# Educational Codeforces Round 64 (Rated for Div. 2)

A 题出锅所以 Unrated 了…于是愉快的去睡觉了。

## Inscribed Figures

#include <bits/stdc++.h>
using namespace std;
int n, ans, a[127];
int main()
{
scanf("%d%d", &n, &a[0]);
for (int i = 1; i < n; ++i)
{
scanf("%d", &a[i]);
if (a[i - 1] != 1 && a[i] != 1)
return printf("Infinite"), 0;
ans += a[i] + a[i - 1];
if (i > 1 && a[i] == 2 && a[i - 1] == 1 && a[i - 2] == 3)
--ans;
}
printf("Finite\n%d", ans);
}


## Ugly Pairs

#include <bits/stdc++.h>
using namespace std;
int main()
{
int t;
for (cin >> t; t--;)
{
string s, r[2];
cin >> s;
sort(s.begin(), s.end());
for (auto c : s)
r[c & 1] += c;
if (r[0].empty() || r[1].empty())
cout << r[0] + r[1] << '\n';
else if (abs(r[0].back() - r[1].front()) != 1)
cout << r[0] + r[1] << '\n';
else if (abs(r[1].back() - r[0].front()) != 1)
cout << r[1] + r[0] << '\n';
else
}
}


## Match Points

#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 9;
int n, z, k, x[N];
int main()
{
scanf("%d%d", &n, &z);
for (int i = 0; i < n; ++i)
scanf("%d", &x[i]);
sort(x, x + n);
for (int i = 0; i < n; ++i)
if (x[i] - x[k] >= z)
++k;
printf("%d", min(k, n / 2));
}


## 0-1-Tree

#include <bits/stdc++.h>
using namespace std;
struct UnionfindSet : vector<int>
{
vector<int> siz;
UnionfindSet(int n) : vector<int>(n), siz(n, 1)
{
for (int i = 0; i < n; ++i)
at(i) = i;
}
void merge(int u, int w)
{
siz[at(w) = u] += siz[w];
}
int ask(int u) { return at(u) != u ? at(u) = ask(at(u)) : u; }
};
int main()
{
int n;
scanf("%d", &n);
UnionfindSet ufs[2]{n, n};
for (int i = 1, x, y, z; i < n; ++i)
{
scanf("%d%d%d", &x, &y, &z);
ufs[z].merge(x - 1, y - 1);
}
long long ans = 0;
for (int i = 0; i < n; ++i)
printf("%lld", ans);
}


## Special Segments of Permutation

#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 9;
int n, ans, p[N], b[N], l[N], r[N];
int main()
{
scanf("%d", &n);
p[0] = p[n + 1] = n + 1;
for (int i = 1; i <= n; ++i)
{
scanf("%d", &p[i]);
b[p[i]] = i;
for (l[i] = i - 1; p[l[i]] < p[i];)
l[i] = l[l[i]];
}
for (int i = n; i; --i)
{
for (r[i] = i + 1; p[r[i]] < p[i];)
r[i] = r[r[i]];
int s1 = l[i], t1 = i, s2 = i, t2 = r[i];
if (t1 - s1 > t2 - s2)
swap(s1, s2), swap(t1, t2);
for (int j = s1 + 1; j < t1; ++j)
if (s2 < b[p[i] - p[j]] && b[p[i] - p[j]] < t2)
++ans;
}
printf("%d", ans);
}


## Card Bag

#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 9;
typedef long long ll;
struct Mod
{
const ll M;
Mod(ll M) : M(M) {}
ll qadd(ll a, ll b) const { return a += b, a < M ? a : a - M; }
ll add(ll a, ll b) const { return qadd((a + b) % M, M); }
ll mul(ll a, ll b) const { return add(a * b, 0); }
};
struct Factorial : Mod
{
vector<ll> fac, ifac;
Factorial(int N, ll M) : fac(N, 1), ifac(N, 1), Mod(M)
{
for (int i = 2; i < N; ++i)
fac[i] = mul(fac[i - 1], i), ifac[i] = mul(M - M / i, ifac[M % i]);
for (int i = 2; i < N; ++i)
ifac[i] = mul(ifac[i], ifac[i - 1]);
}
} f(N, 998244353);
int n, ans, cnt[N], dp[N];
int main()
{
scanf("%d", &n);
for (int i = 0, t; i < n; ++i)
scanf("%d", &t), ++cnt[t];
for (int i = dp[0] = 1, tot = 0; i <= n; ++i)
if (cnt[i])
for (int j = tot++, t = f.mul(f.mul(cnt[i], cnt[i] - 1), f.ifac[n]); ~j; --j)
ans = f.qadd(ans, f.mul(f.mul(t, f.fac[n - j - 2]), dp[j])),
dp[j + 1] = f.qadd(dp[j + 1], f.mul(cnt[i], dp[j]));
printf("%d", ans);
}


## Optimizer

#include <bits/stdc++.h>
using namespace std;
typedef unsigned long long ll;
const int N = 1023;
set<int> vec[N];
map<string, int> mmp;
vector<string> ans;
ll Key[N];
set<string> used;
string a[N], b[N], c[N], op(N, '='), alphabet("abcdefghijklmnopqrstuvwxyz1234567890");
string solve(const string &res, int n)
{
if (!mmp.count(res))
return res;
int p = mmp[res];
auto it = vec[p].lower_bound(n);
if (it == vec[p].begin())
return res;
n = *--it;
static map<ll, string> calced;
if (calced.count(Key[n]))
return calced[Key[n]];
if (op[n] == '=')
return calced[Key[n]] = solve(b[n], n);
string ret("aaaa");
while (isdigit(ret[0]) || used.count(ret))
for (int i = 0; i < 4; ++i)
ret[i] = alphabet[rand() % alphabet.size()];
used.insert(ret);
ans.push_back(ret + '=' + solve(b[n], n) + op[n] + solve(c[n], n));
return calced[Key[n]] = ret;
}
ll calc(ll a, ll b, char c) { return (a + c * 3131441) * (b + c * 2332424); }
int main()
{
map<string, ll> key;
int n;
cin >> n;
for (int i = 1, p; i <= n; ++i)
{
string str;
cin >> str;
for (int j = p = 0; j < str.size(); ++j)
{
if (str[j] == '=')
p = j, a[i] = str.substr(0, j);
else if (str[j] == '\$' || str[j] == '^' || str[j] == '#' || str[j] == '&')
b[i] = str.substr(p + 1, j - p - 1), c[i] = str.substr(j + 1, str.size() - j - 1), op[i] = str[j];
}
if (op[i] == '=')
b[i] = str.substr(p + 1, str.size() - p - 1);
if (!key.count(b[i]))
key[b[i]] = key.size();
if (!c[i].empty() && !key.count(c[i]))
key[c[i]] = key.size();
if (op[i] == '=')
key[a[i]] = key[b[i]];
else
key[a[i]] = calc(key[b[i]], key[c[i]], op[i]);
Key[i] = key[a[i]];
used.insert(a[i]);
used.insert(b[i]);
used.insert(c[i]);
if (!mmp.count(a[i]))
mmp[a[i]] = i;
vec[mmp[a[i]]].insert(i);
}
string r = solve("res", n + 1);
if (r != "res")
{
for (int i = ans.size() - 1; ~i; --i)
if (~ans[i].find(r))
{
ans[i].replace(0, r.size(), "res");
cout << ans.size() << '\n';
for (auto i : ans)
cout << i << "\n";
return 0;
}
ans.push_back("res=" + r);
}
cout << ans.size() << '\n';
for (auto i : ans)
cout << i << '\n';
}