/*
IOI 2008 Pyramid Base
- Case B = 0:
- Let r[l] be the right x-coordinate if the left x-coordinate of the pyramid base is l
- Notice how r[l] >= r[l - 1]
- This means we can use 2 pointers to find the largest r - l
- To find the maximum height of a pyramid with x-coordinates in the range [l, r], we can use
a segment tree that supports range increment and stores the maximum number of consecutive 0s
- We don't actually need lazy propagation because we only care about the number of consecutive 0s
- See SACO 2018 Stadium for a similar problem
- Complexity: O((N + P) log N)
- Case B > 0:
- Binary search for the side length L
- Cosider an array C where C[i] is the cost to build a pyramid with bottom y-coordinate at i
- When we add an obstacle, we increase all values C[y1] to C[y2 + L - 1] by its cost
- We can now just use a lazy segment tree to keep track of the minimum value of all values C[L] to C[W]
- Complexity: O((N + P) log^2 N)
*/
#include <bits/stdc++.h>
#pragma GCC target("sse4,avx2,fma,avx")
#define FOR(i, x, y) for (int i = x; i < y; i++)
using namespace std;
namespace no_remove {
struct Node {
int sm, range, mxl, mxr, mxt;
};
Node segtree[3000001];
vector<pair<int, int>> add[1000002], subtr[1000002];
void combine(int node, Node l, Node r) {
if (l.sm) l.mxl = l.mxr = l.mxt = 0;
if (r.sm) r.mxl = r.mxr = r.mxt = 0;
segtree[node] = {segtree[node].sm, l.range + r.range,
l.mxl + (l.mxl == l.range ? r.mxl : 0),
r.mxr + (r.mxl == r.range ? l.mxr : 0),
max({l.mxt, r.mxt, l.mxr + r.mxl})};
}
void build(int node, int l, int r) {
if (l == r) segtree[node] = {0, 1, 1, 1, 1};
else {
int mid = (l + r) / 2;
build(node * 2, l, mid);
build(node * 2 + 1, mid + 1, r);
combine(node, segtree[node * 2], segtree[node * 2 + 1]);
}
}
void update(int a, int b, int val, int node, int l, int r) {
if (l > b || r < a) return;
if (l >= a && r <= b) segtree[node].sm += val;
else {
int mid = (l + r) / 2;
update(a, b, val, node * 2, l, mid);
update(a, b, val, node * 2 + 1, mid + 1, r);
combine(node, segtree[node * 2], segtree[node * 2 + 1]);
}
}
void solve(int H, int W) {
add[H + 1].push_back({1, W});
int N, C;
cin >> N;
FOR(i, 0, N) {
int x1, y1, x2, y2;
cin >> x1 >> y1 >> x2 >> y2 >> C;
add[x1].push_back({y1, y2});
subtr[x2 + 1].push_back({y1, y2});
}
build(1, 1, W);
int ans = 0, rptr = 1;
FOR(lptr, 1, H + 1) {
for (pair<int, int> i : subtr[lptr]) update(i.first, i.second, -1, 1, 1, W);
while ((segtree[1].sm ? 0 : segtree[1].mxt) >= rptr - lptr) {
for (pair<int, int> i : add[rptr]) update(i.first, i.second, 1, 1, 1, W);
ans = max(ans, rptr++ - lptr);
}
}
cout << ans;
}
}
namespace yes_remove {
int lazy[3000001], segtree[3000001];
vector<array<int, 3>> add[1000002], subtr[1000002];
inline void push_lazy(int node, int l, int r) {
segtree[node] += lazy[node];
if (l != r) {
lazy[node * 2] += lazy[node];
lazy[node * 2 + 1] += lazy[node];
}
lazy[node] = 0;
}
void update(int a, int b, int val, int node, int l, int r) {
push_lazy(node, l, r);
if (l > b || r < a) return;
if (l >= a && r <= b) {
lazy[node] = val;
push_lazy(node, l, r);
} else {
int mid = (l + r) / 2;
update(a, b, val, node * 2, l, mid);
update(a, b, val, node * 2 + 1, mid + 1, r);
segtree[node] = min(segtree[node * 2], segtree[node * 2 + 1]);
}
}
bool check(int len, int H, int W, int B) {
