#include <bits/stdc++.h>
using namespace std;
#define dbg(x) //x
#define prt(x) dbg(cerr << x)
#define pv(x) prt(#x << " = " << x << '\n')
#define parr(x) dbg(prt(#x << " = "); for (auto y : x) prt(y << ' '); prt('\n'));
#define parr2d(x) dbg(prt(#x << " = \n"); for (auto y : x) {parr(y)}; prt('\n'));
/*
which ties are possible?
a can convince b if sum(a) > sum(b)
note that nodes are weighted
note that the tie with the strictly least number can't be 1 in the end
one with strictly most can be 1 in the end
how to greedily make 1 the largest?
dfs from the node
and keep adding the smallest adj greedily
and make sure that the size of this color's comp is greater than any other color's comp
subtask 1: brute force
subtask 2: tree; every node's parent has greater value than self
you can always get everything in your own subtree
go to the root
and for every node on the path to the root
you also absorb the parent
and everything else in the parent's subtree - note that that is guaranteed to be possible
if you've already absorbed the parent
this dp cond is checkable as you go up the tree
(this node's subtree sum >= parent's value?)
all the values to the root have to be true
for a node to work
subtask 3: just some weird stuff with set ig
*/
int main() {
ios::sync_with_stdio(0); cin.tie(0);
int n, m;
cin >> n >> m;
vector<long long> s(n);
for (int i = 0; i < n; i++) {
cin >> s[i];
}
bool inc = false;
for (int i = 0; i < n - 1; i++) {
if (s[i + 1] > s[i]) {
inc = true;
}
}
bool dif1 = true;
vector<vector<int>> edges(n);
for (int i = 0; i < m; i++) {
int x, y;
cin >> x >> y;
x--; y--;
pv(x); pv(y); pv(abs(x - y));
if (abs(x - y) > 1) dif1 = false;
edges[x].push_back(y);
edges[y].push_back(x);
}
pv(dif1);
if (n <= 2000 && m <= 2000) {
for (int i = 0; i < n; i++) {
vector<bool> vis(n, false);
vis[i] = true;
priority_queue<array<long long, 2>> que;
que.push({-s[i], i});
bool ok = true;
long long tot = s[i];
while (que.size()) {
long long sz = -que.top()[0], node = que.top()[1];
que.pop();
if (sz > tot) {
ok = false;
break;
}
if (node != i) {
tot += sz;
}
for (auto next : edges[node]) {
if (!vis[next]) {
vis[next] = true;
que.push({-s[next], next});
}
}
}
cout << (ok ? 1 : 0);
}
cout << '\n';
} else if (m == n - 1 && !inc) {
vector<bool> ok(n, true);
vector<long long> sum = s;
function<void(int, int)> dfs1 = [&] (int node, int par) {
for (auto next : edges[node]) {
if (next != par) {
dfs1(next, node);
sum[node] += sum[next];
}
}
};
dfs1(0, 0);
function<void(int, int)> dfs2 = [&] (int node, int par) {
if (node != 0) {
ok[node] = ok[par];
if (s[par] > sum[node]) {
ok[node] = false;
}
}
for (auto next : edges[node]) {
if (next != par) {
dfs2(next, node);
}
}
};
dfs2(0, 0);
for (int i = 0; i < n; i++) {
cout << (ok[i] ? 1 : 0);
}
cout << '\n';
} else if (dif1) {
/*
sum(l + 1, r - 1) < both a[l] and a[r]
so for each l find the min r so that sum(l + 1, r - 1) >= a[l]
for each r find the max l so that sum(l + 1, r - 1) >= a[r]
if mxl[r] <= l && mnr[l] >= r, they work probably
so probably find the l with the max mnr
or just an increasing seq of them that you can binary search
so you have n ranges of invalid elems
probably use set to remove all the elems
implies that if we start in [6, 6] we can't escape to the left OR right
*/
vector<long long> ps = s;
for (int i = 1; i < n; i++) {
ps[i] += ps[i - 1];
}
vector<int> mxl(n), mnr(n);
for (int i = 1; i < n; i++) {
if (i > 0) mxl[i] = upper_bound(ps.begin(), ps.end(), ps[i - 1] - s[i]) - ps.begin();
if (i < n - 1) mnr[i] = lower_bound(ps.begin(), ps.end(), ps[i] + s[i]) - ps.begin();
}
vector<int> ord(n);
iota(ord.begin(), ord.end(), 0);
sort(ord.begin(), ord.end(), [&] (int x, int y) {
return mxl[x] > mxl[y];
});
int ptr = n - 1;
vector<array<int, 2>> arr, bad;
array<int, 2> tmp;
for (int i = 0; i < n; i++) {
pv(i); pv(ord[i]);
while (ptr >= mxl[ord[i]]) {
while (arr.size() && -arr.back()[0] <= mnr[ptr]) arr.pop_back();
arr.push_back({-mnr[ptr], ptr});
ptr--;
}
parr2d(arr);
// GOAL: find the first >= i
// ACTUAL GOAL: find the last <= -i
tmp = {-mxl[ord[i]], (int) 1e9};
int lb = upper_bound(arr.begin(), arr.end(), tmp) - arr.begin() - 1;
if (lb != -1 && arr[lb][1] < ord[i] - 1) {
bad.push_back({arr[lb][1] + 1, ord[i ] - 1});
parr(bad.back());
