diff --git a/algorithms/math/chinese_remainder_theorem.cpp b/algorithms/math/chinese_remainder_theorem.cpp
index a28c5d27baf5f8e2dd20e88624eb6216869e041c..8e3f5de86a5a1a0d87be80ef13282ec9bc8cb97c 100644
--- a/algorithms/math/chinese_remainder_theorem.cpp
+++ b/algorithms/math/chinese_remainder_theorem.cpp
@@ -16,7 +16,10 @@
/// - It is very easy to get overflow, since the $LCM$ is computed from
/// all $m_i$, BigInt or Python should be considered if inputs are too large
-ll norm(ll a, ll b) { return (a + b) % b; }
+ll norm(ll a, ll b) {
+ a %= b;
+ return (a < 0) ? a + b : a;
+}
pair<ll,ll> crt_single(ll a, ll n, ll b, ll m) {
ans_t e = ext_gcd(n, m);
@@ -24,24 +27,24 @@ pair<ll,ll> crt_single(ll a, ll n, ll b, ll m) {
if ((a - b) % e.d != 0)
return {-1,-1}; // No solution
- ll ans = norm(a + e.x*(b-a) / e.d % (m/e.d)*n, n *m / e.d);
- ll lcm = (n*m) / e.d;
+ ll lcm = (m/e.d) * n;
+ ll ans = norm(a + e.x*(b-a) / e.d % (m/e.d)*n, lcm);
return {norm(ans, lcm), lcm};
}
ll crt(vector<ll> a, vector<ll> m) {
- ll res = a[0];
+ ll ans = a[0];
ll lcm = m[0];
- int t = s.size();
+ int t = a.size();
for (int i = 1; i < t; ++i) {
- auto ss = crt(res, lcm, a[i], m[i]);
+ auto ss = crt_single(ans, lcm, a[i], m[i]);
if (ss.fi == -1)
return -1; // No solution
- res = ss.fi;
+ ans = ss.fi;
lcm = ss.se;
}
- return res;
+ return ans;
}
diff --git a/caderno.pdf b/caderno.pdf
index aa8baf52d7e241dfcb6f1668061ae0b42606296c..fc4729e8045c647ef5f437a46b407711e31e7563 100644
Binary files a/caderno.pdf and b/caderno.pdf differ
diff --git a/contests/ICPC_LA18/F.cpp b/contests/ICPC_LA18/F.cpp
index 48d59be9b56b74fac067afb16a1e854b47170a42..712db75f6c92a968fa4cb14392dbc3e876affcf8 100644
--- a/contests/ICPC_LA18/F.cpp
+++ b/contests/ICPC_LA18/F.cpp
@@ -19,435 +19,87 @@ using namespace std;
using ll = long long;
using ii = pair<ll,ll>;
-vector<ll> karatsuba(const vector<ll> &a,
- const vector<ll> &b)
-{
- int n = a.size();
- vector<ll> res(n + n);
+struct ans_t { ll x, y, d; };
- if (n <= 32) {
- for (int i = 0; i < n; i++)
- for (int j = 0; j < n; j++)
- res[i + j] += a[i] * b[j];
-
- return res;
- }
-
- int k = n >> 1;
- vector<ll> a1(a.begin(), a.begin() + k);
- vector<ll> a2(a.begin() + k, a.end());
- vector<ll> b1(b.begin(), b.begin() + k);
- vector<ll> b2(b.begin() + k, b.end());
-
- vector<ll> a1b1 = karatsuba(a1, b1);
- vector<ll> a2b2 = karatsuba(a2, b2);
-
- for (int i = 0; i < k; i++)
- a2[i] += a1[i];
- for (int i = 0; i < k; i++)
- b2[i] += b1[i];
-
- vector<ll> r = karatsuba(a2, b2);
- for (int i = 0; i < a1b1.size(); i++)
- r[i] -= a1b1[i];
- for (int i = 0; i < a2b2.size(); i++)
- r[i] -= a2b2[i];
-
- for (int i = 0; i < r.size(); i++)
- res[i + k] += r[i];
- for (int i = 0; i < a1b1.size(); i++)
- res[i] += a1b1[i];
- for (int i = 0; i < a2b2.size(); i++)
- res[i + n] += a2b2[i];
-
- return res;
-}
-
-const int base = 1000000000;
-const int base_d = 9;
-
-struct BigInt {
- int sign;
- vector<int> num;
-
- BigInt() : sign(1) {}
