diff options
| -rw-r--r-- | content/math/divSum.cpp | 9 | ||||
| -rw-r--r-- | test/math/divSum.cpp | 48 |
2 files changed, 57 insertions, 0 deletions
diff --git a/content/math/divSum.cpp b/content/math/divSum.cpp new file mode 100644 index 0000000..dc4bc4d --- /dev/null +++ b/content/math/divSum.cpp @@ -0,0 +1,9 @@ +// Calculates the sum of (a*i+b)/m for i=0..(n-1) in O(log(n)) +// Note that b should not be negative! +ll divSum(ll n, ll m, ll a, ll b){ + if(m == 0) return 0; + ll ans = a/m * n*(n-1) / 2 + b/m * n; + a %= m, b %= m; + ll y = (a*(n-1)+b)/m; + return ans + y*(n-1) - divSum(y, a, m, m-b-1); +}
\ No newline at end of file diff --git a/test/math/divSum.cpp b/test/math/divSum.cpp new file mode 100644 index 0000000..1f82387 --- /dev/null +++ b/test/math/divSum.cpp @@ -0,0 +1,48 @@ +#include "../util.h" +#include <math/divSum.cpp> + +ll naive(ll n, ll m, ll a, ll b){ + ll ans = 0; + for(ll i = 0; i < n; i++){ + ans += (a*i+b)/m; + } + return ans; +} + +void stress_test() { + ll queries = 0; + for (ll i = 0; i < 10'000; i++) { + int n = Random::integer<int>(1, 100); + int m = Random::integer<int>(1, 100); + int a = Random::integer<int>(0, 100); + int b = Random::integer<int>(0, 100); + ll expected = naive(n, m, a, b); + ll got = divSum(n, m, a, b); + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + queries++; + } + cerr << "tested queries: " << queries << endl; +} + +constexpr int N = 1'000'000; +void performance_test() { + timer t; + hash_t hash = 0; + for (int operations = 0; operations < N; operations++) { + ll n = Random::integer<ll>(1, 1'000'000'000); + ll m = Random::integer<ll>(1, 1'000'000'000); + ll a = Random::integer<ll>(0, 1'000'000'000); + ll b = Random::integer<ll>(0, 1'000'000'000); + t.start(); + hash += divSum(n, m, a, b); + t.stop(); + } + if (t.time > 750) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(); + performance_test(); +} + |