CCPC2025郑州区域赛题解

//B
#include <iostream>
#include<vector>
#include<algorithm>
using namespace std;

using ll = long long;
const ll mod = 1e9 + 7;

void solve() {
    const int D = 3;
    vector<ll> sz(D);
    for (int i = 0; i < D; i++) cin >> sz[i];

    vector<ll> cut(D); // p, q, r
    for (int i = 0; i < D; i++) {
        cin >> cut[i];
        cut[i]++;
    }

    ll n;
    cin >> n;
    vector<vector<ll>> pts(n, vector<ll>(D));
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < D; j++) {
            cin >> pts[i][j];
        }
    }

    ll total = 1;
    for (int w = 0; w < D; w++) total *= cut[w];
    if (n % total != 0) {
        cout << 0 << endl;
        return;
    }
    ll each = n / total;


    vector<vector<ll>> pos(D);
    ll ans = 1;

    for (int w = 0; w < D; w++) {
        vector<ll> v(n);
        for (int i = 0; i < n; i++) v[i] = pts[i][w];
        sort(v.begin(), v.end());

        ll step = n / cut[w];
        for (int i = 0; i < n; i += step) {
            pos[w].push_back(v[i]);
            if (i != 0) {
                ans = ans * (v[i] - v[i - 1]) % mod;
            }
        }
    }

    vector<ll> cnt(total, 0);
    for (auto& p : pts) {
        ll id = 0;
        for (int w = 0; w < D; w++) {
            ll j = upper_bound(pos[w].begin(), pos[w].end(), p[w]) - pos[w].begin() - 1;
            id = id * cut[w] + j;
        }
        cnt[id]++;
    }

    for (ll x : cnt) {
        if (x != each) ans = 0;
    }

    cout << ans << endl;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    solve();
    return 0;
}

//G
#include <bits/stdc++.h>
#define int long long 
using namespace std;
int T,a,b,c,dis[2010][2010],inq[2010][2010],md;
queue<pair<int,int> > q;
void dijkstra(){
    md=(1<<((int)floor(log2(b))+1));
    for(int i=0;i<md;i++){
        for(int j=0;j<b;j++){
            dis[i][j]=2e18;
        }
    }
    dis[a%md][a%b]=a;
    q.push({a%md,a%b});
    while(!q.empty()){
        int x=q.front().first,y=q.front().second;
        q.pop();
        inq[x][y]=0;
        if(dis[(x+b)%md][y]>dis[x][y]+b){
            dis[(x+b)%md][y]=dis[x][y]+b;
            if(!inq[(x+b)%md][y]){
                q.push({(x+b)%md,y});
                inq[(x+b)%md][y]=1;
            }
        }
        if(dis[x^b][(y-x+(x^b)+b)%b]>(dis[x][y]^b)){
            dis[x^b][(y-x+(x^b)+b)%b]=dis[x][y]^b;
            if(!inq[x^b][(y-x+(x^b)+b)%b]){
                q.push({x^b,(y-x+(x^b)+b)%b});
                inq[x^b][(y-x+(x^b)+b)%b]=1;
            }
        }
    }
    for(int i=0;i<md;i++){
        if(dis[i][c%b]<=c){
            cout<<"YES"<<endl;
            return ;
        }
    }
    cout<<"NO"<<endl;
}
signed main(){
    ios::sync_with_stdio(0);
    cin>>T;
    while(T--){
        cin>>a>>b>>c;
        dijkstra();
    }
    return 0;
}
/*
5
1 6 7
7 5 13
8 3 16
7 6 17
2 7 8
*/

