oj.uz

Submission #320503

# Submission time Handle Problem Language Result Execution time Memory
320503 2020-11-08T21:39:17 Z jc713 Split the sequence (APIO14_sequence) C++17
100 / 100
 1014 ms 82404 KB 
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <bits/stdc++.h>

using namespace std;
using namespace __gnu_pbds;
template <class T> using Tree = tree<T, null_type, less<T>,
    rb_tree_tag, tree_order_statistics_node_update>;
 
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using db = double; 
using str = string; // yay python!

using pi = pair<int,int>;
using pl = pair<ll,ll>;
using pd = pair<db,db>;

using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>; 
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>; 
using vpd = vector<pd>;

#define tcT template<class T
// ^ lol this makes everything look weird but I'll try it
tcT> using V = vector<T>; 
tcT, size_t SZ> using AR = array<T,SZ>; 

// pairs
#define mp make_pair
#define f first
#define s second

// vectors
#define sz(x) (int)(x).size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend() 
#define sor(x) sort(all(x)) 
#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 

// loops
#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; // not too close to LLONG_MAX
const int IINF = 1e9;
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 

// helper funcs
constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
constexpr int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x)) 
ll cdiv(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
ll fdiv(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down

tcT> bool ckmin(T& a, const T& b) {
    return b < a ? a = b, 1 : 0; } // set a = min(a,b)
tcT> bool ckmax(T& a, const T& b) {
    return a < b ? a = b, 1 : 0; }

#define tcTU tcT, class U
tcTU> T fstTrue(T lo, T hi, U f) {
    hi ++; assert(lo <= hi); // assuming f is increasing
    while (lo < hi) { // find first index such that f is true 
        T mid = lo+(hi-lo)/2;
        f(mid) ? hi = mid : lo = mid+1; 
    } 
    return lo;
}
tcTU> T lstTrue(T lo, T hi, U f) {
    lo --; assert(lo <= hi); // assuming f is decreasing
    while (lo < hi) { // find first index such that f is true 
        T mid = lo+(hi-lo+1)/2;
        f(mid) ? lo = mid : hi = mid-1;
    } 
    return lo;
}
tcT> void remDup(vector<T>& v) { // sort and remove duplicates
    sort(all(v)); v.erase(unique(all(v)),end(v)); }
tcTU> void erase(T& t, const U& u) { // don't erase
    auto it = t.find(u); assert(it != end(t));
    t.erase(u); } // element that doesn't exist from (multi)set

// INPUT
#define tcTUU tcT, class ...U
tcT> void re(complex<T>& c);
tcTU> void re(pair<T,U>& p);
tcT> void re(vector<T>& v);
tcT, size_t SZ> void re(AR<T,SZ>& a);

tcT> 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); }
tcTUU> void re(T& t, U&... u) { re(t); re(u...); }

tcT> void re(complex<T>& c) { T a,b; re(a,b); c = {a,b}; }
tcTU> void re(pair<T,U>& p) { re(p.f,p.s); }
tcT> void re(vector<T>& x) { trav(a,x) re(a); }
tcT, size_t SZ> void re(AR<T,SZ>& x) { trav(a,x) re(a); }

// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) { 
    #ifdef LOCAL
        return b ? "true" : "false"; 
    #else 
        return ts((int)b);
    #endif
}
tcT> str ts(complex<T> c) { 
    stringstream ss; ss << c; return ss.str(); }
str ts(vector<bool> v) {
    str res = "{"; F0R(i,sz(v)) res += char('0'+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; }
tcTU> str ts(pair<T,U> p);
tcT> str ts(T v) { // containers with begin(), end()
    #ifdef LOCAL
        bool fst = 1; str res = "{";
        for (const auto& x: v) {
            if (!fst) res += ", ";
            fst = 0; res += ts(x);
        }
        res += "}"; return res;
    #else
        bool fst = 1; str res = "";
        for (const auto& x: v) {
            if (!fst) res += " ";
            fst = 0; res += ts(x);
        }
        return res;

    #endif
}
tcTU> str ts(pair<T,U> p) {
    #ifdef LOCAL
        return "("+ts(p.f)+", "+ts(p.s)+")"; 
    #else
        return ts(p.f)+" "+ts(p.s);
    #endif
}

// OUTPUT
tcT> void pr(T x) { cout << ts(x); }
tcTUU> void pr(const T& t, const U&... u) { 
    pr(t); pr(u...); }
void ps() { pr("\n"); } // print w/ spaces
tcTUU> void ps(const T& t, const U&... u) { 
    pr(t); if (sizeof...(u)) pr(" "); ps(u...); }

