Submission #768956

#	Time	Username	Problem	Language	Result	Execution time	Memory
768956		hafo	Split the sequence (APIO14_sequence)	C++14	71 / 100	1506 ms	131072 KiB

sequence

#include <bits/stdc++.h>
#define ll long long
#define ull unsigned ll
#define pb push_back
#define pa pair<int, int>
#define pall pair<ll, int>
#define fi first
#define se second
#define TASK "test"
#define Size(x) (int) x.size()
#define all(x) x.begin(), x.end()
using namespace std;
 
template<typename T1, typename T2> bool mini (T1 &a, T2 b) {if(a > b) a = b; else return 0; return 1;}
template<typename T1, typename T2> bool maxi (T1 &a, T2 b) {if(a < b) a = b; else return 0; return 1;}
 
const int MOD = 1e9 + 7;
const int LOG = 20;
const int maxn = 1e5 + 7;
const ll oo = 1e18 + 69;
 
int n, k, a[maxn], trace[207][maxn];
ll f[maxn], dp[207][maxn];
 
struct line {
    ll m, b;
    int id;
};
 
double inter(line &c, line &d) {
    return (double) (d.b - c.b) / (double) (c.m - d.m);
}
 
struct cht {
    line lines[maxn];
    int sz = 0;
    
    void init() {
        sz = 0;
    }
 
    bool bad(line &a, line &b, line &c) {
        return inter(a, c) > inter(a, b);
    }
 
    ll calc(line a, ll x) {
        return a.m * x + a.b;
    }
 
    pair<ll, int> query(ll x) {
        pair<ll, int> res = {calc(lines[0], x), lines[0].id};
        int l = 0, r = sz - 1, mid;
        while(l < r) {
            mid = l + r >> 1;
            ll s1 = calc(lines[mid], x);
            ll s2 = calc(lines[mid + 1], x);
            if(maxi(res.fi, s1)) res.se = lines[mid].id;
            if(maxi(res.fi, s2)) res.se = lines[mid + 1].id;
            if(s1 > s2) {
                r = mid;
            } else {
                l = mid + 1;
            }
        }
        return res;
    }
 
    void add(line new_line) {
        int l = 1, r = sz - 1, mid, res = sz;
        while(l <= r) {
            mid = l + r >> 1;
            if(!bad(lines[mid - 1], lines[mid], new_line)) {
                r = mid - 1;
                res = mid;
            }
            else {
                l = mid + 1;
            }
        }
        
        lines[res] = new_line;
        sz = res + 1;
    }
 
} cht;
 
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
 
    // freopen(TASK".inp", "r", stdin);
    // freopen(TASK".out", "w", stdout);
 
    cin>>n>>k;
    for(int i = 1; i <= n; i++) {
        cin>>a[i];
        f[i] = f[i - 1] + a[i];
    }
    
    for(int c = 1; c <= k; c++) {
        cht.init();
        cht.add({f[c - 1], -f[c - 1] * f[n] + dp[c - 1][c - 1], c - 1});
        for(int i = 1; i <= n; i++) {
            // for(int j = 1; j <= i; j++) {
            //     if(maxi(dp[c][i], f[i] * f[n] - f[i] * f[i] + f[j - 1] * f[i] - f[j - 1] * f[n] + dp[c - 1][j - 1])) trace[c][i] = j - 1;
            // }
            if(i < c) continue;
            auto tmp = cht.query(f[i]);
            dp[c][i] = f[i] * f[n] - f[i] * f[i] + tmp.fi;
            trace[c][i] = tmp.se;    
            cht.add({f[i], -f[i] * f[n] + dp[c - 1][i], i});
        }
    }  
    
    ll ans = -oo;
    int pos;
    vector<int> res;
    for(int i = 1; i <= n; i++) {
        if(maxi(ans, dp[k][i])) pos = i;
    }  
    res.pb(pos);
    pos = trace[k][pos];
    for(int i = k - 1; i >= 1; i--) {
        res.pb(pos);
        pos = trace[i][pos];
    }
    reverse(all(res));
    cout<<ans<<"\n";
    for(auto i:res) cout<<i<<" ";
    return 0;
}

Compilation message (stderr)

sequence.cpp: In member function 'std::pair<long long int, int> cht::query(long long int)':
sequence.cpp:54:21: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   54 |             mid = l + r >> 1;
      |                   ~~^~~
sequence.cpp: In member function 'void cht::add(line)':
sequence.cpp:71:21: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   71 |             mid = l + r >> 1;
      |                   ~~^~~

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