Submission #213493

#	Time	Username	Problem	Language	Result	Execution time	Memory
213493		rqi	Split the sequence (APIO14_sequence)	C++14	100 / 100	973 ms	92536 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
 
typedef long long ll;
typedef long double ld;
typedef double db; 
typedef string str; 

typedef pair<int,int> pi;
typedef pair<ll,ll> pl; 
typedef pair<db,db> pd; 

typedef vector<int> vi; 
typedef vector<ll> vl; 
typedef vector<db> vd; 
typedef vector<str> vs; 
typedef vector<pi> vpi;
typedef vector<pl> vpl; 
typedef vector<pd> vpd; 

#define mp make_pair 
#define f first
#define s second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend() 
#define rsz resize
#define ins insert 
#define ft front() 
#define bk back()
#define pf push_front 
#define pb push_back
#define eb emplace_back 
#define lb lower_bound 
#define ub upper_bound 

#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)

const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5; 
const ll INF = 1e18; 
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1}; 

template<class T> bool ckmin(T& a, const T& b) { 
  return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { 
  return a < b ? a = b, 1 : 0; } 
int pct(int x) { return __builtin_popcount(x); } 
int bit(int x) { return 31-__builtin_clz(x); } // floor(log2(x)) 
int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0 

// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);

template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }

template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }

// TO_STRING
#define ts to_string
template<class A, class B> str ts(pair<A,B> p);
template<class A> str ts(complex<A> c) { return ts(mp(c.real(),c.imag())); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(char c) { str s = ""; s += c; return s; }
str ts(str s) { return s; }
str ts(const char* s) { return (str)s; }
str ts(vector<bool> v) { 
  bool fst = 1; str res = "{";
  F0R(i,sz(v)) {
    if (!fst) res += ", ";
    fst = 0; res += ts(v[i]);
  }
  res += "}"; return res;
}
template<size_t SZ> str ts(bitset<SZ> b) {
  str res = ""; F0R(i,SZ) res += char('0'+b[i]);
  return res; }
template<class T> str ts(T v) {
  bool fst = 1; str res = "{";
  for (const auto& x: v) {
    if (!fst) res += ", ";
    fst = 0; res += ts(x);
  }
  res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
  return "("+ts(p.f)+", "+ts(p.s)+")"; }

// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) { 
  pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) { 
  pr(h); if (sizeof...(t)) pr(" "); ps(t...); }

// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
  cerr << to_string(h); if (sizeof...(t)) cerr << ", ";
  DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "[" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 42
#endif

// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string s = "") {
  unsyncIO();
  // cin.exceptions(cin.failbit); 
  // throws exception when do smth illegal
  // ex. try to read letter into int
  if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}

mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 


/**
 * Description: LineContainer assuming both slopes and queries monotonic.
 * Time: O(1)
 * Source: Own
 * Verification: http://acm.hdu.edu.cn/diy/contest_showproblem.php?cid=36005&pid=1009
 */

/**
 * Description: LineContainer; add lines of the form $kx+m$, 
   * compute greatest $y$-coordinate for any $x$.
 * Time: O(\log N)
 * Source: KACTL
   * https://github.com/kth-competitive-programming/kactl/commit/165807e28402c9be906f6e6a09452431787bb70d?diff=unified
 * Verification: 
   * CSA Squared Ends not working :(
   * https://codeforces.com/contest/1083/problem/E
   * https://atcoder.jp/contests/arc066/tasks/arc066_d
 */

bool Q;
struct Line {
  mutable ll k, m, p; // slope, y-intercept, last optimal x
  ll eval (ll x) { return k*x+m; }
  bool operator<(const Line& o) const { return Q?p<o.p:k<o.k; }
};

// for doubles, use inf = 1/.0, divi(a,b) = a/b
const ll inf = LLONG_MAX;
// floored div
ll divi(ll a, ll b) { return a/b-((a^b) < 0 && a%b); } 
// last x such that first line is better
ll bet(const Line& x, const Line& y) { 
  if (x.k == y.k) return x.m >= y.m ? inf : -inf;
  return divi(y.m-x.m,x.k-y.k); }

