oj.uz

Submission #428144

# Submission time Handle Problem Language Result Execution time Memory
428144 2021-06-15T08:22:33 Z Kevin_Zhang_TW Long Distance Coach (JOI17_coach) C++17
100 / 100
 291 ms 59820 KB 
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define pb emplace_back
#define AI(i) begin(i), end(i)
template<class T> bool chmin(T &a, T b) { return b < a && (a = b, true); }
template<class T> bool chmax(T &a, T b) { return a < b && (a = b, true); }
#ifdef KEV
#define DE(args...) kout("[ " + string(#args) + " ] = ", args)
void kout() { cerr << endl; }
template<class T, class ...U> void kout(T a, U ...b) { cerr << a << ' ', kout(b...); }
template<class T> void debug(T l, T r) { while (l != r) cerr << *l << " \n"[next(l)==r], ++l; }
#else
#define DE(...) 0
#define debug(...) 0
#endif
// My bug list :
// integer overflow
// 0based, 1based forgotten
// index out of bound
// n, m, i, j typo
// some cases are missing

const int MAX_N = 200010, MAX_K = 18;
const ll inf = 2e18;

ll X, n, m, W, T;
ll s[MAX_N];

ll dp[MAX_N], sp[MAX_N], pfc[MAX_N];

pair<ll,ll> man[MAX_N];

int nxt[MAX_K][MAX_N];
ll jsum[MAX_K][MAX_N];

void init_cost() {
	{
		ll sum = 0;
		for (int i = 0;i < m;++i) {
			pfc[i] = sum += man[i].second;
		}
	}
	debug(sp, sp+m);
	vector<int> stk {0};
	sp[0] = 0;
	for (int i = 0;i < m;++i) {
		while (stk.size()) {
			int id = stk.back();
			if (sp[i] >= sp[id]) break;
			stk.pop_back();
		}
		nxt[0][i] = stk.back();
		jsum[0][i] = W * (i-stk.back()) * sp[i];
		stk.pb(i);
	}
	for (int d = 1;d < MAX_K;++d) {
		for (int i = 0;i < m;++i) {
			nxt[d][i] = nxt[d-1][ nxt[d-1][i] ];
			jsum[d][i] = jsum[d-1][i] + jsum[d-1][ nxt[d-1][i] ];
		}
	}
}
ll pay(int l, int r) {
	if (l > r) return 0;
	ll ret = pfc[r] - (l?pfc[l-1]:0);
	for (int d = MAX_K-1;d >= 0;--d) {
		if (nxt[d][r] < l) continue;
		ret += jsum[d][r];
		r = nxt[d][r];
	}
//	assert(r >= l);
//	assert(nxt[0][r] < l);
	ret += sp[r] * (r-l+1) * W;

	return ret;
}
ll cost(int l, int r) {
	return dp[l] + pay(l+1, r-1);
}

// N refill points, and M people
// remember the driver need water too

ll F(pair<ll,ll> a, ll x) { return a.first * x + a.second; }

// floor ( y / x )
ll fdiv(ll a, ll b) {
	assert( b >= 0 );
	if (b == 0) return 0;
	return a / b - (a < 0 && a % b);
}

ll inter(pair<ll,ll> a, pair<ll,ll> b) {
	if (a < b) swap(a, b);
	auto [m1, v1] = a;
	auto [m2, v2] = b;
	assert(m1 >= m2);
	return fdiv(v2 - v1, m1 - m2);
}
pair<ll,ll> get_line(int ind) { 
	return make_pair(-ind, dp[ind] - pfc[ind]);
}
ll inter(ll a, ll b) { return inter(get_line(a), get_line(b)); }
ll F(ll a, ll x) { return F(get_line(a), x); }

