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Submission #39272

# Submission time Handle Problem Language Result Execution time Memory
39272 2018-01-10T13:10:14 Z qoo2p5 Split the sequence (APIO14_sequence) C++14
100 / 100
 1063 ms 86656 KB 
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;

const int INF = (int) 1e9 + 1e6 + 123;
const ll LINF = (ll) 1e18 + 1e9 + 123;
const ld EPS = (ld) 1e-7;
const ll MOD = (ll) 1e9 + 7;

#define sz(x) (int) (x).size()
#define mp(x, y) make_pair(x, y)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define lb(s, t, x) (int) (lower_bound(s, t, x) - s)
#define ub(s, t, x) (int) (upper_bound(s, t, x) - s)
#define rep(i, f, t) for (int i = f; i < t; i++)
#define per(i, f, t) for (int i = f; i >= t; i--)

ll power(ll x, ll y, ll mod = MOD) {
    if (y == 0) {
        return 1;
    }
    if (y & 1) {
        return power(x, y - 1, mod) * x % mod;
    } else {
        ll tmp = power(x, y / 2, mod);
        return tmp * tmp % mod;
    }
}

template<typename A, typename B> bool mini(A &x, const B &y) {
    if (y < x) {
        x = y;
        return true;
    }
    return false;
}

template<typename A, typename B> bool maxi(A &x, const B &y) {
    if (y > x) {
        x = y;
        return true;
    }
    return false;
}

void add(ll &x, ll y) {
	x += y;
	if (x >= MOD) x -= MOD;
	if (x < 0) x += MOD;
}

ll mult(ll x, ll y) {
	return x * y % MOD;
}

void run();

#define TASK ""

int main() {
#ifdef LOCAL
    if (strlen(TASK) > 0) {
        cerr << "Reminder: you are using file i/o, filename: " TASK "!" << endl << endl;
    }
#endif
#ifndef LOCAL
    if (strlen(TASK)) {
        freopen(TASK ".in", "r", stdin);
        freopen(TASK ".out", "w", stdout);
    }
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
#endif
    cout << fixed << setprecision(12);
    run();
    return 0;
}

// == SOLUTION == //

const int N = (int) 1e5 + 123;
const int K = 202;

int n, k;
ll a[N];
ll cur[N], nxt[N];
int from[K][N];

struct Line {
	ll k, b;
	int id;
	
	ll value(ll x) const {
		return k * x + b;
	}
};

ll div_up(ll x, ll y) {
	if (y < 0) {
		x = -x;
		y = -y;
	}
	if (x >= 0) {
		return (x + y - 1) / y;
	} else {
		return x / y;
	}
}

ll inter(const Line &a, const Line &b) {
	return div_up(a.b - b.b, b.k - a.k);
}

struct Convex {
	vector<Line> lines;
	vector<ll> points;
	int ptr;
	
	Convex() {
		lines.reserve(N);
		points.reserve(N);
	}
	
	void add(const Line &line) {
		while (sz(lines) && lines.back().k == line.k) {
			if (lines.back().b >= line.b) {
				return;
			}
			lines.pop_back();
			if (sz(points)) {
				points.pop_back();
			}
		}
		while (sz(points) && inter(line, lines.back()) <= points.back()) {
			lines.pop_back();
			points.pop_back();
		}
		if (sz(lines)) {
			points.pb(inter(line, lines.back()));
		}
		lines.push_back(line);
		mini(ptr, sz(points));
	}
	
	pair<ll, int> get(ll x) {
		while (ptr < sz(points) && points[ptr] <= x) {
			ptr++;
		}
		return {lines[ptr].value(x), lines[ptr].id};
	}
	
	void clear() {
		ptr = 0;
		lines.clear();
		points.clear();
	}
};

Convex cht;

void run() {
	cin >> n >> k;
	rep(i, 1, n + 1) {
		cin >> a[i];
	}
	
	fill(nxt, nxt + N, -LINF);
	cur[0] = -LINF;
	
	rep(t, 1, k + 1) {
		cht.clear();
		ll sum = 0;
		rep(i, 1, n + 1) {
			cht.add({sum, cur[i - 1] - sum * sum, i});
			sum += a[i];
			auto res = cht.get(sum);
			nxt[i] = res.first;
			from[t][i] = res.second;
		}
		memcpy(cur, nxt, sizeof cur);
	}
	
	cout << cur[n] << "\n";
	vector<int> what(k);
	per(i, k, 1) {
		what[i - 1] = from[i][n] - 1;
		n = from[i][n] - 1;
	}
	for (int pos : what) {
		cout << pos << " ";
	}
	cout << "\n";
}

Compilation message

sequence.cpp: In function 'int main()':
sequence.cpp:72:40: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
         freopen(TASK ".in", "r", stdin);
                                        ^
sequence.cpp:73:42: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
         freopen(TASK ".out", "w", stdout);
                                          ^

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 86656 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 86656 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 86656 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 86656 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 86656 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 86656 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 86656 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 86656 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 86656 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 86656 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 86656 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 86656 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 86656 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 86656 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 86656 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 86656 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 86656 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 86656 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 86656 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 3 ms 86656 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 86656 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 86656 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 86656 KB contestant found the optimal answer: 933702 == 933702
7 Correct 3 ms 86656 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 3 ms 86656 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 86656 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 3 ms 86656 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 86656 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 86656 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 23 ms 86656 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 86656 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 13 ms 86656 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 16 ms 86656 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 16 ms 86656 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 3 ms 86656 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 0 ms 86656 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 6 ms 86656 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 86656 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 0 ms 86656 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 23 ms 86656 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 0 ms 86656 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 26 ms 86656 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 26 ms 86656 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 33 ms 86656 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 29 ms 86656 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 6 ms 86656 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 6 ms 86656 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 86656 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 3 ms 86656 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 99 ms 86656 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 86656 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 63 ms 86656 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 86 ms 86656 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 93 ms 86656 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 69 ms 86656 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 79 ms 86656 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 96 ms 86656 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 19 ms 86656 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 16 ms 86656 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 963 ms 86656 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 26 ms 86656 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1063 ms 86656 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 756 ms 86656 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 896 ms 86656 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 733 ms 86656 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 666 ms 86656 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 896 ms 86656 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845