oj.uz

Submission #428031

# Submission time Handle Problem Language Result Execution time Memory
428031 2021-06-15T07:26:42 Z Kevin_Zhang_TW Long Distance Coach (JOI17_coach) C++17
71 / 100
 2000 ms 52208 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 );
	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);
}

// 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) {
		assert(dq.size());

		ll v = inf, ret = 0;
		for (int i = 0;i < dq.size();++i)
			if (chmin(v, F(dq[i], x)))
				ret = dq[i].first;
		return ret;

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

pair<ll,ll> get_line(int ind) { 
	return make_pair(ind, dp[ind] - pfc[ind]);
}
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));
	bst.pb(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]);
		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));

		for (auto &c : conv)
			chmin(dp[i], sum + cost( c.qq(i), i ));

		minconv cur;
		cur.pb(get_line(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() || cost(bst.back(), i+1) > cost(id, i+1) ? id : bst.back() );
		stk.pb(i);
		conv.pb();
		swap(cur, conv.back());

		//for (int j = 0;j < i;++j) chmin(dp[i], sum + cost(j, i));
	}
//
//	for (int i = 1;i < m;++i) {
//		auto [d, c] = man[i];
//		ll sum = (X / T + (X % T > d)) * W ;// + (i-1) * sp[i-1];
//
//		for (int j = 0;j < i;++j) {
//			chmin(dp[i], sum + cost(j, i));
//		}
//	}
}

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::qq(int)':
coach.cpp:128:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::deque<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  128 |   for (int j = 0;j < dq.size();++j)
      |                  ~~^~~~~~~~~~~
coach.cpp: In member function 'int minconv::qrypoint(ll)':
coach.cpp:137:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::deque<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  137 |   for (int i = 0;i < dq.size();++i)
      |                  ~~^~~~~~~~~~~
coach.cpp:144:12: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  144 |    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:238:2: note: in expansion of macro 'DE'
  238 |  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 460 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 460 KB Output is correct
6 Correct 1 ms 504 KB Output is correct
7 Correct 1 ms 460 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 460 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 588 KB Output is correct
17 Correct 1 ms 460 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 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 460 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 460 KB Output is correct
6 Correct 1 ms 504 KB Output is correct
7 Correct 1 ms 460 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 460 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 588 KB Output is correct
17 Correct 1 ms 460 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 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 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 2 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 2 ms 716 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 588 KB Output is correct
36 Correct 1 ms 588 KB Output is correct
37 Correct 2 ms 588 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 460 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 460 KB Output is correct
6 Correct 1 ms 504 KB Output is correct
7 Correct 1 ms 460 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 460 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 588 KB Output is correct
17 Correct 1 ms 460 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 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 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 2 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 2 ms 716 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 588 KB Output is correct
36 Correct 1 ms 588 KB Output is correct
37 Correct 2 ms 588 KB Output is correct
38 Correct 66 ms 1108 KB Output is correct
39 Correct 63 ms 1100 KB Output is correct
40 Correct 64 ms 1120 KB Output is correct
41 Correct 90 ms 1104 KB Output is correct
42 Correct 81 ms 1100 KB Output is correct
43 Correct 85 ms 1232 KB Output is correct
44 Correct 82 ms 1108 KB Output is correct
45 Correct 87 ms 1100 KB Output is correct
46 Correct 276 ms 2968 KB Output is correct
47 Correct 61 ms 1100 KB Output is correct
48 Correct 62 ms 1116 KB Output is correct
49 Correct 180 ms 1228 KB Output is correct
50 Correct 72 ms 1232 KB Output is correct
51 Correct 70 ms 1100 KB Output is correct

Subtask #4
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 460 KB Output is correct
2 Correct 1 ms 460 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 460 KB Output is correct
6 Correct 1 ms 504 KB Output is correct
7 Correct 1 ms 460 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 460 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 588 KB Output is correct
17 Correct 1 ms 460 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 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 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 2 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 2 ms 716 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 588 KB Output is correct
36 Correct 1 ms 588 KB Output is correct
37 Correct 2 ms 588 KB Output is correct
38 Correct 66 ms 1108 KB Output is correct
39 Correct 63 ms 1100 KB Output is correct
40 Correct 64 ms 1120 KB Output is correct
41 Correct 90 ms 1104 KB Output is correct
42 Correct 81 ms 1100 KB Output is correct
43 Correct 85 ms 1232 KB Output is correct
44 Correct 82 ms 1108 KB Output is correct
45 Correct 87 ms 1100 KB Output is correct
46 Correct 276 ms 2968 KB Output is correct
47 Correct 61 ms 1100 KB Output is correct
48 Correct 62 ms 1116 KB Output is correct
49 Correct 180 ms 1228 KB Output is correct
50 Correct 72 ms 1232 KB Output is correct
51 Correct 70 ms 1100 KB Output is correct
52 Execution timed out 2056 ms 52208 KB Time limit exceeded
53 Halted 0 ms 0 KB -