// slope in deque is decreasing
//
//struct minconv {
//	deque< pair<ll,ll> > dq;
//	// put a line, and the line has the maximum slope
//	void pb(pair<ll,ll> line) {
//		//if (false)
//		while (dq.size() > 1) {
//			auto a = dq[0], b = dq[1];
//			if (inter(line, a) < inter(a, b)) break;
//			dq.pop_front();
//		}
//		dq.push_front(line);
//	}
//	// put a line, and the line has the minimum slope
//	void pf(pair<ll,ll> line) {
//		//if (false)
//		while (dq.size() > 1) {
//			auto a = end(dq)[-2], b = end(dq)[-1];
//			if (inter(a, b) < inter(b, line)) break;
//			dq.pop_back();
//		}
//		dq.push_back(line);
//	}
//	pair<ll,ll> pop_back() { auto ret = dq.back(); dq.pop_back(); return ret; }
//	pair<ll,ll> pop_front() { auto ret = dq.front(); dq.pop_front(); return ret; }
//	int qq(int i) {
//		ll v = inf, ret = 0;
//		for (int j = 0;j < dq.size();++j)
//			if (chmin(v, cost(dq[j].first, i)))
//				ret = dq[j].first;
//		return ret;
//	}
//	int qrypoint(ll x) {
//		if (dq.empty()) return 0;
//
//		int l = 0, r = (int) dq.size() - 1, mid;
//		while (l < r) {
//			mid = l + r >> 1;
//			if (F(dq[mid], x) <= F(dq[mid+1], x))
//				r = mid;
//			else
//				l = mid+1;
//		}
//		return dq[l].first;
//	}
//	void clear() {
//		deque<pair<ll,ll>>().swap(dq);
//	}
//};

//
struct minconv_old {
	deque< ll > dq;
	int size() { return dq.size(); }
	// put a line, and the line has the miminum slope
	void pb(ll line) {
		while (dq.size() > 1) {
			auto a = end(dq)[-2], b = end(dq)[-1];
			if (inter(a, b) < inter(b, line)) break;
			dq.pop_back();
		}
		dq.push_back(line);
	}
	// put a line, and the line has the maximum slope
	void pf(ll line) {
		while (dq.size() > 1) {
			auto a = dq[0], b = dq[1];
			if (inter(line, a) < inter(a, b)) break;
			dq.pop_front();
		}
		dq.push_front(line);
	}
	ll pop_back() { auto ret = dq.back(); dq.pop_back(); return ret; }
	ll pop_front() { auto ret = dq.front(); dq.pop_front(); return ret; }
	int qrypoint(ll x) {
		if (dq.empty()) return 0;
		int l = 0, r = (int) dq.size() - 1, mid;
		while (l < r) {
			mid = l + r >> 1;
			if (F(dq[mid], x) <= F(dq[mid+1], x))
				r = mid;
			else
				l = mid+1;
		}
		return dq[l];
		//return dq[l].first;
	}
	void clear() {
		deque<ll>().swap(dq);
	}
};

// put to b

int all_line[MAX_N];

struct minconv {
	int h, e;
	minconv(int i) {
		h = all_line[i] = i;
		e = h + 1;
	}
	minconv() { h = e = 0; }
	int size() { return e - h; }
	// make sure that line has the minimum slope
	void pf(int line) {
		while (e-h > 1) {
			auto a = all_line[h], b = all_line[h+1];
			if (inter(line, a) < inter(a, b)) break;
			++h;
		}
		all_line[--h] = line;
	}
	void pb(int line) {
		while (e-h > 1) {
			auto a = all_line[e-2], b = all_line[e-1];
			if (inter(a, b) < inter(b, line)) break;
			--e;
		}
		all_line[e++] = line;
	}
	int pop_front() { return all_line[h++]; }
	int pop_back() { return all_line[--e]; }
	int qrypoint(ll x) {
		assert(h < e);
		int l = h, r = e - 1, mid;
		while (l < r) {
			mid = l + r >> 1;
			if (F(all_line[mid], x) <= F(all_line[mid+1], x))
				r = mid;
			else
				l = mid+1;
		}
		return all_line[l];
	}

};
void merge_conv(minconv &a, minconv &b) {
	if (a.size() < b.size()) 
		while (a.size()) b.pf(a.pop_back());
	else {
		while (b.size()) a.pb(b.pop_front());
		swap(a, b);
	}
}

vector<int> stk;
vector<minconv> conv;
vector<int> bst;

void solve() {
	fill(dp, dp + m, inf);
	fill(sp, sp + m, X / T + 10);
	sort(s, s + n);
	sort(man, man + m);

	for (int i = 0;i < n;++i) {
		ll spt = s[i] / T;
		int p = lower_bound(man, man + m, make_pair(s[i] % T, 0ll)) - man;
		chmin(sp[p-1], spt);
	}

	init_cost();

	dp[0] = (X / T + (X % T > man[0].first)) * W;