//I
#include<bits/stdc++.h>
using namespace std;
#define int long long

const int mod = 998244353;
const int maxn = 5010;
int n, k, ans;
int fact[maxn], inv_fact[maxn], v[maxn];

int inv(int a)
{
    int res = 1;
    int b = mod - 2;
    while (b)
    {
        if (b & 1)
            res = res * a % mod;
        a = a * a % mod;
        b >>= 1;
    }
    return res;
}

int C(int n, int m)
{
    if (n < m) return 0;
    return fact[n] * inv_fact[m] % mod * inv_fact[n - m] % mod;
}

signed main()
{
    cin >> n >> k;

    fact[0] = 1;
    for (int i = 1; i <= maxn - 10; i++)
        fact[i] = fact[i - 1] * i % mod;
    for (int i = 0; i <= maxn - 10; i++)
        inv_fact[i] = inv(fact[i]);
    
    for (int i = 1; i <= n; i++)
        v[i] = i;
    
    int base_poss = inv_fact[n];
    int poss = 1;

    for (int i = 1; i <= k; i++)
    {
        int res = 1ll;
        for (int j = 1; j < n; j++)
        {
            res = res * (1ll + v[j]) % mod;
            v[j] = v[j] * j % mod;
        }

        if (i % 2 == 0)
            res = (mod - res) % mod;
        res = res * C(k, i) % mod;

        poss = poss * base_poss % mod;
        ans = (ans + res * poss) % mod;
    }

    cout << ans;
    return 0;
}

//J
#include <iostream>
#include<vector>
#include<map>
using namespace std;

using ll = long long;
const int BIT = 32;
const ll mod = 998244353;

ll qpow(ll a, ll b) {
    ll res = 1;
    while (b) {
        if (b & 1) res = res * a % mod;
        b >>= 1;
        a = a * a % mod;
    }
    return res;
}

void solve() {
    int n, m;
    cin >> n >> m;
    vector<ll> row(n), col(m);
    for (ll& x : row) 
        cin >> x;
    for (ll& x : col) 
        cin >> x;

    vector<map<ll, ll>> mp(BIT);

    for (int j = 0; j + 1 < m; j++) {
        if ((col[j] ^ col[j + 1]) != 1) continue;
        for (int d = 2; d < BIT; d++) {
            ll mask = 1LL << d;
            mp[d][col[j] % mask]++;
        }
    }

    ll ans = 0;
    for (int i = 0; i + 1 < n; i++) {
        ll delta = row[i] ^ row[i + 1];
        for (int d = 2; d < BIT; d++) {
            ll mask = 1LL << d;
            if (delta != mask - 2) continue;

            ll tar = (mask - 2) - (1LL << (d - 1));
            tar ^= row[i];
            tar %= mask;
            ans += mp[d][tar];
        }
    }

    cout << ans << endl;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int T;
    cin >> T;
    while (T--) 
        solve();

