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// d POPs + 1 HALT, with variable g1[] and gy[]
// Use topological sort on dependency graph instead of recursive solve.
#include <bits/stdc++.h>
using namespace std;
constexpr long long P = 998244353;
int d;
int g1_arr[30]; // pop-match goto for POP j
int gy_arr[30]; // push goto for POP j
// State (i, x) for i in 0..d, x in 0..d
// For POP i (i < d):
// x == i+1: result = (g1[i], 1), depends on nothing
// x != i+1: depends on (gy[i], i+1) and then (return_of_that, x)
// For HALT (i = d):
// x == 0: result = (-1, 1)
// x != 0: depends on (d, 1) and then (return_of_that, x)
// Build dependency graph and solve topologically
// Each state (i, x) can depend on at most 2 other states.
// If there's a cycle, the program is infinite.
struct State {
int i, x;
int ret_instr;
long long cost;
bool computed;
bool in_cycle_check;
};
// Encode state as i * (d+1) + x
inline int encode(int i, int x) { return i * (d + 1) + x; }
long long eval_fast() {
int num_states = (d + 1) * (d + 1);
vector<int> ret_instr(num_states, -2); // -2 = not computed
vector<long long> cost(num_states, 0);
vector<int8_t> status(num_states, 0); // 0=unvisited, 1=in_progress, 2=done
// Iterative DFS with explicit stack
struct Frame {
int state;
int phase; // 0=initial, 1=after dep1, 2=after dep2
int dep1_state, dep2_state;
};
vector<Frame> stk;
auto get_result = [&](int s) -> pair<int, long long> {
return {ret_instr[s], cost[s]};
};
auto process = [&](int start) -> bool {
stk.push_back({start, 0, -1, -1});
while (!stk.empty()) {
auto& f = stk.back();
int s = f.state;
int i = s / (d + 1);
int x = s % (d + 1);
if (f.phase == 0) {
if (status[s] == 2) { stk.pop_back(); continue; }
if (status[s] == 1) return false; // cycle
status[s] = 1;
if (i < d) {
if (x == i + 1) {
ret_instr[s] = g1_arr[i];
cost[s] = 1;
status[s] = 2;
stk.pop_back();
continue;
} else {
f.dep1_state = encode(gy_arr[i], i + 1);
f.phase = 1;
stk.push_back({f.dep1_state, 0, -1, -1});
continue;
}
} else {
// HALT
if (x == 0) {
ret_instr[s] = -1;
cost[s] = 1;
status[s] = 2;
stk.pop_back();
continue;
} else {
f.dep1_state = encode(d, 1);
f.phase = 1;
stk.push_back({f.dep1_state, 0, -1, -1});
continue;
}
}
} else if (f.phase == 1) {
// dep1 is computed
if (status[f.dep1_state] != 2) return false;
int j = ret_instr[f.dep1_state];
if (j < 0 || j > d) {
// dep1 leads to halt, then continue with x
// Actually if j == -1, it halted.
// For POP: solve(gy[i], i+1) returned (-1, u). Then solve(-1, x) - invalid!
// This shouldn't happen in a valid program.
// If the subprogram halts, then the "return instruction" is -1.
// The next step is solve(-1, x) which is undefined.
// This means the program structure is broken.
return false;
}
f.dep2_state = encode(j, x);
f.phase = 2;
stk.push_back({f.dep2_state, 0, -1, -1});
continue;
} else {
// phase 2: both deps computed
if (status[f.dep2_state] != 2) return false;
long long u = cost[f.dep1_state];
long long v = cost[f.dep2_state];
ret_instr[s] = ret_instr[f.dep2_state];
cost[s] = (u + v + 1) % P;
status[s] = 2;
stk.pop_back();
}
}
return true;
};
if (!process(encode(0, 0))) return -1;
if (status[encode(0, 0)] != 2) return -1;
return cost[encode(0, 0)];
}
int main(int argc, char* argv[]) {
d = argc > 1 ? atoi(argv[1]) : 26;
long long target1 = 150994941;
long long target2 = 150994939;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
auto startTime = chrono::steady_clock::now();
auto elapsed_ms = [&]() {
return chrono::duration_cast<chrono::milliseconds>(chrono::steady_clock::now() - startTime).count();
};
fprintf(stderr, "Starting search d=%d...\n", d);
bool found = false;
int restarts = 0;
int valid = 0;
while (elapsed_ms() < 120000 && !found) {
restarts++;
// Initialize
for (int j = 0; j < d; j++) {
g1_arr[j] = j + 1; // standard initially
gy_arr[j] = rng() % (j + 1);
}
// Randomly modify some g1 values
int num_g1_changes = rng() % 4;
for (int c = 0; c < num_g1_changes; c++) {
int j = rng() % d;
g1_arr[j] = rng() % (d + 1);
}
long long T = eval_fast();
if (T < 0) continue;
valid++;
if (T == target1 || T == target2) {
found = true;
fprintf(stderr, "FOUND! d=%d T=%lld\n", d, T);
break;
}
// Hill climbing
for (int iter = 0; iter < 100000 && !found; iter++) {
int what = rng() % 3;
int j = rng() % d;
int sv_g1 = g1_arr[j], sv_gy = gy_arr[j];
if (what == 0) gy_arr[j] = rng() % (j + 1);
else if (what == 1) g1_arr[j] = rng() % (d + 1);
else { gy_arr[j] = rng() % (j + 1); g1_arr[j] = rng() % (d + 1); }
long long nT = eval_fast();
if (nT < 0) {
g1_arr[j] = sv_g1; gy_arr[j] = sv_gy;
continue;
}
if (nT == target1 || nT == target2) {
found = true;
T = nT;
fprintf(stderr, "FOUND! d=%d T=%lld\n", d, T);
break;
}
long long nd = min(min((nT - target1 + P) % P, (target1 - nT + P) % P),
min((nT - target2 + P) % P, (target2 - nT + P) % P));
long long od = min(min((T - target1 + P) % P, (target1 - T + P) % P),
min((T - target2 + P) % P, (target2 - T + P) % P));
if (nd <= od) T = nT;
else { g1_arr[j] = sv_g1; gy_arr[j] = sv_gy; }
}
if (restarts % 200 == 0) {
fprintf(stderr, "d=%d restart=%d valid=%d elapsed=%ldms\n", d, restarts, valid, elapsed_ms());
}
}
if (found) {
fprintf(stderr, "g1:");
for (int j = 0; j < d; j++) fprintf(stderr, " %d", g1_arr[j]);
fprintf(stderr, "\ngy:");
for (int j = 0; j < d; j++) fprintf(stderr, " %d", gy_arr[j]);
fprintf(stderr, "\n");
int n = d + 1;
printf("%d\n", n);
for (int j = 0; j < d; j++) {
printf("POP %d GOTO %d PUSH %d GOTO %d\n",
j+1, g1_arr[j]+1, j+1, gy_arr[j]+1);
}
printf("HALT PUSH 1 GOTO %d\n", n);
} else {
fprintf(stderr, "NOT FOUND d=%d after %d restarts (%d valid) in %ldms\n",
d, restarts, valid, elapsed_ms());
}
return 0;
}
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