- BigInt(ll x) { *this = x; }
-
- void operator=(const BigInt &x) {
- sign = x.sign;
- num = x.num;
- }
-
- void operator=(ll x) {
- sign = 1;
- if (x < 0) sign = -1, x = -x;
- for (; x > 0; x /= base)
- pb(x % base);
- }
-
- BigInt operator+(const BigInt &x) const {
- if (sign != x.sign) return *this - (-x);
-
- int carry = 0;
- BigInt res = x;
-
- for (int i = 0; i < max(size(), x.size()) || carry; ++i) {
- if (i == (int) res.size())
- res.push_back(0);
-
- res[i] += carry + (i < size() ? num[i] : 0);
- carry = res[i] >= base;
- if (carry) res[i] -= base;
- }
-
- return res;
- }
-
- BigInt operator-(const BigInt &x) const {
- if (sign != x.sign) return *this + (-x);
- if (abs() < x.abs()) return -(x - *this);
-
- int carry = 0;
- BigInt res = *this;
-
- for (int i = 0; i < x.size() || carry; ++i) {
- res[i] -= carry + (i < x.size() ? x[i] : 0);
- carry = res[i] < 0;
- if (carry) res[i] += base;
- }
-
- res.trim();
- return res;
- }
-
- void operator*=(int x) {
- if (x < 0) sign = -sign, x = -x;
-
- int carry = 0;
- for (int i = 0; i < size() || carry; ++i) {
- if (i == size()) pb(0);
- ll cur = num[i] * (ll) x + carry;
-
- carry = (int) (cur / base);
- num[i] = (int) (cur % base);
- }
-
- trim();
- }
-
- BigInt operator*(int x) const {
- BigInt res = *this;
- res *= x;
- return res;
- }
-
- friend pair<BigInt, BigInt> divmod(const BigInt &a1,
- const BigInt &b1)
- {
- int norm = base / (b1.back() + 1);
- BigInt a = a1.abs() * norm;
- BigInt b = b1.abs() * norm;
- BigInt q, r;
- q.resize(a.size());
-
- for (int i = a.size() - 1; i >= 0; i--) {
- r *= base;
- r += a[i];
-
- int s1 = r.size() <= b.size() ? 0 : r[b.size()];
- int s2 = r.size() <= b.size() - 1 ? 0 : r[b.size() - 1];
- int d = ((ll) base * s1 + s2) / b.back();
-
- r -= b * d;
- while (r < 0) r += b, --d;
- q[i] = d;
- }
-
- q.sign = a1.sign * b1.sign;
- r.sign = a1.sign;
- q.trim(); r.trim();
-
- return make_pair(q, r / norm);
- }
-
- BigInt operator/(const BigInt &x) const {
- return divmod(*this, x).fi;
- }
-
- BigInt operator%(const BigInt &x) const {
- return divmod(*this, x).se;
- }
-
- void operator/=(int x) {
- if (x < 0) sign = -sign, x = -x;
-
- for (int i = size() - 1, rem = 0; i >= 0; --i) {
- ll cur = num[i] + rem * (ll) base;
- num[i] = (int) (cur / x);
- rem = (int) (cur % x);
- }
-
- trim();
- }
-
- BigInt operator/(int x) const {
- BigInt res = *this;
- res /= x;
- return res;
- }
-
- int operator%(int x) const {
- if (x < 0) x = -x;
-
- int m = 0;
- for (int i = size() - 1; i >= 0; --i)
- m = (num[i] + m * (ll) base) % x;
-
- return m * sign;
- }
-
- void operator+=(const BigInt &x) { *this = *this + x; }
- void operator-=(const BigInt &x) { *this = *this - x; }
- void operator*=(const BigInt &x) { *this = *this * x; }
- void operator/=(const BigInt &x) { *this = *this / x; }
-
- bool operator<(const BigInt &x) const {
- if (sign != x.sign)
- return sign < x.sign;
-
- if (size() != x.size())
- return size() * sign < x.size() * x.sign;
