Video Editorial
Idea: amul_agrawal
Problem Setting: menavlikar.rutvij JadeReaper rahulgoel amul_agrawal
Editorial: menavlikar.rutvij rahulgoel
Video Editorial: rahulgoel
This is hint 1.
This is hint 2.
#include <bits/stdc++.h>
using namespace std;
int main()
{
int t;
cin >> t;
while (t--)
{
int n;
cin >> n;
vector<int> a(n);
for (int i = 0; i < n; ++i)
cin >> a[i];
int num_odd = 0;
for (auto x : a)
if (x & 1)
num_odd++;
cout << min(num_odd, n - num_odd) << endl;
}
return 0;
}
1691B - Обмен обувью
Video Editorial
Idea: amul_agrawal
Problem Setting: rahulgoel menavlikar.rutvij JadeReaper
Editorial: menavlikar.rutvij rahulgoel
Video Editorial: rahulgoel
This is hint 1.
This is hint 2.
#include <iostream>
using namespace std;
int main() {
cout << "Hello World!" << endl;
return 0;
}
1691C - Сумма подстрок
Video Editorial
Idea: amul_agrawal
Problem Setting: rahulgoel amul_agrawal
Editorial: amul_agrawal rahulgoel
Video Editorial: rahulgoel
This is hint 1.
This is hint 2.
#include <bits/stdc++.h>
using namespace std;
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t;
cin >> t;
while (t--) {
int n, k;
cin >> n >> k;
string s;
cin >> s;
int ones = 0, p1_first = n, p1_last = -1;
for (int p = 0; p < n; p++) {
if (s[p] != '1')
continue;
ones += 1;
if (p1_first == n)
p1_first = p;
p1_last = p;
}
int add = 0;
// moving the last one to last position
if (ones > 0 and (n - 1 - p1_last) <= k) {
k -= (n - 1 - p1_last);
add += 1;
ones -= 1;
}
// moving the first one to first position
if (ones > 0 and p1_first <= k) {
k -= (p1_first);
add += 10;
ones -= 1;
}
cout << 11 * ones + add << "\n";
}
return 0;
}
1691D - Максимум не меньше суммы
Video Editorial
Idea: amul_agrawal
Problem Setting: fangahawk amul_agrawal rahulgoel keyurchd_11
Editorial: fangahawk rahulgoel
Video Editorial: rahulgoel
This is hint 1.
This is hint 2.
#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
const ll ninf = -1e15;
vector<int> nextGreater(vector<ll>& arr, int n) {
stack<int> s;
vector<int> result(n, n);
for (int i = 0; i < n; i++) {
while (!s.empty() && arr[s.top()] < arr[i]) {
result[s.top()] = i;
s.pop();
}
s.push(i);
}
return result;
}
vector<int> prevGreater(vector<ll>& arr, int n) {
stack<int> s;
vector<int> result(n, -1);
for (int i = n - 1; i >= 0; i--) {
while (!s.empty() && arr[s.top()] < arr[i]) {
result[s.top()] = i;
s.pop();
}
s.push(i);
}
return result;
}
ll query(vector<ll> &tree, int node, int ns, int ne, int qs, int qe) {
if (qe < ns || qs > ne) return ninf;
if (qs <= ns && ne <= qe) return tree[node];
int mid = ns + (ne - ns) / 2;
ll leftQuery = query(tree, 2 * node, ns, mid, qs, qe);
ll rightQuery = query(tree, 2 * node + 1, mid + 1, ne, qs, qe);
return max(leftQuery, rightQuery);
}
int main() {
int t;
cin >> t;
while (t--) {
int n, _n;
cin >> n;
vector<ll> arr(n, 0);
for (auto& a : arr)
cin >> a;
// Round off n to next power of 2
_n = n;
while (__builtin_popcount(_n) != 1) _n++;
// Prefix sums
vector<ll> prefixSum(n, 0), suffixSum(n, 0);
prefixSum[0] = arr[0];
for (int i = 1; i < n; i++) {
