제출 #1226813

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1226813		shoeib	Feast (NOI19_feast)	C++20	100 / 100	116 ms	9800 KiB

feast

// Author: Muhammed Khaled Shoeib

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;
//....................................................
// struct to speed-up the unordered data structures like map/set.
struct hash_function // unordered + modified hash >> ordered
{   static uint64_t splitmix64(uint64_t x) {
        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); } };
//....................................................
template < typename T, typename Compare = less < T > > // O(logn)
using ordered_set = tree < T, null_type, Compare, rb_tree_tag, tree_order_statistics_node_update>;
// less_equal:    asc.  not_unique, st.order_of_key(k) --> no. of items < k,  less: unique
// greater_equal: desc. not_unique, st.order_of_key(k) --> no. of items > k,  greater: unique
// *st.find_by_order(k) --> st[k] (Zero-indexed)
// less_equal (u can't erase here!) == multi-set
template < class K, class V > using HT = gp_hash_table < K, V, hash_function>; // faster than unordered_map
template < typename T > using maxpq = priority_queue < T >;
template < typename T > using minpq = priority_queue < T, vector< T >, greater< T > >;
//....................................................
#define     boost                  ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
#define     precision(a)           cout << fixed << setprecision(a)
#define     alo                    cout << "alooooooooooo!" << endl
#define     YES                    cout << "YES" << endl
#define     Yes                    cout << "Yes" << endl
#define     yes                    cout << "yes" << endl
#define     NO                     cout << "NO" << endl
#define     No                     cout << "No" << endl
#define     no                     cout << "no" << endl
#define     ne                     cout << -1 << endl
#define     endl                   "\n"
#define     mem(mat, val)          memset(mat, val, sizeof(mat))
#define     ones(x)               __builtin_popcountll(x)
#define     msb(x)                63ll - __builtin_clzll(x)
#define     lsb(x)                __builtin_ffsll(x) - 1ll
//....................................................
#define     all(x)                 x.begin(), x.end()
#define     rall(x)                x.rbegin(),x.rend()
#define     _ceil(a, b)            (((ll)(a) + (ll)(b - 1)) / (ll)(b)) // up
#define     _floor(a, b)           (a / b) // down
#define     _round(a, b)           ((a + (b / 2ll)) / b) // nearest
//....................................................
// using ll  = int;                                                                     // take care of this shit!
using ll  = long long;
using i64 = long long; using i32 = int; using lli = long long int; using LL = __int128;
using ld  = long double; using LD = __float128; using ull = unsigned long long;
using cld = complex < long double >; using cd = complex < double >;
//......................................................
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#define getrand(l, r) uniform_int_distribution<long long>(l, r)(rng)
//......................................................
int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, 1, 0, -1};
int dx_diag[4] = { 1, 1, -1, -1 }, dy_diag[4] = { 1, -1, -1, 1 };
int dx_all[8] = {-1, -1, -1, 0, 1, 1, 1, 0}, dy_all[8] = {-1, 0, 1, 1, 1, 0, -1, -1};
int dx_knight[8] = {2, 2, 1, 1, -2, -2, -1, -1}, dy_knight[8] = {1, -1, 2, -2, 1, -1, 2, -2};
const ld  pi  = acos(-1); // 3.141592653589793238462643383279
const ld eps = 1e-9;
const ll inf = (ll)INT32_MAX; // 2e9
const ll oo = (ll)1e18;       // 1e15 (may cause OF in DP, Binary Search, ...)
const ll OO = (ll)INT64_MAX;  // 9e18
const ll mod  = (ll)998244353;  // 1e9 + 7, 998244353
//..................................................... // string(len, char);
/*
 * think twice, code once.
 * think of different approaches to tackle a problem, write them down.
 * think of different views of the problem, don't look from only one side.
 * don't get stuck in one approach/problem.
 * common mistakes: line 49, overflow (sum of many numbers), corner cases (n = 1), over/under count, infinite loops,
 * TLE, MLE (int instead of ll, using memset, Recursive DP, ...), RTE (out of bounds indexing), ....
 */
///____________________________________________ Shoeib __________________________________________________________




ll n, k;
vector < ll > a, pre;

pair < ll, ll > dp[300001];

void slv(ll mid)
{
    // dp[i] = max(dp[j] + (pre[i] - pre[j]) - mid), where j < i
    // dp[i] = max(dp[j] - pre[j]) + pre[i] - mid, where j < i
    // dp[i] =          best       + pre[i] - mid, where j < i

    dp[0] = {0, 0};
    pair < ll, ll > best = {dp[0].first - pre[0], dp[0].second};

    for(ll i = 1; i <= n; i++)
    {
        pair < ll, ll > &ret = dp[i];

        // skip
        ret = dp[i - 1];

        // take
        pair < ll, ll > ch = {best.first + pre[i] - mid, best.second + 1};
        if((ch.first > ret.first) || (ch.first == ret.first && ch.second < ret.second)) ret = ch;


        pair < ll, ll > best2 = {dp[i].first - pre[i], dp[i].second};
        if((best2.first > best.first) || (best2.first == best.first && best2.second < best.second)) best = best2;
    }

}

void solve()
{

    cin >> n >> k;
    a.assign(n + 1, 0); pre.assign(n + 1, 0);
    for(ll i = 1; i <= n; i++) cin >> a[i], pre[i] = pre[i - 1] + a[i];


    ll low = 0, high = oo, mid;
    while(low < high) // ... f f t t ...
    {
        mid = low + (high - low)/2;
        slv(mid);
        if(dp[n].second > k) low = mid + 1;
        else high = mid;
    }

    slv(low);
    cout << dp[n].first + low*k << endl;



    return;
}



signed main()
{
    boost;

    // freopen("tallbarn.in", "r", stdin);
    // freopen("tallbarn.out", "w", stdout);

    precision(15);

    i32 _ = 1; //cin >> _;
    // cout.flush();
    while(_--) solve();
    return 0;
}

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