(vec[0].begin(), vec[0].end());
    reverse(vec[1].begin(), vec[1].end());
    while (!vec[0].empty() || !vec[1].empty()) {
        if (vec[0].empty()) {
            out(vec[1]);
        } else if (vec[1].empty()) {
            out(vec[0]);
        } else {
            if (vec[0].back() < vec[1].back()) {
                out(vec[0]);
            } else {
                out(vec[1]);
            }
        }
    }
    cout << endl;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr); cout.tie(nullptr);
    cout << fixed << setprecision(20);
    int _T; cin >> _T;
    while (_T--) run();
    return 0;
}

D. Salary Changing

题意：
有(n)个人，你是老板，你手里有(s)元钱，要给这(n)个人发工资，每个人工资的范围是([l_i, r_i])，要如何发工资使得你的钱够用并且(n)个人工资的中位数最高。

思路：
首先给每个人发(l_i)工资，那么得到一个答案的下界，那么发现这个下界到(INF)这个范围，答案具有单调性，二分然后贪心(check)即可。

代码：

view code

#pragma GCC optimize("Ofast,unroll-loops,no-stack-protector,fast-math")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
#define fi first
#define se second
#define endl "
" 
using namespace std;
using db = double;
using ll = long long;
using ull = unsigned long long; 
using pII = pair <int, int>;
using pLL = pair <ll, ll>;
constexpr int mod = 1e9 + 7;
template <class T1, class T2> inline void chadd(T1 &x, T2 y) { x += y; while (x >= mod) x -= mod; while (x < 0) x += mod; } 
template <class T1, class T2> inline void chmax(T1 &x, T2 y) { if (x < y) x = y; }
template <class T1, class T2> inline void chmin(T1 &x, T2 y) { if (x > y) x = y; }
inline int rd() { int x; cin >> x; return x; }
template <class T> inline void rd(T &x) { cin >> x; }
template <class T> inline void rd(vector <T> &vec) { for (auto &it : vec) cin >> it; }  
#define dbg(x...) do { cout << "33[32;1m" << #x << " -> "; err(x); } while (0) 
void err() { cout << "33[39;0m" << endl; } 
template <class T, class... Ts> void err(const T& arg, const Ts&... args) { cout << arg << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A> 
void err(const T <t> &arg, const A&... args) { for (auto &v : arg) cout << v << ' '; err(args...); }
inline void pt() { cout << endl; } 
template <class T, class... Ts> void pt(const T& arg, const Ts&... args) { cout << arg << ' '; pt(args...); }
template <template<typename...> class T, typename t, typename... A> 
void pt(const T <t> &arg, const A&... args) { for (auto &v : arg) cout << v << ' '; pt(args...); }
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll qpow(ll base, ll n) { ll res = 1; while (n) { if (n & 1) res = res * base % mod; base = base * base % mod; n >>= 1; } return res; }
//head
constexpr int N = 2e5 + 10;
int n; ll s;
pII a[N];
bool check(ll x) {
    int l = 0, r = 0;
    ll remind = s;
    for (int i = 1; i <= n; ++i) {
        if (a[i].se < x) {
            remind -= a[i].fi;
            ++l;
        } else if (a[i].fi > x) {
            remind -= a[i].fi;
            ++r;
        } 
    }
    if (l > n / 2 || r > n / 2) return false;
    for (int i = 1; i <= n; ++i) {
        if (a[i].fi <= x && a[i].se >= x) {
            if (l < n / 2) {
                ++l;
                remind -= a[i].fi;
            } else {
                remind -= x;
            }
        }
    }
    return remind >= 0;
}
void run() {
    cin >> n >> s;
    for (int i = 1; i <= n; ++i) a[i].fi = rd(), a[i].se = rd();
    sort(a + 1, a + 1 + n);
    ll l = a[n / 2 + 1].fi, r = 1e9, res = l;
    while (r - l >= 0) {
        ll mid = (l + r) >> 1;
        if (check(mid)) {
            res = mid;
            l = mid + 1;
        } else {
            r = mid - 1;
        }
    }
    pt(res);
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr); cout.tie(nullptr);
    cout << fixed << setprecision(20);
    int _T = rd();
    while (_T--) run();
    return 0;
}