struct LC : multiset<Line> { 
  // updates x->p, determines if y is unneeded
  bool isect(iterator x, iterator y) { 
    if (y == end()) { x->p = inf; return 0; }
    x->p = bet(*x,*y); return x->p >= y->p; }
  void add(ll k, ll m) {
    auto z = insert({k,m,0}), y = z++, x = y;
    while (isect(y, z)) z = erase(z);
    if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
    while ((y = x) != begin() && (--x)->p >= y->p) 
      isect(x, erase(y));
  }
  ll query(ll x) {
    assert(!empty());
    Q = 1; auto l = *lb({0,0,x}); Q = 0;
    return l.k*x+l.m;
  }
};


struct LCdeque : deque<Line> { 
  void addBack(Line L) { // assume nonempty
    while (1) {
      auto a = bk; pop_back(); a.p = bet(a,L);
      if (size() && bk.p >= a.p) continue;
      pb(a); break;
    }
    L.p = inf; pb(L);
  }
  void addFront(Line L) {
    while (1) {
      if (!size()) { L.p = inf; break; }
      if ((L.p = bet(L,ft)) >= ft.p) pop_front();
      else break;
    }
    push_front(L);
  }
  void add(ll k, ll m) { // line goes to one end of deque
    k = -k; //neg
    m = -m; //neg
    if (!size() || k <= ft.k) addFront({k,m,0}); 
    else assert(k >= bk.k), addBack({k,m,0}); 
  }
  int ord = 0; // 1 = increasing, -1 = decreasing
  pair<ll, int> query(ll x) { 
    assert(ord);
    if(size() == 0) return mp(INF, -1);
    if (ord == 1) { 
      while (ft.p < x) pop_front();
      return mp(-ft.eval(x), -ft.k); //neg
    } else {
      while(size()>1&&prev(prev(end()))->p>=x)pop_back();
      return mp(-bk.eval(x), -ft.k); //neg
    }
  }  
};

ll a[100005];
pair<ll, int> dp[100005];
int stor[100005][205];
pair<ll, int> ndp[100005];
map<ll, int> m;
int main() {
    setIO();
    
    
    int n, k;
    cin >> n >> k;
    for(int i = 1; i <= n; i++){
        cin >> a[i];
    }
    for(int i = 1; i <= n; i++){
        a[i]+=a[i-1];
        //ps(i, a[i]);
    }

    for(int i = 1; i <= n; i++){
        m[a[i]] = i;
    }

    for(int i = 0; i <= n; i++){
        dp[i].f = ndp[i].f = INF; //overflow with line?
    }
    dp[0].f = 0;
    
    for(int i = 1; i <= k+1; i++){
        LCdeque lc;
        lc.ord = 1;

        if(dp[0].f != INF) lc.add(-2*a[0], dp[0].f+a[0]*a[0]);

        for(int j = 1; j <= n; j++){
            if(a[j] != INF){
                pair<ll, int> res = lc.query(a[j]);
                res.f+=a[j]*a[j];
                ckmin(ndp[j], res);
                if(dp[j].f != INF) lc.add(-2*a[j], dp[j].f+a[j]*a[j]);
            }
        }

        for(int j = 0; j <= n; j++){
            stor[j][i] = (ndp[j].s)/(-2);
        }
        for(int j = 0; j <= n; j++){
            dp[j] = ndp[j];

            ndp[j] = mp(INF, 0);
        }
    }
    
    
    

    ll ans = (a[n]*a[n]-dp[n].f)/2;
    ps(ans);

    
    vi sol;
    sol.pb(n);
    for(int i = k+1; i >= 2; i--){

        sol.pb((m[stor[sol.bk][i]]));
    }
    //ps(sol);
    for(int i = 0; i < sz(sol); i++){
        if(sol[i] <= sol[i+1]){
            sol[i+1] = sol[i]-1;
        }
    }
    reverse(all(sol));
    for(int i = 0; i < sz(sol)-1; i++){
        cout << sol[i] << " ";
    }
  // you should actually read the stuff at the bottom
}

/* stuff you should look for
  * int overflow, array bounds
  * special cases (n=1?)
  * do smth instead of nothing and stay organized
  * WRITE STUFF DOWN
*/

Compilation message (stderr)

sequence.cpp: In function 'void setIn(std::__cxx11::string)':
sequence.cpp:123:31: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
 void setIn(string s) { freopen(s.c_str(),"r",stdin); }
                        ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
sequence.cpp: In function 'void setOut(std::__cxx11::string)':
sequence.cpp:124:32: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
 void setOut(string s) { freopen(s.c_str(),"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