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Gennady and a Card Game
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#include <bits/stdc++.h>
using namespace std;
char t[9], s[9];
int main()
{
for (scanf("%s", t); ~scanf("%s", s);)
if (s[0] == t[0] || s[1] == t[1])
return printf("YES"), 0;
printf("NO");
}
Petr and a Combination Lock
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#include <bits/stdc++.h>
using namespace std;
int n, a[15];
int main()
{
scanf("%d", &n);
for (int i = 0; i < n; ++i)
scanf("%d", &a[i]);
for (int i = (1 << n) - 1, sum; ~i; --i)
{
for (int j = sum = 0; j < n; ++j)
sum += (i & 1 << j) ? -a[j] : a[j];
if (sum % 360 == 0)
return printf("YES"), 0;
}
printf("NO");
}
Yuhao and a Parenthesis
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#include <bits/stdc++.h>
using namespace std;
const int N = 5e5 + 5;
char s[N], t[N];
int n, cnt[N << 1];
int main()
{
scanf("%d", &n);
for (int i = 0, c[2]; i < n; ++i)
{
scanf("%s", s);
for (int i = c[0] = c[1] = 0, siz = 0; s[i]; ++i)
{
if (siz && t[siz - 1] == '(' && s[i] == ')')
--c[0], --siz;
else
++c[s[i] == ')'], t[siz++] = s[i];
}
if (!c[0] || !c[1])
++cnt[N - c[0] + c[1]];
}
for (int i = n = 0; i < N; ++i)
n += min(cnt[N - i], cnt[N + i]);
printf("%d", n + cnt[N] / 2 - cnt[N]);
}
Makoto and a Blackboard
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#include <bits/stdc++.h>
#define FI first
#define SE second
using namespace std;
typedef long long ll;
struct Mod
{
const ll M;
Mod(ll M) : M(M) {}
ll add(ll a, ll b) const { return ((a + b) % M + M) % M; }
ll mul(ll a, ll b) const { return a * b % M; }
ll pow(ll a, ll b) const
{
ll r = 1;
for (a %= M; b; b >>= 1, a = mul(a, a))
if (b & 1)
r = mul(r, a);
return r;
}
ll inv(ll a) const { return pow(a, M - 2); }
} M(1e9 + 7);
ll n, k, ans;
int main()
{
scanf("%lld%lld", &n, &k);
vector<pair<ll, ll>> v;
ans = n;
for (ll i = 2; i * i <= n; ++i)
if (ans % i == 0)
for (v.push_back({i, 0}); ans % i == 0; ans /= i)
++v.back().SE;
if (ans > 1)
v.push_back({ans, 1}), ans = 1;
for (auto it : v)
{
vector<ll> sum(it.SE + 1, 0);
sum[it.SE] = 1;
for (ll j = 0; j < k; ++j)
{
vector<ll> f(it.SE + 1, 0);
for (ll i = 1; i <= it.SE; ++i)
f[0] = M.add(f[0], f[i] = M.mul(sum[i - 1], M.inv(i)));
sum[0] = M.add(f[0], M.mul(sum[it.SE], M.inv(it.SE + 1)));
for (ll i = 1; i <= it.SE; ++i)
sum[i] = M.add(sum[i - 1], -f[i]);
}
ll res = sum[0];
for (ll i = 1, p = 1; i <= it.SE; ++i)
res = M.add(res, M.mul(p = M.mul(p, it.FI), sum[i]));
ans = M.mul(ans, res);
}
printf("%lld", ans);
}