#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));
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);
assert(conv.back().empty());
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;
| ~~^~~
In file included from /usr/include/c++/10/cassert:44,
from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:33,
from coach.cpp:1:
coach.cpp: In function 'void solve()':
coach.cpp:208:23: error: '__gnu_cxx::__alloc_traits<std::allocator<minconv>, minconv>::value_type' {aka 'struct minconv'} has no member named 'empty'
208 | assert(conv.back().empty());
| ^~~~~
coach.cpp: In function 'int32_t main()':
coach.cpp:14:17: warning: statement has no effect [-Wunused-value]
14 | #define DE(...) 0
| ^
coach.cpp:236:2: note: in expansion of macro 'DE'
236 | DE(X, n, m, W, T);
| ^~