E2. Voting (Hard Version)

题意：
有(n)个人，你可以花费(p_i)让第(i)个人投票，或者拉够(m_i)个人为你投票，这个人就会为你投票。
现在你想让所有人都为你投票，需要花费的最小代价是多少？

思路：
假设我知道有(x)个人不需要花费代价能让他们为我免费投票，那么我假设刚开始对每个人都付了钱让他们投票，现在就是要去除(x)个人的花费，使得去除的花费最大。
那么我们从(i in [x, n])扫一遍，用一个大根堆维护(m_i < i)的所有人的最大(p_i)，每次取出堆顶的(p_i)即可。
并且容易发现(x)具有单调性，直接二分即可。

代码：

view code

#pragma GCC optimize("Ofast,unroll-loops,no-stack-protector,fast-math")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
#define fi first
#define se second
#define endl "
" 
using namespace std;
using db = double;
using ll = long long;
using ull = unsigned long long; 
using pII = pair <int, int>;
using pLL = pair <ll, ll>;
constexpr int mod = 1e9 + 7;
template <class T1, class T2> inline void chadd(T1 &x, T2 y) { x += y; while (x >= mod) x -= mod; while (x < 0) x += mod; } 
template <class T1, class T2> inline void chmax(T1 &x, T2 y) { if (x < y) x = y; }
template <class T1, class T2> inline void chmin(T1 &x, T2 y) { if (x > y) x = y; }
inline int rd() { int x; cin >> x; return x; }
template <class T> inline void rd(T &x) { cin >> x; }
template <class T> inline void rd(vector <T> &vec) { for (auto &it : vec) cin >> it; }  
#define dbg(x...) do { cout << "33[32;1m" << #x << " -> "; err(x); } while (0) 
void err() { cout << "33[39;0m" << endl; } 
template <class T, class... Ts> void err(const T& arg, const Ts&... args) { cout << arg << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A> 
void err(const T <t> &arg, const A&... args) { for (auto &v : arg) cout << v << ' '; err(args...); }
inline void pt() { cout << endl; } 
template <class T, class... Ts> void pt(const T& arg, const Ts&... args) { cout << arg << ' '; pt(args...); }
template <template<typename...> class T, typename t, typename... A> 
void pt(const T <t> &arg, const A&... args) { for (auto &v : arg) cout << v << ' '; pt(args...); }
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll qpow(ll base, ll n) { ll res = 1; while (n) { if (n & 1) res = res * base % mod; base = base * base % mod; n >>= 1; } return res; }
//head
constexpr int N = 2e5 + 10;
int n; vector <vector<int>> vec;
ll gao(int x) {
    ll tot = 0;
    priority_queue <int, vector<int>, less<int>> pq;
    for (int i = 1; i <= n; ++i) {
        for (auto &it : vec[i]) pq.push(it);
        if (i >= x) {
            if (pq.empty()) return 0;
            tot += pq.top(); pq.pop();
        }
    }
    return tot;
}
void run() {
    n = rd();
    vec.clear(); vec.resize(n + 1);
    ll tot = 0;
    for (int i = 1, m, p; i <= n; ++i) {
        m = rd(); p = rd();
        vec[m + 1].push_back(p);
        tot += p;
    }
    int l = 1, r = n; ll Max = 0;
    while (r - l >= 0) {
        int mid = (l + r) >> 1;
        ll tmp = gao(mid);
        chmax(Max, tmp);
        //dbg(l, r, mid, Max);
        if (tmp > 0) {
            r = mid - 1;
        } else {
            l = mid + 1;
        }
    }
    pt(tot - Max);
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr); cout.tie(nullptr);
    cout << fixed << setprecision(20);
    int _T = rd();
    while (_T--) run();
    return 0;
}