memset(segtree, 0, sizeof(segtree));
memset(lazy, 0, sizeof(lazy));
update(1, len - 1, B + 1, 1, 1, W);
FOR(i, 1, len) for (auto j : add[i]) update(j[0], j[1] + len - 1, j[2], 1, 1, W);
FOR(i, len, H + 1) {
for (auto j : add[i]) update(j[0], j[1] + len - 1, j[2], 1, 1, W);
for (auto j : subtr[i - len + 1]) update(j[0], j[1] + len - 1, -j[2], 1, 1, W);
if (segtree[1] <= B) return true;
}
return false;
}
void solve(int H, int W, int B) {
int N;
cin >> N;
FOR(i, 0, N) {
int x1, y1, x2, y2, c;
cin >> x1 >> y1 >> x2 >> y2 >> c;
add[x1].push_back({y1, y2, c});
subtr[x2 + 1].push_back({y1, y2, c});
}
int l = 1, r = min(H, W);
while (l != r) {
int mid = (l + r + 1) / 2;
if (check(mid, H, W, B)) l = mid;
else r = mid - 1;
}
cout << l;
}
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int H, W, B;
cin >> H >> W >> B;
if (B) yes_remove::solve(H, W, B);
else no_remove::solve(H, W);
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
63 ms |
94328 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
66 ms |
94328 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
65 ms |
94328 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
63 ms |
95016 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
69 ms |
99448 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
110 ms |
135416 KB |
Output is correct |
| 2 |
Correct |
115 ms |
135584 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
108 ms |
135416 KB |
Output is correct |
| 2 |
Correct |
112 ms |
135416 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
143 ms |
118008 KB |
Output is correct |
| 2 |
Correct |
180 ms |
118008 KB |
Output is correct |
| 3 |
Correct |
166 ms |
118052 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
335 ms |
118648 KB |
Output is correct |
| 2 |
Correct |
412 ms |
118776 KB |
Output is correct |
| 3 |
Correct |
367 ms |
118520 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
509 ms |
119060 KB |
Output is correct |
| 2 |
Correct |
121 ms |
119032 KB |
Output is correct |
| 3 |
Correct |
280 ms |
118648 KB |
Output is correct |
| 4 |
Correct |
670 ms |
119032 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
793 ms |
119356 KB |
Output is correct |
| 2 |
Correct |
1141 ms |
119344 KB |
Output is correct |
| 3 |
Correct |
545 ms |
119372 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
815 ms |
119672 KB |
Output is correct |
| 2 |
Correct |
1328 ms |
119672 KB |
Output is correct |
| 3 |
Correct |
1331 ms |
119544 KB |
Output is correct |
| 4 |
Correct |
1376 ms |
119508 KB |
Output is correct |
| 5 |
Correct |
1329 ms |
119672 KB |
Output is correct |
| 6 |
Correct |
618 ms |
119680 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
697 ms |
146808 KB |
Output is correct |
| 2 |
Correct |
428 ms |
105720 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
959 ms |
151800 KB |
Output is correct |
| 2 |
Correct |
923 ms |
148420 KB |
Output is correct |
| 3 |
Correct |
599 ms |
141764 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1154 ms |
156152 KB |
Output is correct |
| 2 |
Correct |
1399 ms |
154088 KB |
Output is correct |
| 3 |
Correct |
1377 ms |
154084 KB |
Output is correct |
| 4 |
Correct |
1252 ms |
152288 KB |
Output is correct |
| 5 |
Correct |
838 ms |
146764 KB |
Output is correct |