}
}
for (int i = n - 1; i > 0; i--) {
if (s[i] > ps[i - 1]) {
bad.push_back({0, i - 1});
break;
}
}
for (int i = 0; i < n - 1; i++) {
if (s[i] > ps[n - 1] - ps[i]) {
bad.push_back({i + 1, n - 1});
break;
}
}
parr2d(bad);
set<int> st;
for (int i = 0; i < n; i++) {
st.insert(i);
}
for (auto [l, r] : bad) {
auto it = st.lower_bound(l);
while (it != st.end() && *it <= r) {
st.erase(it);
it = st.lower_bound(l);
}
}
parr(mxl); parr(mnr); parr(ord);
for (int i = 0; i < n; i++) {
cout << (st.count(i) ? 1 : 0);
}
cout << '\n';
}
}
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
344 KB |
Output is correct |
2 |
Correct |
0 ms |
348 KB |
Output is correct |
3 |
Correct |
0 ms |
348 KB |
Output is correct |
4 |
Correct |
134 ms |
556 KB |
Output is correct |
5 |
Correct |
118 ms |
348 KB |
Output is correct |
6 |
Correct |
199 ms |
540 KB |
Output is correct |
7 |
Correct |
132 ms |
348 KB |
Output is correct |
8 |
Correct |
92 ms |
348 KB |
Output is correct |
9 |
Correct |
200 ms |
600 KB |
Output is correct |
10 |
Correct |
47 ms |
348 KB |
Output is correct |
11 |
Correct |
45 ms |
348 KB |
Output is correct |
12 |
Correct |
43 ms |
348 KB |
Output is correct |
13 |
Correct |
82 ms |
344 KB |
Output is correct |
14 |
Correct |
72 ms |
344 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
0 ms |
348 KB |
Output is correct |
2 |
Correct |
0 ms |
348 KB |
Output is correct |
3 |
Correct |
84 ms |
22248 KB |
Output is correct |
4 |
Correct |
86 ms |
22096 KB |
Output is correct |
5 |
Correct |
75 ms |
14248 KB |
Output is correct |
6 |
Correct |
79 ms |
14676 KB |
Output is correct |
7 |
Correct |
89 ms |
14852 KB |
Output is correct |
8 |
Correct |
83 ms |
14672 KB |
Output is correct |
9 |
Correct |
69 ms |
14672 KB |
Output is correct |
10 |
Correct |
53 ms |
15300 KB |
Output is correct |
11 |
Correct |
53 ms |
15304 KB |
Output is correct |
12 |
Correct |
77 ms |
14928 KB |
Output is correct |
13 |
Correct |
78 ms |
33452 KB |
Output is correct |
14 |
Correct |
94 ms |
33620 KB |
Output is correct |
15 |
Correct |
88 ms |
33476 KB |
Output is correct |
16 |
Correct |
64 ms |
33020 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
0 ms |
348 KB |
Output is correct |
2 |
Incorrect |
151 ms |
27688 KB |
Output isn't correct |
3 |
Halted |
0 ms |
0 KB |
- |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
0 ms |
344 KB |
Output is correct |
2 |
Incorrect |
61 ms |
12764 KB |
Output isn't correct |
3 |
Halted |
0 ms |
0 KB |
- |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
344 KB |
Output is correct |
2 |
Correct |
0 ms |
348 KB |
Output is correct |
3 |
Correct |
0 ms |
348 KB |
Output is correct |
4 |
Correct |
134 ms |
556 KB |
Output is correct |
5 |
Correct |
118 ms |
348 KB |
Output is correct |
6 |
Correct |
199 ms |
540 KB |
Output is correct |
7 |
Correct |
132 ms |
348 KB |
Output is correct |
8 |
Correct |
92 ms |
348 KB |
Output is correct |
9 |
Correct |
200 ms |
600 KB |
Output is correct |
10 |
Correct |
47 ms |
348 KB |
Output is correct |
11 |
Correct |
45 ms |
348 KB |
Output is correct |
12 |
Correct |
43 ms |
348 KB |
Output is correct |
13 |
Correct |
82 ms |
344 KB |
Output is correct |
14 |
Correct |
72 ms |
344 KB |
Output is correct |
15 |
Correct |
0 ms |
348 KB |
Output is correct |
16 |
Correct |
0 ms |
348 KB |
Output is correct |
17 |
Correct |
84 ms |
22248 KB |
Output is correct |
18 |
Correct |
86 ms |
22096 KB |
Output is correct |
19 |
Correct |
75 ms |
14248 KB |
Output is correct |
20 |
Correct |
79 ms |
14676 KB |
Output is correct |
21 |
Correct |
89 ms |
14852 KB |
Output is correct |
22 |
Correct |
83 ms |
14672 KB |
Output is correct |
23 |
Correct |
69 ms |
14672 KB |
Output is correct |
24 |
Correct |
53 ms |
15300 KB |
Output is correct |
25 |
Correct |
53 ms |
15304 KB |
Output is correct |
26 |
Correct |
77 ms |
14928 KB |
Output is correct |
27 |
Correct |
78 ms |
33452 KB |
Output is correct |
28 |
Correct |
94 ms |
33620 KB |
Output is correct |
29 |
Correct |
88 ms |
33476 KB |
Output is correct |
30 |
Correct |
64 ms |
33020 KB |
Output is correct |
31 |
Correct |
0 ms |
348 KB |
Output is correct |
32 |
Incorrect |
151 ms |
27688 KB |
Output isn't correct |
33 |
Halted |
0 ms |
0 KB |
- |