tests/Min_of_Mod_of_Linear.test.cpp

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Last update: 2025-11-28 02:09:51+07:00
Problem: https://judge.yosupo.jp/problem/min_of_mod_of_linear

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/min_of_mod_of_linear"

#include "../misc/macros.h"
#include "../math/DivModSum.h"

void solve() {
  int n, m, a, b;
  cin >> n >> m >> a >> b;
  cout << minmod(n, m, a, b) << '\n';
}

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int tc;
  cin >> tc;
  while (tc--) solve();
}

#line 1 "tests/Min_of_Mod_of_Linear.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/min_of_mod_of_linear"

#line 1 "misc/macros.h"
// #pragma GCC optimize("Ofast,unroll-loops")       // unroll long, simple loops
// #pragma GCC target("avx2,fma")                   // vectorizing code
// #pragma GCC target("lzcnt,popcnt,abm,bmi,bmi2")  // for fast bitset operation

#include <bits/extc++.h>
#include <tr2/dynamic_bitset>

using namespace std;
using namespace __gnu_pbds;  // ordered_set, gp_hash_table
// using namespace __gnu_cxx; // rope

// for templates to work
#define all(x) (x).begin(), (x).end()
#define sz(x) (int) (x).size()
#define pb push_back
#define eb emplace_back
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
using ld = long double;
using pii = pair<i32, i32>;
using vi = vector<i32>;

// fast map
const int RANDOM = chrono::high_resolution_clock::now().time_since_epoch().count();
struct chash {  // customize hash function for gp_hash_table
  int operator()(int x) const { return x ^ RANDOM; }
};
gp_hash_table<int, int, chash> table;

/* ordered set
    find_by_order(k): returns an iterator to the k-th element (0-based)
    order_of_key(k): returns the number of elements in the set that are strictly less than k
*/
template <class T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

/*  rope
    rope <int> cur = v.substr(l, r - l + 1);
    v.erase(l, r - l + 1);
    v.insert(v.mutable_begin(), cur);
*/
#line 1 "math/DivModSum.h"
// Tính sum_{x=0}^{n-1} floor((a*x + b) / m)
u64 divsum(u64 n, u64 m, i64 a, i64 b) {
  u64 ans = 0;
  if (a < 0) {
    i64 a2 = (a % (i64) m + m) % m;
    ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m), a = a2;
  }
  if (b < 0) {
    i64 b2 = (b % (i64) m + m) % m;
    ans -= 1ULL * n * ((b2 - b) / m), b = b2;
  }
  u64 ua = a, ub = b;
  while (true) {
    if (ua >= m) ans += (n - 1) * n / 2 * (ua / m), ua %= m;
    if (ub >= m) ans += n * (ub / m), ub %= m;
    u64 y_max = ua * n + ub;
    if (y_max < m) break;
    n = y_max / m, ub = y_max % m, swap(m, ua);
  }
  return ans;
}

// Tính sum_{x=0}^{n-1} ((a*x + b) % m)
u64 modsum(u64 n, u64 m, i64 a, i64 b) {
  i128 sum = (i128) a * n * (n - 1) / 2 + (i128) b * n;
  return (u64) (sum - (i128) m * divsum(n, m, a, b));
}

// Tính min_{x=0}^{n-1} ((a*x + b) % m)
i64 minmod(u64 n, u64 m, i64 a, i64 b) {
  i64 lo = 0, hi = m - 1, ans = b;
  while (lo <= hi) {
    auto mid = (lo + hi) / 2;
    auto cnt = divsum(n, m, a, b) - divsum(n, m, a, b - mid - 1);
    if (cnt > 0) ans = mid, hi = mid - 1;
    else lo = mid + 1;
  }
  return ans;
}
#line 5 "tests/Min_of_Mod_of_Linear.test.cpp"

void solve() {
  int n, m, a, b;
  cin >> n >> m >> a >> b;
  cout << minmod(n, m, a, b) << '\n';
}

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int tc;
  cin >> tc;
  while (tc--) solve();
}