// DEBUG
void DBG() { cerr << "]" << endl; }
tcTUU> void DBG(const T& t, const U&... u) {
    cerr << ts(t); if (sizeof...(u)) cerr << ", ";
    DBG(u...); }
#ifdef LOCAL // compile with -DLOCAL, chk -> fake assert
    #define dbg(...) cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
    #define chk(...) if (!(__VA_ARGS__)) cerr << "Line(" << __LINE__ << ") -> function(" \
         << __FUNCTION__  << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n", exit(0);
#else
    #define dbg(...) 0
    #define chk(...) 0
#endif

// FILE I/O
void setIn(str s) { freopen(s.c_str(),"r",stdin); }
void setOut(str s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
void setIO(str 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
}

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        // http://xorshift.di.unimi.it/splitmix64.c
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

ull dp[2][100005];
int previ[205][100005];
ull seq[100005];
ull pref[100005];
int n, K;


ull pre(int a, int b){
	a++, b++;
	return pref[b] - pref[a - 1];
}

void rec(int l, int r, int k, int L, int R){
	if(l > r)
		return;
	int m = (l + r) / 2;
	FOR(a, L, min(R + 1, m)){
		if(dp[(k - 1 + 2) % 2][a] + pre(a, m - 1) * pre(m, n - 1) >= dp[k % 2][m]){
			dp[k % 2][m] = dp[(k - 1 + 2) % 2][a] + pre(a, m - 1) * pre(m, n - 1);
			previ[k][m] = a;
		}
	}
	if(l != r){
		rec(l, m - 1, k, L, previ[k][m]);
		rec(m + 1, r, k, previ[k][m], R);
	}
}

int main(){
    setIO();
	cin >> n >> K;
	F0R(a, n)
		cin >> seq[a];
	FOR(a, 1, n + 1)
		pref[a] = pref[a - 1] + seq[a - 1];
	FOR(a, 1, K + 1){
		memset(dp[a % 2], 0, sizeof dp[a % 2]);
		rec(0, n - 1, a, 0, n - 1);
	}
	ull ans = 0;
	int idx = -1;
	F0R(a, n){
		if(dp[K % 2][a] >= ans){
			ans = dp[K % 2][a];
			idx = a;
		}
	}
	cout << ans << endl;
	vi ANS;
	ROF(a, 1, K + 1){
		ANS.pb(idx);
		idx = previ[a][idx];
	}
	R0F(a, sz(ANS))
		cout << ANS[a] << " ";
	cout << endl;
    // 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
    * DON'T GET STUCK ON ONE APPROACH
*/

Compilation message

sequence.cpp: In function 'void setIn(str)':
sequence.cpp:190:28: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
  190 | void setIn(str s) { freopen(s.c_str(),"r",stdin); }
      |                     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
sequence.cpp: In function 'void setOut(str)':
sequence.cpp:191:29: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
  191 | void setOut(str s) { freopen(s.c_str(),"w",stdout); }
      |                      ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1900 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 1900 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 1132 KB contestant found the optimal answer: 0 == 0
4 Correct 2 ms 1900 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 2 ms 2028 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 1132 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 1132 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 1132 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 1900 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 1900 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 1900 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 1900 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 2 ms 1900 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 1900 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 2 ms 1900 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 1900 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 1900 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1900 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 1900 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 3 ms 2156 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 1900 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 2 ms 2028 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 2 ms 1900 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 2028 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 2 ms 2028 KB contestant found the optimal answer: 687136 == 687136
9 Correct 2 ms 1900 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 2 ms 2028 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1900 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 1900 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 9 ms 3052 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 1900 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 6 ms 2668 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 8 ms 2924 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 8 ms 3052 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 3 ms 2156 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 3 ms 2028 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 3 ms 2284 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2028 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 2 ms 2028 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 13 ms 3692 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 2 ms 2028 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 14 ms 3692 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 13 ms 3436 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 15 ms 3692 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 13 ms 3692 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 5 ms 2284 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 8 ms 2584 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 2284 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 3 ms 2284 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 74 ms 10852 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 2284 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 60 ms 7396 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 57 ms 8292 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 73 ms 8676 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 59 ms 7524 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 58 ms 8292 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 72 ms 9956 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 22 ms 4844 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 21 ms 4836 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 729 ms 82404 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 21 ms 5228 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1014 ms 82084 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 593 ms 58516 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 810 ms 62948 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 522 ms 51556 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 559 ms 58724 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 712 ms 74468 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845