	stk.pb(0);
	conv.pb();// conv[0].pb(get_line(0));
	conv[0].pb(0);

	bst.pb(0);

	sp[0] = 0;


	for (int i = 1;i < m;++i) {
		auto [d, c] = man[i];
		ll sum = (X / T + (X % T > d)) * W ;

		int id = conv.back().qrypoint( sp[i-1] * W );
		//int id = conv.back().qq(i);

		if (bst.size() > 1) 
			chmin(dp[i], sum + cost(end(bst)[-2], i));

		chmin(dp[i], sum + cost(id, i));

		if (cost(id, i) <= cost(bst.back(), i))
			bst.back() = id;

		minconv cur(i);

		while (stk.size()) {
			int r = stk.back();
			if (sp[r] < sp[i]) break;
			merge_conv(conv.back(), cur);
			bst.pop_back();
			conv.pop_back();
			stk.pop_back();
		}

		bst.pb(bst.empty() ? 0 : bst.back());
		stk.pb(i);
		conv.pb();
		swap(cur, conv.back());

	}
}

int32_t main() {
	ios_base::sync_with_stdio(0), cin.tie(0);

	cin >> X >> n >> m >> W >> T;

	DE(X, n, m, W, T);
	for (int i = 0;i < n;++i)
		cin >> s[i];
	s[n++] = X;

	for (int i = 0;i < m;++i) {
		auto &[d, c] = man[i];
		cin >> d >> c;
	}
	man[m++] = make_pair(0, inf);
	
	solve();

	ll res = inf;

	ll req = (X / T + 10), sum = 0;
	for (int i = m-1;i >= 0;--i) {
		chmin(res, dp[i] + sum);
		chmin(req, sp[i]);
		sum += req * W + man[i].second;
	}

	cout << res << '\n';
}

Compilation message

coach.cpp: In function 'void init_cost()':
coach.cpp:15:20: warning: statement has no effect [-Wunused-value]
   15 | #define debug(...) 0
      |                    ^
coach.cpp:44:2: note: in expansion of macro 'debug'
   44 |  debug(sp, sp+m);
      |  ^~~~~
coach.cpp: In member function 'int minconv_old::qrypoint(ll)':
coach.cpp:186:12: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  186 |    mid = l + r >> 1;
      |          ~~^~~
coach.cpp: In member function 'int minconv::qrypoint(ll)':
coach.cpp:235:12: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  235 |    mid = l + r >> 1;
      |          ~~^~~
coach.cpp: In function 'int32_t main()':
coach.cpp:14:17: warning: statement has no effect [-Wunused-value]
   14 | #define DE(...) 0
      |                 ^
coach.cpp:322:2: note: in expansion of macro 'DE'
  322 |  DE(X, n, m, W, T);
      |  ^~

