Codeforces Round #404 (Div. 2) 题解

Posted 2022-11-24 AC_Arthur

题目链接：点击打开链接

这次比赛AC了4个水题， 然而我zz了Ｅ题写了个ｂｕｇ调了很久没时间写Ｄ啦。

A. Anton and Polyhedrons
水题， 加一加就行了。

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <string>
#include <vector>
#include <stack>
#include <bitset>
#include <cstdlib>
#include <cmath>
#include <set>
#include <list>
#include <deque>
#include <map>
#include <queue>
#define Max(a,b) ((a)>(b)?(a):(b))
#define Min(a,b) ((a)<(b)?(a):(b))
using namespace std;
typedef long long ll;
typedef long double ld;
const double eps = 1e-6;
const int mod = 1000000000 + 7;
const int INF = 0x3f3f3f3f;
const int seed = 131;
const ll INF64 = ll(1e18);
const int maxn = 3000+10;

int n;
char s[100];

int main() 
    scanf("%d", &n);
    int ans = 0;
    for(int i = 1; i <= n; i++) 
        scanf("%s", s);
        if(s[0] == 'T') ans += 4;
        else if(s[0] == 'C') ans += 6;
        else if(s[0] == 'O') ans += 8;
        else if(s[0] == 'D') ans += 12;
        else ans += 20;
    
    printf("%d\\n", ans);


    return 0;

B. Anton and Classes
排序就行了， 我们肯定是在一个区间集合中找一个右端点最小的， 在另一个集合里找一个左端点最大的。

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <string>
#include <vector>
#include <stack>
#include <bitset>
#include <cstdlib>
#include <cmath>
#include <set>
#include <list>
#include <deque>
#include <map>
#include <queue>
#define Max(a,b) ((a)>(b)?(a):(b))
#define Min(a,b) ((a)<(b)?(a):(b))
using namespace std;
typedef long long ll;
typedef long double ld;
const double eps = 1e-6;
const int mod = 1000000000 + 7;
const int INF = 0x3f3f3f3f;
const int seed = 131;
const ll INF64 = ll(1e18);
const int maxn = 200000+10;

int n, m;
struct node 
    int l, r;
    node(int l=0, int r=0):l(l), r(r) 
a[maxn], b[maxn];
bool cmp1(const node& a, const node& b) 
    if(a.l != b.l) return a.l < b.l;
    else return a.r < b.r;

bool cmp2(const node& a, const node& b) 
    if(a.r != b.r) return a.r < b.r;
    else return a.l < b.l;



int main() 
    scanf("%d", &n);
    for(int i = 1; i <= n; i++) 
        scanf("%d%d", &a[i].l, &a[i].r);
    
    scanf("%d", &m);
    for(int i = 1; i <= m; i++) 
        scanf("%d%d", &b[i].l, &b[i].r);
    
    int ans = 0;
    sort(a+1, a+1+n, cmp2);
    sort(b+1, b+1+m, cmp1);
    if(a[1].r <= b[m].l) 
        ans = max(ans, b[m].l - a[1].r);
    
    sort(a+1, a+1+n, cmp1);
    sort(b+1, b+1+m, cmp2);
    if(b[1].r <= a[n].l) 
        ans = max(ans, a[n].l - b[1].r);
    
    printf("%d\\n", ans);


    return 0;

C. Anton and Fairy Tale
我们可以发现， 当ｎ＞ｍ时，　前ｍ天的每天早上一定会被加满谷仓，　在第ｍ＋１天开始，　下午的时候，　谷仓里谷子会少ｍ＋１个，ｍ＋２个．．．．，　所以我们只需要判断某一天ｃｎｔ，　当ｃｎｔ（ｃｎｔ＋１）／２　＋　ｍ　＞＝　ｎ，　我们可以发现，　这个是可以二分的，　二分他就行了。

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <string>
#include <vector>
#include <stack>
#include <bitset>
#include <cstdlib>
#include <cmath>
#include <set>
#include <list>
#include <deque>
#include <map>
#include <queue>
#define Max(a,b) ((a)>(b)?(a):(b))
#define Min(a,b) ((a)<(b)?(a):(b))
using namespace std;
typedef long long ll;
typedef long double ld;
const double eps = 1e-6;
const int mod = 1000000000 + 7;
const int INF = 0x3f3f3f3f;
const int seed = 131;
const ll INF64 = ll(1e18 + 10);
const int maxn = 200000+10;
ll n, m;

bool ok(ll mid) 
    ll cur = mid * (mid + 1) / 2;
    return cur + m >= n;



int main() 
    scanf("%I64d%I64d", &n, &m);
    if(n <= m) 
        printf("%I64d\\n", n);
        return 0;
    

    ll l = 1, r = 2e9, ans = INF64;
    while(l <= r) 
        ll mid = (l + r) >> 1;
        if(ok(mid)) 
            r = mid - 1;
            ans = min(ans, mid);
        
        else l = mid + 1;
    
    printf("%I64d\\n", m + ans);

    return 0;

D. Anton and School - 2
Ｄ题其实很简单，　最后没时间写了，　我们如果从左向右枚举，　当枚举到一个（的时候，　我们假设一定选这个左括号，　那么我们要在之前的左括号里选０个，１个，２个．．．，　假设我们枚举到当前左括号，　左边有ｎ个，　右边有ｍ个右括号，　那么我们对答案贡献　ｓｕｍ（Ｃ（ｎ，０￣ｎ）×Ｃ（ｍ，１～ｎ＋１）＝　Ｃ（ｎ＋ｍ，　ｎ＋１）；

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int MOD = 1e9 + 7;
const int maxn = 2e5 + 10;
LL fac[maxn];
void init()

