oj.uz

Submission #428125

# Submission time Handle Problem Language Result Execution time Memory
428125 2021-06-15T08:15:10 Z Kevin_Zhang_TW Long Distance Coach (JOI17_coach) C++17
100 / 100
 409 ms 231352 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 {
	deque< ll > dq;
	// 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;
//	}
//	// make sure that line has the minimum slope
//	void pf(int line) {
//	}
//};
void merge_conv(minconv &a, minconv &b) {
	if (a.dq.size() < b.dq.size()) 
		while (a.dq.size()) b.pf(a.pop_back());
	else {
		while (b.dq.size()) a.pb(b.pop_front());
		swap(a, b);
	}
	a.clear();
}

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;

		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();
		cur.pb(i);
		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::qrypoint(ll)':
coach.cpp:185:12: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  185 |    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:292:2: note: in expansion of macro 'DE'
  292 |  DE(X, n, m, W, T);
      |  ^~

Subtask #1
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 588 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 460 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 588 KB Output is correct
10 Correct 1 ms 588 KB Output is correct
11 Correct 1 ms 572 KB Output is correct
12 Correct 1 ms 576 KB Output is correct
13 Correct 1 ms 460 KB Output is correct
14 Correct 1 ms 588 KB Output is correct
15 Correct 1 ms 576 KB Output is correct
16 Correct 1 ms 572 KB Output is correct
17 Correct 1 ms 588 KB Output is correct
18 Correct 1 ms 460 KB Output is correct
19 Correct 1 ms 460 KB Output is correct
20 Correct 1 ms 588 KB Output is correct
21 Correct 1 ms 588 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 588 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 460 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 588 KB Output is correct
10 Correct 1 ms 588 KB Output is correct
11 Correct 1 ms 572 KB Output is correct
12 Correct 1 ms 576 KB Output is correct
13 Correct 1 ms 460 KB Output is correct
14 Correct 1 ms 588 KB Output is correct
15 Correct 1 ms 576 KB Output is correct
16 Correct 1 ms 572 KB Output is correct
17 Correct 1 ms 588 KB Output is correct
18 Correct 1 ms 460 KB Output is correct
19 Correct 1 ms 460 KB Output is correct
20 Correct 1 ms 588 KB Output is correct
21 Correct 1 ms 588 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 588 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 588 KB Output is correct
28 Correct 1 ms 588 KB Output is correct
29 Correct 1 ms 588 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 588 KB Output is correct
35 Correct 1 ms 572 KB Output is correct
36 Correct 1 ms 588 KB Output is correct
37 Correct 1 ms 588 KB Output is correct

Subtask #3
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 588 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 460 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 588 KB Output is correct
10 Correct 1 ms 588 KB Output is correct
11 Correct 1 ms 572 KB Output is correct
12 Correct 1 ms 576 KB Output is correct
13 Correct 1 ms 460 KB Output is correct
14 Correct 1 ms 588 KB Output is correct
15 Correct 1 ms 576 KB Output is correct
16 Correct 1 ms 572 KB Output is correct
17 Correct 1 ms 588 KB Output is correct
18 Correct 1 ms 460 KB Output is correct
19 Correct 1 ms 460 KB Output is correct
20 Correct 1 ms 588 KB Output is correct
21 Correct 1 ms 588 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 588 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 588 KB Output is correct
28 Correct 1 ms 588 KB Output is correct
29 Correct 1 ms 588 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 588 KB Output is correct
35 Correct 1 ms 572 KB Output is correct
36 Correct 1 ms 588 KB Output is correct
37 Correct 1 ms 588 KB Output is correct
38 Correct 4 ms 1100 KB Output is correct
39 Correct 4 ms 1100 KB Output is correct
40 Correct 4 ms 1100 KB Output is correct
41 Correct 3 ms 1100 KB Output is correct
42 Correct 3 ms 1100 KB Output is correct
43 Correct 3 ms 1096 KB Output is correct
44 Correct 3 ms 1100 KB Output is correct
45 Correct 3 ms 1100 KB Output is correct
46 Correct 4 ms 2508 KB Output is correct
47 Correct 3 ms 1100 KB Output is correct
48 Correct 3 ms 1100 KB Output is correct
49 Correct 4 ms 1148 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 588 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 460 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 588 KB Output is correct
10 Correct 1 ms 588 KB Output is correct
11 Correct 1 ms 572 KB Output is correct
12 Correct 1 ms 576 KB Output is correct
13 Correct 1 ms 460 KB Output is correct
14 Correct 1 ms 588 KB Output is correct
15 Correct 1 ms 576 KB Output is correct
16 Correct 1 ms 572 KB Output is correct
17 Correct 1 ms 588 KB Output is correct
18 Correct 1 ms 460 KB Output is correct
19 Correct 1 ms 460 KB Output is correct
20 Correct 1 ms 588 KB Output is correct
21 Correct 1 ms 588 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 588 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 588 KB Output is correct
28 Correct 1 ms 588 KB Output is correct
29 Correct 1 ms 588 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 588 KB Output is correct
35 Correct 1 ms 572 KB Output is correct
36 Correct 1 ms 588 KB Output is correct
37 Correct 1 ms 588 KB Output is correct
38 Correct 4 ms 1100 KB Output is correct
39 Correct 4 ms 1100 KB Output is correct
40 Correct 4 ms 1100 KB Output is correct
41 Correct 3 ms 1100 KB Output is correct
42 Correct 3 ms 1100 KB Output is correct
43 Correct 3 ms 1096 KB Output is correct
44 Correct 3 ms 1100 KB Output is correct
45 Correct 3 ms 1100 KB Output is correct
46 Correct 4 ms 2508 KB Output is correct
47 Correct 3 ms 1100 KB Output is correct
48 Correct 3 ms 1100 KB Output is correct
49 Correct 4 ms 1148 KB Output is correct
50 Correct 3 ms 1100 KB Output is correct
51 Correct 3 ms 1100 KB Output is correct
52 Correct 312 ms 54944 KB Output is correct
53 Correct 304 ms 54492 KB Output is correct
54 Correct 257 ms 54596 KB Output is correct
55 Correct 250 ms 54604 KB Output is correct
56 Correct 261 ms 54596 KB Output is correct
57 Correct 271 ms 54340 KB Output is correct
58 Correct 281 ms 54648 KB Output is correct
59 Correct 252 ms 54600 KB Output is correct
60 Correct 253 ms 54548 KB Output is correct
61 Correct 253 ms 54604 KB Output is correct
62 Correct 335 ms 54512 KB Output is correct
63 Correct 409 ms 231352 KB Output is correct
64 Correct 270 ms 58688 KB Output is correct
65 Correct 302 ms 57868 KB Output is correct
66 Correct 325 ms 57712 KB Output is correct
67 Correct 313 ms 57760 KB Output is correct
68 Correct 315 ms 57796 KB Output is correct
69 Correct 303 ms 57412 KB Output is correct
70 Correct 299 ms 57396 KB Output is correct
71 Correct 297 ms 57496 KB Output is correct
72 Correct 297 ms 57540 KB Output is correct
73 Correct 304 ms 57524 KB Output is correct
74 Correct 301 ms 57540 KB Output is correct
75 Correct 297 ms 57696 KB Output is correct
76 Correct 299 ms 57668 KB Output is correct
77 Correct 286 ms 57824 KB Output is correct
78 Correct 279 ms 58156 KB Output is correct
79 Correct 294 ms 57196 KB Output is correct
80 Correct 301 ms 57024 KB Output is correct