-
- for (int i = size() - 1; i >= 0; i--)
- if (num[i] != x[i])
- return num[i] * sign < x[i] * sign;
-
- return false;
- }
-
- bool operator>(const BigInt &x) const {
- return x < *this;
- }
- bool operator<=(const BigInt &x) const {
- return !(x < *this);
- }
- bool operator>=(const BigInt &x) const {
- return !(*this < x);
- }
- bool operator==(const BigInt &x) const {
- return !(*this < x) && !(x < *this);
- }
- bool operator!=(const BigInt &x) const {
- return *this < x || x < *this;
- }
-
- void trim() {
- while (!empty() && !back()) pop_back();
- if (empty()) sign = 1;
- }
-
- bool is_zero() const {
- return empty() || (size() == 1 && !num[0]);
- }
-
- BigInt operator-() const {
- BigInt res = *this;
- res.sign = -sign;
- return res;
- }
-
- BigInt abs() const {
- BigInt res = *this;
- res.sign *= res.sign;
- return res;
- }
-
- ll to_long() const {
- ll res = 0;
- for (int i = size() - 1; i >= 0; i--)
- res = res * base + num[i];
- return res * sign;
- }
-
- void read(const string &s) {
- sign = 1;
- num.clear();
-
- int pos = 0;
- while (pos < s.size() &&
- (s[pos] == '-' || s[pos] == '+')) {
- if (s[pos] == '-')
- sign = -sign;
- ++pos;
- }
-
- for (int i = s.size() - 1; i >= pos; i -= base_d) {
- int x = 0;
- for (int j = max(pos, i - base_d + 1); j <= i; j++)
- x = x * 10 + s[j] - '0';
- num.push_back(x);
- }
-
- trim();
- }
-
- friend istream& operator>>(istream &stream, BigInt &v) {
- string s; stream >> s;
- v.read(s);
- return stream;
- }
-
- friend ostream& operator<<(ostream &stream, const BigInt &x) {
- if (x.sign == -1)
- stream << '-';
-
- stream << (x.empty() ? 0 : x.back());
- for (int i = x.size() - 2; i >= 0; --i)
- stream << setw(base_d) << setfill('0') << x.num[i];
-
- return stream;
- }
-
- static vector<int> convert_base(
- const vector<int> &a,
- int oldd, int newd) {
- vector<ll> p(max(oldd, newd) + 1);
- p[0] = 1;
- for (int i = 1; i < p.size(); i++)
- p[i] = p[i - 1] * 10;
-
- ll cur = 0;
- int curd = 0;
- vector<int> res;
-
- for (int i = 0; i < a.size(); i++) {
- cur += a[i] * p[curd];
- curd += oldd;
-
- while (curd >= newd) {
- res.pb(int(cur % p[newd]));
- cur /= p[newd];
- curd -= newd;
- }
- }
-
- res.pb((int) cur);
- while (!res.empty() && !res.back())
- res.pop_back();
- return res;
- }
-
- BigInt operator*(const BigInt &x) const {
- vector<int> a6 = convert_base(this->num, base_d, 6);
- vector<int> b6 = convert_base(x.num, base_d, 6);
-
- vector<ll> a(all(a6));
- vector<ll> b(all(b6));
-
- while (a.size() < b.size()) a.pb(0);
- while (b.size() < a.size()) b.pb(0);
- while (a.size() & (a.size() - 1))
- a.pb(0), b.pb(0);
-
- vector<ll> c = karatsuba(a, b);
-
- BigInt res;
- int carry = 0;
- res.sign = sign * x.sign;
-
- for (int i = 0; i < c.size(); i++) {
- ll cur = c[i] + carry;
- res.pb((int) (cur % 1000000));
- carry = (int) (cur / 1000000);
- }
-
- res.num = convert_base(res.num, 6, base_d);
- res.trim();
- return res;
- }
-
- // Handles vector operations.
