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Improve floor_sum #114

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5d41c79
Improve floor_sum
mizar Jan 21, 2023
1b48ab9
Fix comment in math
mizar Jan 21, 2023
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12 changes: 5 additions & 7 deletions src/math.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -135,7 +135,7 @@ pub fn crt(r: &[i64], m: &[i64]) -> (i64, i64) {
// r2 % m0 = r0
// r2 % mi = ri
// -> (r0 + x*m0) % mi = ri
// -> x*u0*g % (u1*g) = (ri - r0) (u0*g = m0, u1*g = mi)
// -> x*u0*g = ri-r0 (mod u1*g) (u0*g = m0, u1*g = mi)
// -> x = (ri - r0) / g * inv(u0) (mod u1)

// im = inv(u0) (mod u1) (0 <= im < u1)
Expand Down Expand Up @@ -188,21 +188,19 @@ pub fn crt(r: &[i64], m: &[i64]) -> (i64, i64) {
pub fn floor_sum(n: i64, m: i64, mut a: i64, mut b: i64) -> i64 {
let mut ans = 0;
if a >= m {
ans += (n - 1) * n * (a / m) / 2;
ans += (n - 1) * n / 2 * (a / m);
a %= m;
}
if b >= m {
ans += n * (b / m);
b %= m;
}

let y_max = (a * n + b) / m;
let x_max = y_max * m - b;
if y_max == 0 {
let y_max = a * n + b;
if y_max < m {
return ans;
}
ans += (n - (x_max + a - 1) / a) * y_max;
ans += floor_sum(y_max, a, m, (a - x_max % a) % a);
ans += floor_sum(y_max / m, a, m, y_max % m);
ans
}

Expand Down