    return 0;
}

//K
#include<bits/stdc++.h>
using namespace std;
const int inf=1e9;
int T,n,a[500050],st0[500050][30],st1[500050][30],vis[1000010],mx[1000010];
int ed0[500050][30],ed1[500050][30],mxr[1000010];
stack<int> s;
int Ask(int l,int r,int id){
    if(l>r){
        return inf;
    }
    int k=log2(r-l+1),x=r-(1<<k)+1;
    if(id){
        return min(st0[l][k],st0[x][k]);
    }
    return min(st1[l][k],st1[x][k]);
}
int Askr(int l,int r,int id){
    if(l>r){
        return inf;
    }
    int k=log2(r-l+1),x=r-(1<<k)+1;
    if(id){
        if(st0[l][k]<st0[x][k]){
            return ed0[l][k];
        }
        return ed0[x][k];
    }
    if(st1[l][k]<st1[x][k]){
        return ed1[l][k];
    }
    return ed1[x][k];
}
void solve(){
    cin>>n;
    while(!s.empty()){
        s.pop();
    }
    for(int i=1;i<=n;i++){
        vis[i]=mx[i]=mxr[i]=0;
    }
    for(int j=0;j<25;j++){
        for(int i=1;i+(1<<(j+1))-1<=n;i++){
            st0[i][j]=st1[i][j]=ed0[i][j]=ed1[i][j]=0;
        }
    }
    for(int i=1;i<=n;i++){
        cin>>a[i];
        if(i%2==1){
            ed0[i][0]=i;
            st0[i][0]=a[i];
            st1[i][0]=inf;
            continue;
        }
        ed1[i][0]=i;
        st1[i][0]=a[i];
        st0[i][0]=inf;
    }
    for(int j=0;j<25;j++){
        for(int i=1;i+(1<<(j+1))-1<=n;i++){
            if(st0[i][j]<st0[i+(1<<j)][j]){
                st0[i][j+1]=st0[i][j];
                ed0[i][j+1]=ed0[i][j];
            }
            else{
                st0[i][j+1]=st0[i+(1<<j)][j];
                ed0[i][j+1]=ed0[i+(1<<j)][j];
            }
            if(st1[i][j]<st1[i+(1<<j)][j]){
                st1[i][j+1]=st1[i][j];
                ed1[i][j+1]=ed1[i][j];
            }
            else{
                st1[i][j+1]=st1[i+(1<<j)][j];
                ed1[i][j+1]=ed1[i+(1<<j)][j];
            }
        }
    }
    //cout<<777<<endl;
    for(int i=1;i<=n;i++){
    //    cout<<i<<endl;
        if(s.empty()){
            s.push(i);
            vis[i]=0;
            mx[i]=Ask(i,n,(i+1)%2);
            mxr[i]=Askr(i,n,(i+1)%2);
            //cout<<777<<endl;
            continue;
        }
        int u=s.top();
        //cout<<778<<endl;
        mx[i]=Ask(i,mxr[u]-1,(i+1)%2);
        if(mx[i]>=a[u]&&mx[u]==a[i]){
            vis[i]=1;
            //cout<<777<<endl;
            s.pop();
            continue;
        }
    //    cout<<777<<endl;
        vis[i]=0;
        mxr[i]=Askr(i,mxr[u]-1,(i+1)%2);
        s.push(i);
    }
    for(int i=1;i<=n;i++){
        if(vis[i]){
            cout<<")";
            continue;
        }
        cout<<"(";
    }
    cout<<endl;
}
int main(){
    ios::sync_with_stdio(0);
    cin>>T;
    while(T--){
        solve();
    }
    return 0;
}
/*
5
6
4 1 5 4 1 1
4
1 2 3 2
4
1 3 1 2
2
2 1
8
8 5 2 6 1 4 3 7
*/

//M
#include<bits/stdc++.h>
using namespace std;

int T;
string s;

string oplus(string a, string b)
{
    int alen = a.size(), blen = b.size();
// cout <<"A:" << a << ' ' <<"B:" << b << '\n';
    int i;
    for (i = 0; i < alen && a[i] == '0'; i++);

    if (i == alen)
        a = "0";
    else
        a = a.substr(i);

    for (i = 0; i < blen && b[i] == '0'; i++);

    if (i == blen)
        b = "0";
    else b = b.substr(i);

    alen = a.size(), blen = b.size();
    
    string ans = "";

    for (int j = 0; j < min(alen, blen); j++)
        ans += (a[alen - j - 1] == b[blen - j - 1] ? '0' : '1');
    
    if (alen > blen)
    {
        for (int j = alen - blen - 1; j >= 0; j--)
            ans += a[j];
    }
    else if (alen < blen)
    {
        for (int j = blen - alen - 1; j >= 0; j--)
            ans += b[j];
    }
    
    reverse(ans.begin(), ans.end());

    int len = ans.size();
    for (i = 0; i < len && ans[i] == '0'; i++);

    if (i == len)
        return "0";
    return ans.substr(i);
}

string maxx(string a, string b)
{
    int alen = a.size(), blen = b.size();
    if (alen != blen)
        return alen > blen ? a : b ;
    for (int i = 0; i < alen; i++)
    {
        if (a[i] > b[i])
            return a;
        else if (a[i] < b[i])
            return b;
    }
    return a;
}

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    cin >> T;
    while (T--)
    {
        cin >> s;
        int n = s.size();

        string cuta, cutb;

        if (n == 3)
        {
            cuta = s[0], cutb = s[n - 1];
            cout << oplus(cuta, cutb) << '\n';
            continue;
        }

        cuta = s[0], cutb = s.substr(2);

        string ans1 = oplus(cuta, cutb);

        cuta += s[1];
        cutb = s.substr(3);

        string ans2 = oplus(cuta, cutb);
 
        cuta = s.substr(0, n - 2);
        cutb = s[n - 1];

        string ans3 = oplus(cuta, cutb);

        cout << maxx(ans1, maxx(ans2, ans3)) << '\n';
    }
    return 0;
}