Subtask #1
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 460 KB Output is correct
2 Correct 1 ms 588 KB Output is correct
3 Correct 1 ms 460 KB Output is correct
4 Correct 1 ms 588 KB Output is correct
5 Correct 1 ms 588 KB Output is correct
6 Correct 1 ms 460 KB Output is correct
7 Correct 1 ms 588 KB Output is correct
8 Correct 1 ms 460 KB Output is correct
9 Correct 1 ms 460 KB Output is correct
10 Correct 1 ms 460 KB Output is correct
11 Correct 1 ms 460 KB Output is correct
12 Correct 1 ms 460 KB Output is correct
13 Correct 1 ms 588 KB Output is correct
14 Correct 1 ms 460 KB Output is correct
15 Correct 1 ms 588 KB Output is correct
16 Correct 1 ms 580 KB Output is correct
17 Correct 1 ms 460 KB Output is correct
18 Correct 1 ms 588 KB Output is correct
19 Correct 1 ms 460 KB Output is correct
20 Correct 1 ms 460 KB Output is correct
21 Correct 1 ms 460 KB Output is correct
22 Correct 1 ms 460 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 460 KB Output is correct
2 Correct 1 ms 588 KB Output is correct
3 Correct 1 ms 460 KB Output is correct
4 Correct 1 ms 588 KB Output is correct
5 Correct 1 ms 588 KB Output is correct
6 Correct 1 ms 460 KB Output is correct
7 Correct 1 ms 588 KB Output is correct
8 Correct 1 ms 460 KB Output is correct
9 Correct 1 ms 460 KB Output is correct
10 Correct 1 ms 460 KB Output is correct
11 Correct 1 ms 460 KB Output is correct
12 Correct 1 ms 460 KB Output is correct
13 Correct 1 ms 588 KB Output is correct
14 Correct 1 ms 460 KB Output is correct
15 Correct 1 ms 588 KB Output is correct
16 Correct 1 ms 580 KB Output is correct
17 Correct 1 ms 460 KB Output is correct
18 Correct 1 ms 588 KB Output is correct
19 Correct 1 ms 460 KB Output is correct
20 Correct 1 ms 460 KB Output is correct
21 Correct 1 ms 460 KB Output is correct
22 Correct 1 ms 460 KB Output is correct
23 Correct 1 ms 588 KB Output is correct
24 Correct 1 ms 576 KB Output is correct
25 Correct 1 ms 588 KB Output is correct
26 Correct 1 ms 588 KB Output is correct
27 Correct 1 ms 572 KB Output is correct
28 Correct 1 ms 588 KB Output is correct
29 Correct 1 ms 580 KB Output is correct
30 Correct 1 ms 588 KB Output is correct
31 Correct 1 ms 588 KB Output is correct
32 Correct 1 ms 588 KB Output is correct
33 Correct 1 ms 588 KB Output is correct
34 Correct 1 ms 580 KB Output is correct
35 Correct 1 ms 588 KB Output is correct
36 Correct 1 ms 588 KB Output is correct
37 Correct 1 ms 576 KB Output is correct

Subtask #3
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 460 KB Output is correct
2 Correct 1 ms 588 KB Output is correct
3 Correct 1 ms 460 KB Output is correct
4 Correct 1 ms 588 KB Output is correct
5 Correct 1 ms 588 KB Output is correct
6 Correct 1 ms 460 KB Output is correct
7 Correct 1 ms 588 KB Output is correct
8 Correct 1 ms 460 KB Output is correct
9 Correct 1 ms 460 KB Output is correct
10 Correct 1 ms 460 KB Output is correct
11 Correct 1 ms 460 KB Output is correct
12 Correct 1 ms 460 KB Output is correct
13 Correct 1 ms 588 KB Output is correct
14 Correct 1 ms 460 KB Output is correct
15 Correct 1 ms 588 KB Output is correct
16 Correct 1 ms 580 KB Output is correct
17 Correct 1 ms 460 KB Output is correct
18 Correct 1 ms 588 KB Output is correct
19 Correct 1 ms 460 KB Output is correct
20 Correct 1 ms 460 KB Output is correct
21 Correct 1 ms 460 KB Output is correct
22 Correct 1 ms 460 KB Output is correct
23 Correct 1 ms 588 KB Output is correct
24 Correct 1 ms 576 KB Output is correct
25 Correct 1 ms 588 KB Output is correct
26 Correct 1 ms 588 KB Output is correct
27 Correct 1 ms 572 KB Output is correct
28 Correct 1 ms 588 KB Output is correct
29 Correct 1 ms 580 KB Output is correct
30 Correct 1 ms 588 KB Output is correct
31 Correct 1 ms 588 KB Output is correct
32 Correct 1 ms 588 KB Output is correct
33 Correct 1 ms 588 KB Output is correct
34 Correct 1 ms 580 KB Output is correct
35 Correct 1 ms 588 KB Output is correct
36 Correct 1 ms 588 KB Output is correct
37 Correct 1 ms 576 KB Output is correct
38 Correct 3 ms 1100 KB Output is correct
39 Correct 4 ms 1020 KB Output is correct
40 Correct 3 ms 1100 KB Output is correct
41 Correct 3 ms 1100 KB Output is correct
42 Correct 4 ms 1100 KB Output is correct
43 Correct 2 ms 1100 KB Output is correct
44 Correct 3 ms 1136 KB Output is correct
45 Correct 3 ms 1020 KB Output is correct
46 Correct 4 ms 1100 KB Output is correct
47 Correct 2 ms 1100 KB Output is correct
48 Correct 3 ms 1096 KB Output is correct
49 Correct 4 ms 1100 KB Output is correct
50 Correct 3 ms 1100 KB Output is correct
51 Correct 3 ms 1100 KB Output is correct