- int back() const { return num.back(); }
- bool empty() const { return num.empty(); }
- size_t size() const { return num.size(); }
-
- void pop_back() { num.pop_back(); }
- void resize(int x) { num.resize(x); }
- void push_back(int x) { num.push_back(x); }
-
- int &operator[](int i) { return num[i]; }
- int operator[](int i) const { return num[i]; }
-};
-
-using pb = pair<BigInt,BigInt>;
-
-template <typename T>
-struct ans_t { T x, y, d; };
-
-template <typename T>
-ans_t<T> ext_gcd(T a, T b) {
+ans_t ext_gcd(ll a, ll b) {
if (a == 0) return {0, 1, b};
- ans_t<T> e = ext_gcd(b % a, a);
+ ans_t e = ext_gcd(b % a, a);
return {e.y - (b/a) * e.x, e.x, e.d};
}
-template <typename T>
-T norm(T a, T b) {
- return (a + b) % b;
+ll norm(ll a, ll b) {
+ a %= b;
+ return (a < 0) ? a + b : a;
}
-template <typename T>
-pb crt(T a, T n, T b, T m) {
- ans_t<T> e = ext_gcd(n, m);
+pair<ll,ll> crt_single(ll a, ll n, ll b, ll m) {
+ ans_t e = ext_gcd(n, m);
if ((a - b) % e.d != 0)
return {-1,-1};
- T ans = norm(a + e.x*(b-a) / e.d % (m/e.d)*n, n *m / e.d);
- T lcm = (n*m) / e.d;
+ ll lcm = (m/e.d) * n;
+ ll ans = norm(a + e.x*(b-a) / e.d % (m/e.d)*n, lcm);
return {norm(ans, lcm), lcm};
}
+ll crt(vector<ll> a, vector<ll> m) {
+ ll ans = a[0];
+ ll lcm = m[0];
+
+ int t = a.size();
+ for (int i = 1; i < t; ++i) {
+ auto ss = crt_single(ans, lcm, a[i], m[i]);
+ if (ss.fi == -1)
+ return -1;
+
+ ans = ss.fi;
+ lcm = ss.se;
+ }
+
+ return ans;
+}
+
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
int b, z; cin >> b >> z;
vector<vector<int>> mat(b, vector<int>(z+1));
- for (int i = 0; i < b; ++i)
- for (int j = 0; j <= z; ++j)
- cin >> mat[i][j];
-
vector<vector<int>> time(z+1, vector<int>(501));
+ vector<vector<ll>> a(z + 1, vector<ll>(b, -1));
+ vector<vector<ll>> m(z + 1, vector<ll>(b, -1));
+
+ for (auto &i : mat)
+ for (auto &j : i) cin >> j;
+
for (int i = 0; i < b; ++i) {
int curr = mat[i][0];
time[curr][0] |= (1 << i);
+
for (int t = 1; t <= 500; ++t) {
curr = mat[i][curr];
time[curr][t] |= (1 << i);
}
}
- vector<vector<int>> a(z + 1, vector<int>(b, -1));
- vector<vector<int>> m(z + 1, vector<int>(b, -1));
for (int i = 1; i <= z; ++i) {
for (int t = 0; t <= 500; ++t) {
if (time[i][t] == (1 << b) - 1)
return cout << i << " " << t << ende, 0;
- for (int j = 0; j < b; ++j) {
+ for (int j = 0; j < b; ++j)
if (time[i][t] & (1 << j)) {
if (a[i][j] == -1)
a[i][j] = t;
else if (m[i][j] == -1)
m[i][j] = t - a[i][j];
}
- }
}
}
- int zoo = 0;
- BigInt ans = llinf*2;
+ ll zoo = 0;
+ ll ans = llinf*2;
for (int i = 1; i <= z; ++i) {
bool poss = true;
for (int j = 0; j < b; ++j)
@@ -456,24 +108,14 @@ int main() {
break;
}
- if (!poss) continue;
-
- BigInt res = a[i][0];
- BigInt lcm = m[i][0];
- for (int j = 1; j < b; ++j) {
- pb ss = crt(res, lcm, BigInt(a[i][j]), BigInt(m[i][j]));
- if (ss.fi == -1) {
- poss = false;
- break;
- }
-
- res = ss.fi;
- lcm = ss.se;
- }
+ if (!poss)
+ continue;
- if (!poss) continue;
+ ll res = crt(a[i], m[i]);
+ if (res == -1)
+ continue;
else {
- if (ans > res)
+ if (ans > res && res > 0)
zoo = i, ans = res;
}
}