prefixSum[i] = prefixSum[i - 1] + arr[i];
}
suffixSum[n - 1] = arr[n - 1];
for (int i = n - 2; i >= 0; i--) {
suffixSum[i] = suffixSum[i + 1] + arr[i];
}
// Two max-segtress, one on the prefix sums, one on the suffix sums
vector<ll> prefixTree(2 * _n, ninf), suffixTree(2 * _n, ninf);
for (int i = 0; i < n; i++) {
prefixTree[_n + i] = prefixSum[i];
suffixTree[_n + i] = suffixSum[i];
}
for (int i = _n - 1; i >= 1; i--) {
prefixTree[i] = max(prefixTree[2 * i], prefixTree[2 * i + 1]);
suffixTree[i] = max(suffixTree[2 * i], suffixTree[2 * i + 1]);
}
vector<int> ng = nextGreater(arr, n);
vector<int> pg = prevGreater(arr, n);
bool flag = true;
for (int i = 0; i < n; i++) {
ll rightMax = query(prefixTree, 1, 0, _n - 1, i + 1, ng[i] - 1) - prefixSum[i];
ll leftMax = query(suffixTree, 1, 0, _n - 1, pg[i] + 1, i - 1) - suffixSum[i];
if (max(leftMax, rightMax) > 0) {
flag = false;
break;
}
}
if (flag)
cout << "YES\n";
else
cout << "NO\n";
}
}
1691E - Число групп отрезков
Video Editorial
Idea: amul_agrawal
Problem Setting: akcube keyurchd_11 rahulgoel amul_agrawal
Editorial: akcube rahulgoel
Video Editorial: rahulgoel
This is hint 1.
This is hint 2.
#include <bits/stdc++.h>
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template <class T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define MOD 1000000007
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
#define pb push_back
#define all(s) s.begin(), s.end()
#define sz(x) (int)(x).size()
#define fastio cin.tie(0) -> sync_with_stdio(0)
struct DSU{
vi dsu, szx;
DSU() = default;
DSU(int n) : dsu(n), szx(n, 1) {
for(int i=0; i<n; i++) dsu[i] = i;
}
int parent(int i){
if(dsu[i]==i) return i;
else return dsu[i] = parent(dsu[i]);
}
int size(int i) { return szx[parent(i)]; }
int operator[](int i){ return parent(i); }
int num_comps(){
int ct = 0;
for(int i=0; i<sz(dsu); i++) if(dsu[i] == i) ct++;
return ct;
}
void unify(int a, int b){
a = parent(a);
b = parent(b);
if(szx[a] < szx[b]) swap(a, b);
if(a!=b) dsu[b] = a, szx[a] += szx[b];
}
};
struct Point{
int t, p, pc, id;
bool close;
bool operator<(Point &other){
if(p == other.p) return close < other.close;
return p < other.p;
}
};
void solve(){
int n; cin>>n;
vector<Point> points;
for(int i=0; i<n; i++){
int t, l, r; cin>>t>>l>>r;
points.pb({t, l, r, i, false});
points.pb({t, r, l, i, true});
}
sort(all(points));
DSU dsu(n);
vector<set<pii>> open(2); // {r, id}
for(auto &p:points){
if(p.close) open[p.t].erase({p.p, p.id});
else{
open[p.t].insert({p.pc, p.id});
while(sz(open[p.t ^ 1]) > 1){
auto [r, id] = *open[p.t ^ 1].begin();
dsu.unify(p.id, id);
open[p.t ^ 1].erase({r, id});
}
if(sz(open[p.t ^ 1]) == 1) dsu.unify(p.id, open[p.t ^ 1].begin()->second);
}
}
cout<<dsu.num_comps()<<endl;
}
int main(){
fastio;
int t;
cin >> t;
while (t--) solve();
}
print("Hello World!")
1691F - Дерево и k-подмножества
Video Editorial
Idea: ltc.groverkss
Problem Setting: ltc.groverkss amul_agrawal rahulgoel
Editorial: rahulgoel
Video Editorial: rahulgoel
This is hint 1.
This is hint 2.
