Submission #369929

#	Time	Username	Problem	Language	Result	Execution time	Memory
369929		EIMONIM	Split the sequence (APIO14_sequence)	C++14	11 / 100	75 ms	12464 KiB

sequence

#include <bits/stdc++.h>
#define pb push_back
#define all(x) x.begin(),x.end()
using namespace std;
namespace Orig{
    typedef long long ll;
    typedef pair<ll, ll> pll;
    
    const ll maxn = 1e5 + 10;
    const ll maxk = 205;
    const ll mod = 1e9 + 7;
    const ll inf = 1e9;
    
    #define fast_io ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    #define file_io freopen("input.txt", "r+", stdin);freopen("output.txt", "w+", stdout);
    #define Mp make_pair
    #define F first
    #define S second
    #define Sz(x) ll((x).size())
    
    ll n, k, a[maxn], ps[maxn], dp[2][maxn];
    int par[maxk][maxn];
    vector<pll> vec;
    vector<int> v2;
    
    void add(ll x, ll y, ll i){
        if(vec.empty()){
            vec.pb(Mp(x, y));
            v2.pb(i);
            return;
        }
        if(vec.back().F == x) return;
        while(Sz(vec) > 1){
            if((y - vec[Sz(vec) - 2].S) * (vec[Sz(vec) - 2].F - vec[Sz(vec) - 1].F) < (vec[Sz(vec) - 1].S - vec[Sz(vec) - 2].S) * (vec[Sz(vec) - 2].F - x)){
            vec.pop_back();
            v2.pop_back();
            }
            else break;
        }
        vec.pb(Mp(x, y));
        v2.pb(i);
        return;
    }
    
    void calc(){
        for(ll i = 1; i <= n; i++){
            ps[i] = ps[i - 1] + a[i];
            dp[0][i] = ps[i] * ps[i];
        }
        for(ll i = 1; i <= k; i++){
            vec.clear();
            v2.clear();
            ll p = 0;
            for(ll j = i + 1; j <= n; j++){
                add(-ps[j - 1], ps[j - 1] * ps[j - 1] + dp[i - 1 & 1][j - 1], j - 1);
                p = min(p, Sz(vec) - 1);
                while(p < Sz(vec) - 1 && 2 * ps[j] * (vec[p + 1].F - vec[p].F) <= (vec[p].S - vec[p + 1].S)) p++;
                dp[i & 1][j] = ps[j] * ps[j] + 2 * ps[j] * vec[p].F + vec[p].S;
                par[i][j] = v2[p];
            }
        }
        // cout << (ps[n] * ps[n] - dp[k & 1][n]) / 2 << "\n";
        for(ll i = 0; i < k; i++){
            n = par[k - i][n];
            cout << n << " ";
        }
    }
};

#define int int64_t
#define ii pair<int,int>
#define x first
#define y second
#define vi vector<int>
#define vvi vector<vi>
#define vii vector<ii>
#define vvii vector<vii>
#define vb vector<bool>
#define vvb vector<vb>

#define loop(i,s,e) for(int i=(s);i<(e);i++)
#define loopr(i,s,e) for(int i=(e)-1;i>=(s);i--)
#define chkmax(a,b) a = max(a,b)
#define chkmin(a,b) a=min(a,b)


const int INF = 1e18, MOD = 1e9 + 7;

/*mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
auto unidist = uniform_int_distribution<int>(0, MAXN);*/

const int N = 2e5;
struct CHT {
    struct Line {
        int m, b, c;
        int operator()(int x) { return m * x + b; }
    } dq[N * 2];
    int l, r;

    void init() {
        dq[0] = {0, 0, 0};
        l = 0, r = 1;
    }
    bool better_ins(Line& L, Line& L1, Line& L2) {
        int b1 = (L.b - L2.b) * (L2.m - L1.m), b2 = (L2.m - L.m) * (L1.b - L2.b);
        return b1 < b2 || (b1 == b2 && L.c > L1.c);
    }
    bool better_qry(Line& L1, Line& L2, int x) {
        int b1 = L1(x), b2 = L2(x);
        return b1 > b2 || (b1 == b2 && L1.c < L2.c);
    }
    void insert(Line L) {
        while(r - l >= 2 && better_ins(L, dq[r - 1], dq[r - 2])) --r;
        dq[r++] = L;
    }
    ii query(int x) {
        while(r - l >= 2 && better_qry(dq[l], dq[l + 1], x)) ++l;
        return {dq[l](x), dq[l].c};
    }
} cht;
int n, k, a[N], pre[N], dp[N], cnt[N];
void init() {
    cin >> n >> k; k++;
    loop(i,0,n) cin >> a[i], pre[i+1] = pre[i] + a[i];
}
ii calc(int x) {
    dp[0] = cnt[0] = 0;
    cht.init();
    loop(i,1,n+1){
        ii qry = cht.query(pre[i]);
        dp[i] = pre[i] * pre[i] + x + qry.x;
        cnt[i] = qry.y + 1;
        cht.insert({-2 * pre[i], dp[i] + pre[i] * pre[i], cnt[i]});
    }
    return {dp[n], cnt[n]};
}
int solve() {
    int l = 0, r = pre[n] * pre[n], ans = -1;
    while(l <= r) {
        int mid = l + (r - l) / 2;
        ii res = calc(mid);
        if(res.y >= k) ans = res.x - k * mid, l = mid + 1;
        else r = mid - 1;
    }
    return ans;
}
int32_t main(){
    init();
    cout << (pre[n]*pre[n] - solve())/2 << endl;
    Orig::n = n, Orig::k = k-1;
    loop(i,0,n) Orig::a[i+1] = a[i];
    Orig::calc();
    return 0;
}
/*
color a
cls
g++ a.cpp -o a & a
7 3
4 1 3 4 0 2 3

for /l %x in (1,1,16) do a < out\big%x.in > out\big%x.out
*/

Compilation message (stderr)

sequence.cpp: In function 'void Orig::calc()':
sequence.cpp:55:62: warning: suggest parentheses around '-' in operand of '&' [-Wparentheses]
   55 |                 add(-ps[j - 1], ps[j - 1] * ps[j - 1] + dp[i - 1 & 1][j - 1], j - 1);
      |                                                            ~~^~~

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