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#include "../util.h"
constexpr ll iINFnf = LL::INF;
#include <other/knuth.cpp>
vector<vector<ll>> gen(int n) {
vector<vector<ll>> res(n, vector<ll>(n));
ll mi = 0;
for (ll a = n-1; a >= 0; a--) {
for (ll c = n-1; c >= a; c--) {
for (ll b = a; b <= c; b++) {
for (ll d = c; d < n; d++) {
res[a][c] = min(res[a][c], res[a][d] + res[b][c] - res[b][d]);
}
}
res[a][c] -= Random::integer<ll>(0, 1000);
mi = min(mi, res[a][c]);
}
}
for (auto& v : res) for (auto& x : v) x -= mi;
for (ll a = 0; a < n; a++) {
for (ll b = a; b < n; b++) {
for (ll c = b; c < n; c++) {
for (ll d = c; d < n; d++) {
if (res[a][d] < 0 || res[a][d] + res[b][c] < res[a][c] + res[b][d]) {
cerr << "invalid C array!" << FAIL;
}
}
}
}
}
return res;
}
vector<vector<ll>> genQuick(int n) {
vector<vector<ll>> res(n, vector<ll>(n));
for (ll a = n-1; a >= 0; a--) {
for (ll c = n-1; c >= a; c--) {
res[a][c] = (c-a) * (c - a) + Random::integer<ll>(0, 2);
}
}
return res;
}
/*ll naive(int n, int m, const vector<vector<ll>>& C) {
vector<vector<ll>> state(m+1, vector<ll>(n+1, INF));
state[0][0] = 0;
for (int i = 1; i <= m; i++) {
for (int j = 1; j <= n; j++) {
for (int k = 1; k <= j; k++) {
state[i][j] = min(state[i][j], state[i-1][k-1] + C[k-1][j-1]);
}
}
}
return state[m][n];
}*/
vector<ll> naive(int n, const vector<vector<ll>>& C) {
vector<vector<ll>> state(n+1, vector<ll>(n+1, INF));
state[0][0] = 0;
vector<ll> res(n+1, INF);
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
for (int k = 1; k <= j; k++) {
state[i][j] = min(state[i][j], state[i-1][k-1] + C[k-1][j-1]);
}
}
res[i] = state[i][n];
}
return res;
}
void stress_test() {
ll tests = 0;
for (ll i = 0; i < 1000; i++) {
auto n = Random::integer(10, 20);
auto C = gen(n);
auto expected = naive(n, C);
for (ll m = 1; m <= n; m++) {
auto got = calc(n, m, C);
if (got != expected[m]) cerr << "got: " << got << ", expected: " << expected[m] << FAIL;
tests++;
}
}
cerr << "tested random queries: " << tests << endl;
}
constexpr int N = 5000;
void performance_test() {
timer t;
auto C = genQuick(N);
t.start();
auto hash = calc(N, N/2, C);
t.stop();
if (t.time > 500) cerr << "too slow: " << t.time << FAIL;
cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl;
}
int main() {
stress_test();
performance_test();
}
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