#include <iostream>
#include <vector>
using namespace std;
using ll = long long;
const ll MOD = 1e9 + 7;
struct Comb {
vector<ll> fac;
vector<ll> invfac;
ll n;
Comb(ll n)
{
this->n = n;
fac.resize(n + 1, 0);
invfac.resize(n + 1, 0);
fac[0] = 1;
for (ll i = 1; i <= n; i++)
fac[i] = (fac[i - 1] * i) % MOD;
invfac[n] = power(fac[n], MOD - 2);
for (ll i = n - 1; i >= 0; i--)
invfac[i] = (invfac[i + 1] * (i + 1)) % MOD;
}
static ll power(ll x, ll y)
{
ll ret = 1;
while (y) {
if (y & 1)
ret = (ret * x) % MOD;
y >>= 1;
x = (x * x) % MOD;
}
return ret;
}
ll nCr(ll n, ll r)
{
if (n < 0 or r < 0 or n < r)
return 0;
ll ans = (fac[n] * ((invfac[r] * invfac[n - r]) % MOD)) % MOD;
return ans;
}
};
vector<vector<int> > adj;
vector<int> sz;
vector<ll> cnt;
vector<ll> cntsz;
Comb C(2e5 + 5);
ll cur_ans = 0;
ll ans = 0;
void dfs1(int v, int p, int k)
{
sz[v] = 1;
ll sub = 0;
for (int u : adj[v]) {
if (u != p) {
dfs1(u, v, k);
sz[v] += sz[u];
sub = (sub + C.nCr(sz[u], k)) % MOD;
}
}
cnt[v] = (C.nCr(sz[v], k) - sub + MOD) % MOD;
cntsz[v] = (cnt[v] * sz[v]) % MOD;
cur_ans = (cur_ans + cntsz[v]) % MOD;
}
void dfs2(int v, int p, int k)
{
ans = (ans + cur_ans) % MOD;
for (int u : adj[v]) {
if (u != p) {
// store
int store_v_sz = sz[v];
ll store_v_cnt = cnt[v];
ll store_v_cntsz = cntsz[v];
int store_u_sz = sz[u];
ll store_u_cnt = cnt[u];
ll store_u_cntsz = cntsz[u];
ll store_cur_ans = cur_ans;
// recalculate size[v], size[u]
sz[v] -= sz[u];
sz[u] = sz.size();
// recalculate cnt[v]
cnt[v] = (cnt[v] - C.nCr(store_v_sz, k) + MOD) % MOD;
cnt[v] = (cnt[v] + C.nCr(sz[v], k)) % MOD;
cnt[v] = (cnt[v] + C.nCr(store_u_sz, k)) % MOD;
// recalculate cnt[u]
cnt[u] = (cnt[u] - C.nCr(store_u_sz, k) + MOD) % MOD;
cnt[u] = (cnt[u] + C.nCr(sz[u], k)) % MOD;
cnt[u] = (cnt[u] - C.nCr(sz[v], k) + MOD) % MOD;
// recalculate cntsz
cntsz[v] = (cnt[v] * sz[v]) % MOD;
cntsz[u] = (cnt[u] * sz[u]) % MOD;
// recalculate cur_ans
cur_ans = (cur_ans - store_v_cntsz - store_u_cntsz + MOD + MOD) % MOD;
cur_ans = (cur_ans + cntsz[v] + cntsz[u]) % MOD;
dfs2(u, v, k);
// restore
sz[v] = store_v_sz;
cnt[v] = store_v_cnt;
cntsz[v] = store_v_cntsz;
sz[u] = store_u_sz;
cnt[u] = store_u_cnt;
cntsz[u] = store_u_cntsz;
cur_ans = store_cur_ans;
}
}
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int n, k;
cin >> n >> k;
adj.resize(n);
sz.resize(n);
cnt.resize(n);
cntsz.resize(n);
for (int i = 0; i < n - 1; ++i) {
int u, v;
cin >> u >> v;
--u, --v;
adj[u].push_back(v);
adj[v].push_back(u);
}
dfs1(0, 0, k);
dfs2(0, 0, k);
cout << ans << endl;
return 0;
}