Submission #949748

#	Time	Username	Problem	Language	Result	Execution time	Memory
949748		VinhLuu	Split the sequence (APIO14_sequence)	C++17	100 / 100	1390 ms	89636 KiB

sequence

#include <bits/stdc++.h>
//#define int long long
#define ll long long
#define fi first
#define se second
#define pb push_back
#define all(lmao) lmao.begin(), lmao.end()

using namespace std;

typedef pair<int,int> pii;
typedef tuple<int,int,int> tp;
const int N = 1e5 + 5;
const ll oo = -1e12;
const int K = 210;
const int mod = 998244353;
//const int base = 23;

ll n, k, a[N];

namespace sub3{
    ll f[222][222], dp[222][222], s[N];
    ll cal(int i,int j){
        return 1ll * (s[j] - s[i]) * (s[n] - s[j]);
    }
    void sol(){
        for(int i = 1; i <= n; i ++){
            s[i] = s[i - 1] + a[i];
        }
        for(int i = 1; i <= n; i ++) dp[i][1] = s[i] * (s[n] - s[i]), f[i][1] = 0;
        for(int j = 2; j <= k; j ++){
            for(int i = j; i < n; i ++){
                dp[i][j] = oo;
                for(int c = j - 1; c < i; c ++){
                    ll val = dp[c][j - 1] + cal(c, i);
                    if(dp[i][j] < val){
                        dp[i][j] = val;
                        f[i][j] = c;
                    }
                }
            }
        }
        ll ans = oo;
        int tmp = 0, cnt = k;
        for(int i = 1; i <= n; i ++){
            if(ans < dp[i][k]){
                ans = dp[i][k];
                tmp = i;
            }
        }
        cout << ans << "\n";

        vector<int> vr;
        vr.pb(tmp);
        while(f[tmp][cnt]){
            vr.pb(f[tmp][cnt]);
            tmp = f[tmp][cnt];
            cnt--;
        }

        for(int i = vr.size() - 1; i >= 0; i --) cout << vr[i] << " ";

    }
}

namespace AC{
    ll dp[N][5], s[N], pre, nx;

    int f[N][K];

    ll cal(int i,int j){
        return 1ll * (s[j] - s[i]) * (s[n] - s[j]);
    }

    void solve(int j,int l,int r,int pl,int pr){
        if(l > r) return;
        int mid = (l + r) / 2;
        dp[mid][nx] = oo;
        for(int i = pl; i <= min(mid - 1, pr); i ++){
            ll val = dp[i][pre] + cal(i, mid);
            if(val > dp[mid][nx]){
                dp[mid][nx] = val;
                f[mid][j] = i;
            }
        }
        solve(j, l, mid - 1, pl, f[mid][j]);
        solve(j, mid + 1, r, f[mid][j], pr);
    }

    void sol(){
        for(int i = 1; i <= n; i ++) s[i] = s[i - 1] + a[i];
        if(k == 0){
            cout << 0;
            return ;
        }
        for(int j = 0; j <= 1; j ++){
            for(int i = 0; i <= n; i ++){
                dp[i][j] = oo;
            }
        }

        pre = 0, nx = 1;
        for(int i = 1; i <= n; i ++) dp[i][0] = 1ll * s[i] * (s[n] - s[i]), f[i][0] = 0;
        for(int j = 2; j <= k; j ++){
            solve(j, j, n, 1, n - 1);
            swap(pre, nx);
        }
        ll ans = oo;
        int tmp = 0, cnt = k;
        for(int i = 1; i <= n; i ++){
            if(ans < dp[i][pre]){
                ans = dp[i][pre];
                tmp = i;
            }
        }
        cout << ans << "\n";

        vector<int> vr;
        vr.pb(tmp);
        while(f[tmp][cnt]){
            vr.pb(f[tmp][cnt]);
            tmp = f[tmp][cnt];
            cnt--;
        }

        for(int i = vr.size() - 1; i >= 0; i --) cout << vr[i] << " ";

    }
}

signed main(){
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);

    #define task "v"
    if(fopen(task ".inp","r")){
        freopen(task ".inp","r",stdin);
        freopen(task ".out","w",stdout);
    }
    cin >> n >> k;
    for(int i = 1; i <= n; i ++){
        cin >> a[i];
    }
    if(n <= 200 && k <= 200) sub3 :: sol();
    else
        AC :: sol();
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:136:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  136 |         freopen(task ".inp","r",stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:137:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  137 |         freopen(task ".out","w",stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 29 / 29