Submission #1090902

#	Time	Username	Problem	Language	Result	Execution time	Memory
1090902		eltu0815	Chorus (JOI23_chorus)	C++14	100 / 100	864 ms	39668 KiB

chorus

#include <bits/stdc++.h>
#define MAX 1000005
#define MOD (ll)(1048573)
#define INF (ll)(1e12)
#define inf (int)(1e9)
#define eps (double)(1e-8)
 
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
 
int tt, N, K;
string str;

int cnt[MAX], pos[MAX], can[MAX], q[MAX], k[MAX];
ll dp[MAX], sum[MAX];

ll cost(int i, int j) {
    return max(sum[j] - sum[pos[i - 1] - 1] - (ll)(j - pos[i - 1] + 1) * (i - 1), -INF);
}

ll func(int i, int j) {
    return dp[i] + cost(i + 1, j);
}

int cross(int i, int j) {
//    int lo = j , hi = N + 1;
//    while(lo + 1 < hi) {
//        int mid = (lo + hi) >> 1;
//        if(func(i, mid) <= func(j, mid)) lo = mid;
//        else hi = mid;
//    }
    
    //sum[j] - j * (i - 1) - sum[pos[i - 1] - 1] + (ll)(pos[i - 1] - 1) * (i - 1)
    //x * (j - i) + C1 <= C2
    ll C1 = dp[i] - sum[pos[i] - 1] + (ll)(pos[i] - 1) * (i), C2 = dp[j] - sum[pos[j] - 1] + (ll)(pos[j] - 1) * (j);
    ll x1 = min((C2 - C1) / (j - i), (ll)N);
    
    //cout << i << ' ' << j << ' ' << x1 <<  ' ' << lo << endl;

    return x1; 
}

void monotoneQueue(ll lambda) {
    int str = 0, ed = 1;
    q[0] = 0; can[0] = N;
    for(int i = 1; i <= N; ++i) {
        while(can[str] < i) ++str;
        dp[i] = func(q[str], i) + lambda; k[i] = k[q[str]] + 1;
        
        while(str + 1 < ed && can[ed - 2] >= cross(q[ed - 1], i)) --ed;
        can[ed - 1] = cross(q[ed - 1], i); q[ed] = i; can[ed] = N;
        ++ed;
    }

    return;
}

ll alienTrick() {
    ll lo = -1, hi = INF;
    ll ans = 0;
    while(lo + 1 < hi) {
        ll mid = (lo + hi) >> 1;
        monotoneQueue(mid);
        
        ans = max(ans, dp[N] - mid * K);
        
        if(k[N] >= K) lo = mid;
        else hi = mid;
    }
    
    return ans;
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(NULL);
    
    cin >> N >> K >> str;
    for(int i = 0, tmp = 0, p = 0; i < 2 * N; ++i) {
        if(str[i] == 'A') cnt[++p] = tmp;
        else ++tmp;
    }
    
    for(int i = 0, j = 1; i <= N; ++i) {
        while(j <= N && cnt[j] < i) ++j;
        pos[i] = max(i + 1, j);
    }
    
    for(int i = 1; i <= N; ++i) sum[i] = sum[i - 1] + cnt[i];
    
//    for(int i = 0; i <= N; ++i) {
//        cout << - sum[pos[i - 1] - 1] + (ll)(pos[i - 1] - 1) * (i - 1) << endl;
//    }

//    for(int i = 1; i <= N; ++i) for(int j = i; j <= N; ++j) {
//        cout << i << ' ' << j << ' ' << cost(i, j) << endl;
//    }
    
    cout << alienTrick();
    return 0;
}

• Subtask 1: 16 / 16
• Subtask 2: 24 / 24
• Subtask 3: 21 / 21
• Subtask 4: 26 / 26
• Subtask 5: 13 / 13