Submission #240710

#	Time	Username	Problem	Language	Result	Execution time	Memory
240710		WhaleVomit	Split the sequence (APIO14_sequence)	C++14	71 / 100	87 ms	131076 KiB

sequence

#include <bits/stdc++.h>
 
using namespace std;
 
#define f first
#define s second
#define pb push_back
#define mp make_pair
#define all(v) v.begin(), v.end()
#define sz(v) (int)v.size()
 
#define MOO(i, a, b) for(int i=a; i<b; i++)
#define M00(i, a) for(int i=0; i<a; i++)
#define MOOd(i,a,b) for(int i = (b)-1; i >= a; i--)
#define M00d(i,a) for(int i = (a)-1; i>=0; i--)
 
#define FAST ios::sync_with_stdio(0); cin.tie(0);
#define finish(x) return cout << x << '\n', 0;
#define dbg(x) cerr << ">>> " << #x << " = " << x << "\n";
#define _ << " _ " <<
 
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef pair<int,int> pi;
typedef pair<ld,ld> pd;
typedef complex<ld> cd;

struct line {
    ll m;
    ll b;
    int idx;
    line(ll mm, ll bb, int idxp) {
        m = mm;
        b = bb;
        idx = idxp;
    }
};

bool leftOf(line l1, line l2, line l3) { // is intersection of l1 and l3 to the left of l1 and l2?
    if(l2.m == l3.m) return 1;
    return (l3.b-l1.b)*(l1.m-l2.m) <= (l2.b-l1.b)*(l1.m-l3.m);
}

ll eval(ll x, line l) {
    return l.m * x + l.b;
}

bool better(ll x, line l1, line l2) { // l2(x) >= l1(x)?
    return eval(x, l2) >= eval(x, l1);
}

const int MAX_N = 100100;
const int MAX_K = 202;
int n, k;
const ll inf = 1e17;
ll arr[MAX_N];
ll psum[MAX_N];
ll dp[MAX_N][MAX_K];
int lastsplit[MAX_N][MAX_K];
 
int main() { FAST
    cin >> n >> k;
    for(int i = 1; i <= n; i++) {
        cin >> arr[i];
        psum[i] = psum[i-1] + arr[i];
    }
    for(int j = 1; j <= k; j++) {
        for(int i = 0; i <= n; i++) {
            dp[i][j] = -inf;
        }
    }
    for(int j = 1; j <= k; j++) {
        deque<line> dq;
        dq.pb(line(psum[n],0,0));
        for(int i = 1; i <= n; i++) {
            while(sz(dq) >= 2 && better(psum[i], dq[0], dq[1])) dq.pop_front();
            
            dp[i][j] = -psum[i] * psum[i] + eval(psum[i], dq[0]);
            lastsplit[i][j] = dq[0].idx;

            line l3 = line(psum[n]+psum[i], dp[i][j-1]-psum[i]*psum[n],i);
            while(sz(dq) >= 2 && leftOf(dq[sz(dq)-2], dq[sz(dq)-1], l3)) dq.pop_back();
            dq.pb(l3);
        }
    }
    int besIdx = 1;
    for(int i = 1; i <= n; i++) {
        if(dp[i][k] > dp[besIdx][k]) {
            besIdx = i;
        }
    }
    ll mx = dp[besIdx][k];
    vi v;
    int cur = k;
    while(cur != 0) {
        v.pb(besIdx);
        besIdx = lastsplit[besIdx][cur];
        cur--;
    }
    cout << mx << "\n";
    M00(i, k) {
        if(i != 0) cout << " ";
        cout << v[i];
    }
    cout << "\n";
}

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 0 / 29