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Submission #369941

# Submission time Handle Problem Language Result Execution time Memory
369941 2021-02-22T19:21:37 Z EIMONIM Split the sequence (APIO14_sequence) C++14
100 / 100
 747 ms 94512 KB 
#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;
typedef __int128_t ll;
typedef pair<ll, ll> pll;
int n, k, a[N];
ll pre[N], dp[N], cnt[N];
struct CHT {
  struct Line {
    ll m, b, c;

    ll operator()(ll 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) {
    ll 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, ll x) {
    ll 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;
  }
  pll query(ll x) {
    while(r - l >= 2 && better_qry(dq[l], dq[l + 1], x)) ++l;
    return {dq[l](x), dq[l].c};
  }
} cht;
pll calc(ll x) {
  dp[0] = cnt[0] = 0;
  cht.init();
  for(int i = 1 ; i <= n ; ++i) {
    pll qry = cht.query(pre[i]);
    dp[i] = pre[i] * pre[i] + x + qry.F;
    cnt[i] = qry.S + 1;
    cht.insert({-2LL * pre[i], dp[i] + pre[i] * pre[i], cnt[i]});
  }
  return {cnt[n], dp[n]};
}

void init() {
  cin >> n >> k; k++;
  for(int i = 1 ; i <= n ; ++i) cin >> a[i], pre[i] = pre[i - 1] + a[i];
}
ll solve() {
  ll l = 0, r = pre[n] * pre[n], ans = -1;
  while(l <= r) {
    ll mid = l + (r - l) / 2;
    pll res = calc(mid);
    if(res.F > k) l = mid + 1;
    else r = mid - 1, ans = res.S - k * mid;
  }
  return ans;
}
int32_t main(){
    init();
    cout << int(pre[n]*pre[n] - solve())/2 << endl;
    Orig::n = n, Orig::k = k-1;
    loop(i,0,n) Orig::a[i+1] = a[i+1];
    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

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
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 364 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 364 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 364 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 364 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 384 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 364 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 364 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 364 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 364 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 384 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 364 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 364 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 492 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 364 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 364 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 364 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 384 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 748 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 364 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 492 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 492 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 492 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 492 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 492 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 492 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 492 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 2 ms 1388 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 492 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 2 ms 1132 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 2 ms 1388 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 2 ms 1388 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 748 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 768 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 748 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 492 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 2 ms 620 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 7 ms 2156 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 2 ms 620 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 7 ms 2156 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 7 ms 1900 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 8 ms 2156 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 6 ms 2156 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 876 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 4 ms 1260 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 14 ms 1772 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 14 ms 2028 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 65 ms 10600 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 20 ms 2028 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 50 ms 7148 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 53 ms 8132 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 66 ms 8552 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 47 ms 7400 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 54 ms 8040 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 63 ms 9756 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 166 ms 14556 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 168 ms 14940 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 651 ms 94512 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 215 ms 15708 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 747 ms 92892 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 558 ms 69212 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 682 ms 74588 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 503 ms 63580 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 537 ms 70236 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 642 ms 85852 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845