    LL i;
    fac[0]=1;
    for (LL i = 1; i < maxn; i++)
    fac[i] = fac[i - 1] * i % MOD;

LL exgcd(LL a, LL b, LL &x, LL &y) 
    if (!b) x = 1; y = 0; return a;
    LL d = exgcd(b, a % b, y, x);
    y -= a / b * x;
    return d;

LL inv(LL a, LL n) 
    LL x, y;
    exgcd(a, n, x, y);
    return (x + n) % n;


LL C(LL n, LL m) 
    return fac[n] * inv(fac[m] * fac[n - m] % MOD, MOD) % MOD;

char s[maxn];

int main() 
    init();
    scanf("%s", s + 1);
    int len = strlen(s+1);
    int cnt1 = 0, cnt2 = 0;
    LL ans = 0;
    for(int i = 1; i <= len; i++) 
        if(s[i] == ')') ++cnt2;
    
    for(int i = 1; i <= len; i++) 
//        printf("case :%d\\n", i);
        if(cnt2 == 0) break;
        if(s[i] == '(') 
//            printf("%d %d=", cnt1, cnt2);
        ans = (ans + C(cnt1+cnt2, cnt1+1)) % MOD;
           // ans = (ans + cnt2) % MOD;
//            printf("%d\\n", C(cnt1+cnt2, min(cnt1, cnt2)));
            ++cnt1;

        
        else --cnt2;
//        printf("%d\\n", ans);
    
    printf("%I64d\\n", ans);

    return 0;

E. Anton and Permutation
这种xjb更新，xjb询问的，我们就分块+二分暴力去搞就行啦。

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <string>
#include <vector>
#include <stack>
#include <bitset>
#include <cstdlib>
#include <cmath>
#include <set>
#include <list>
#include <deque>
#include <map>
#include <queue>
#define Max(a,b) ((a)>(b)?(a):(b))
#define Min(a,b) ((a)<(b)?(a):(b))
using namespace std;
typedef long long ll;
typedef long double ld;
const double eps = 1e-6;
const int mod = 1000000000 + 7;
const int INF = 0x3f3f3f3f;
const int seed = 131;
const ll INF64 = ll(1e18 + 10);
const int maxn = 200000+10;
int n, q;
int belong[maxn];       /// ÿ���������ĸ���
int block;              /// ��Ĵ�С
int num;                /// ��ĸ���
int r[maxn], l[maxn];   /// ÿ������ұ߽�
ll sum[maxn];           /// ����ά������Ϣ
ll cnt[maxn];
int a[maxn];

vector<int> res[maxn/10];

void build() 
    block = sqrt(n);
    num = n / block;
    if(n % block) num++;
    for(int i = 1; i <= num; i++) 
        l[i] = (i-1)*block + 1;
        r[i] = i * block;
        sum[i] = 0;
        cnt[i] = 0;
    
    r[num] = n;
    for(int i = 1; i <= n; i++) belong[i] = (i-1)/block+1;
    int ccc = 1;
    for(int i = 1; i <= num; i++) 
        for(int j = l[i]; j <= r[i]; j++) 
            res[i].push_back(ccc);
            a[ccc] = ccc;
            ++ccc;
        
    


int query(int x, int y, int cal) 
    int ans = 0;
    if(belong[x] == belong[y]) 
        for(int i = x; i <= y; i++) 
            if(a[i] < cal) ++ans;
        
        return ans;
    
    else 
        for(int i = x; i <= r[belong[x]]; i++) 
            if(a[i] < cal) ++ans;
        

        for(int i = belong[x]+1; i < belong[y]; i++) 
            int pos = lower_bound(res[i].begin(), res[i].end(), cal) - res[i].begin();
            if(pos == (int)res[i].size()) ans += pos;
            else if(res[i][pos] != cal) ans += pos;
        


        for(int i = l[belong[y]]; i <= y; i++) 
            if(a[i] < cal) ++ans;
        
        return ans;
    


void update(int l, int r) 
    int be = belong[l];
    int bee = belong[r];

    int pos = lower_bound(res[be].begin(), res[be].end(), a[l]) - res[be].begin();
    res[be].erase(res[be].begin() + pos);
    res[be].push_back(a[r]);
    sort(res[be].begin(), res[be].end());

    pos = lower_bound(res[bee].begin(), res[bee].end(), a[r]) - res[bee].begin();
    res[bee].erase(res[bee].begin() + pos);
    res[bee].push_back(a[l]);
    sort(res[bee].begin(), res[bee].end());


void print() 
    for(int i = 1; i <= num; i++) 
        for(int j = l[i]; j <= r[i]; j++) 
            printf("%d ", res[i][j-l[i]]);
        
        cout<<endl;
    



int main() 
    scanf("%d%d", &n, &q);
    build();
    ll ans = 0;
    while(q--) 
        int l, r;
        scanf("%d%d", &l, &r);
        if(l > r) swap(l, r);
        if(l == r) 
            printf("%I64d\\n", ans);
            continue;
        
        if(l+1 == r) 
            if(a[l] < a[r]) ++ans;
            else --ans;
        
        else 
            int cur = query(l+1, r-1, a[l]);
            int maxv = (r - l - 1) - cur;

            ans -= cur;
            ans += maxv;
            cur = query(l+1, r-1, a[r]);
            maxv = (r - l - 1) - cur;
            ans += cur;
            ans -= maxv;
            if(a[l] < a[r]) ++ans;
            else --ans;
        
        update(l, r);
        swap(a[l], a[r]);
      //  print();
        printf("%I64d\\n", ans);
    
    return 0;