Subtask #4
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 460 KB Output is correct
2 Correct 1 ms 588 KB Output is correct
3 Correct 1 ms 460 KB Output is correct
4 Correct 1 ms 588 KB Output is correct
5 Correct 1 ms 588 KB Output is correct
6 Correct 1 ms 460 KB Output is correct
7 Correct 1 ms 588 KB Output is correct
8 Correct 1 ms 460 KB Output is correct
9 Correct 1 ms 460 KB Output is correct
10 Correct 1 ms 460 KB Output is correct
11 Correct 1 ms 460 KB Output is correct
12 Correct 1 ms 460 KB Output is correct
13 Correct 1 ms 588 KB Output is correct
14 Correct 1 ms 460 KB Output is correct
15 Correct 1 ms 588 KB Output is correct
16 Correct 1 ms 580 KB Output is correct
17 Correct 1 ms 460 KB Output is correct
18 Correct 1 ms 588 KB Output is correct
19 Correct 1 ms 460 KB Output is correct
20 Correct 1 ms 460 KB Output is correct
21 Correct 1 ms 460 KB Output is correct
22 Correct 1 ms 460 KB Output is correct
23 Correct 1 ms 588 KB Output is correct
24 Correct 1 ms 576 KB Output is correct
25 Correct 1 ms 588 KB Output is correct
26 Correct 1 ms 588 KB Output is correct
27 Correct 1 ms 572 KB Output is correct
28 Correct 1 ms 588 KB Output is correct
29 Correct 1 ms 580 KB Output is correct
30 Correct 1 ms 588 KB Output is correct
31 Correct 1 ms 588 KB Output is correct
32 Correct 1 ms 588 KB Output is correct
33 Correct 1 ms 588 KB Output is correct
34 Correct 1 ms 580 KB Output is correct
35 Correct 1 ms 588 KB Output is correct
36 Correct 1 ms 588 KB Output is correct
37 Correct 1 ms 576 KB Output is correct
38 Correct 3 ms 1100 KB Output is correct
39 Correct 4 ms 1020 KB Output is correct
40 Correct 3 ms 1100 KB Output is correct
41 Correct 3 ms 1100 KB Output is correct
42 Correct 4 ms 1100 KB Output is correct
43 Correct 2 ms 1100 KB Output is correct
44 Correct 3 ms 1136 KB Output is correct
45 Correct 3 ms 1020 KB Output is correct
46 Correct 4 ms 1100 KB Output is correct
47 Correct 2 ms 1100 KB Output is correct
48 Correct 3 ms 1096 KB Output is correct
49 Correct 4 ms 1100 KB Output is correct
50 Correct 3 ms 1100 KB Output is correct
51 Correct 3 ms 1100 KB Output is correct
52 Correct 250 ms 56264 KB Output is correct
53 Correct 291 ms 56268 KB Output is correct
54 Correct 190 ms 56316 KB Output is correct
55 Correct 221 ms 54536 KB Output is correct
56 Correct 190 ms 54520 KB Output is correct
57 Correct 217 ms 54504 KB Output is correct
58 Correct 205 ms 54520 KB Output is correct
59 Correct 207 ms 54604 KB Output is correct
60 Correct 199 ms 54616 KB Output is correct
61 Correct 194 ms 54716 KB Output is correct
62 Correct 199 ms 54520 KB Output is correct
63 Correct 173 ms 59820 KB Output is correct
64 Correct 240 ms 54680 KB Output is correct
65 Correct 228 ms 54600 KB Output is correct
66 Correct 263 ms 54608 KB Output is correct
67 Correct 228 ms 54512 KB Output is correct
68 Correct 263 ms 54556 KB Output is correct
69 Correct 246 ms 54608 KB Output is correct
70 Correct 254 ms 54580 KB Output is correct
71 Correct 251 ms 54560 KB Output is correct
72 Correct 240 ms 54544 KB Output is correct
73 Correct 239 ms 54584 KB Output is correct
74 Correct 240 ms 54784 KB Output is correct
75 Correct 243 ms 54604 KB Output is correct
76 Correct 247 ms 54552 KB Output is correct
77 Correct 225 ms 54764 KB Output is correct
78 Correct 258 ms 54704 KB Output is correct
79 Correct 234 ms 54592 KB Output is correct
80 Correct 282 ms 54704 KB Output is correct