File size: 6,674 Bytes
1fd0050 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 | #include <bits/stdc++.h>
using namespace std;
static const long long P = 998244353;
// Use fixed-size array for speed
long long Sv[35];
inline long long computeT(int d, const int* gy) {
Sv[0] = 0;
for (int j = 0; j < d; j++) {
long long c = ((Sv[j] - Sv[gy[j]] + (j - gy[j]) + 1) % P + P) % P;
Sv[j + 1] = (Sv[j] + c) % P;
}
return (Sv[d] + d + 1) % P;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
long long k;
cin >> k;
if (k == 1) {
cout << "1\nHALT PUSH 1 GOTO 1\n";
return 0;
}
long long S = (k - 1) / 2;
long long kmodP = k % P;
// Strategy A: Exact single-modification block
int exactD = -1, exactG = -1;
for (int g = 0; g <= 31; g++) {
long long val = S + (1LL << g);
if (val > 0 && val <= (1LL << 31) && (val & (val - 1)) == 0) {
int d = __builtin_ctzll(val);
if (d > g && (exactD < 0 || d < exactD)) {
exactD = d;
exactG = g;
}
}
}
int bestN = (exactD > 0) ? exactD + 1 : 999;
// Strategy B: Hill climbing mod P
int hillD = -1;
int hillGy[35];
int maxTrialD = min(bestN - 2, 30);
mt19937 rng((unsigned)(kmodP * 1000003ULL + 42));
auto startTime = chrono::steady_clock::now();
auto elapsed_ms = [&]() {
return chrono::duration_cast<chrono::milliseconds>(chrono::steady_clock::now() - startTime).count();
};
int gy[35];
// Determine minimum possible d:
// For d where 2^(d+1) < P: computation is exact, max T = 2^(d+1)-1.
// Skip d where kmodP > 2^(d+1)-1 (impossible).
// For d where 2^(d+1) >= P: modular arithmetic applies, any target possible in theory.
int minPossibleD = 1;
for (int d = 1; d <= 30; d++) {
long long maxT;
if (d + 1 < 30) { // 2^(d+1) fits in long long and < P
maxT = (1LL << (d + 1)) - 1;
if (maxT < P && kmodP > maxT) {
minPossibleD = d + 1;
continue;
}
}
break;
}
// Try d values from smallest possible
for (int d = max(minPossibleD, 15); d <= maxTrialD; d++) {
bool found = false;
// Allocate time based on d
int timeLimit;
if (d <= minPossibleD + 2) timeLimit = 800; // Give the smallest possible d the most time
else if (d <= minPossibleD + 4) timeLimit = 400;
else timeLimit = 100;
// Don't exceed total time budget
if (elapsed_ms() > 1800) timeLimit = min(timeLimit, 50);
int startMs = (int)elapsed_ms();
for (int restart = 0; !found; restart++) {
if ((int)elapsed_ms() - startMs > timeLimit) break;
memset(gy, 0, sizeof(int) * d);
for (int j = 1; j < d; j++) gy[j] = rng() % (j + 1);
long long T = computeT(d, gy);
int maxIter = 20000;
for (int iter = 0; iter < maxIter; iter++) {
if (T == kmodP) { found = true; break; }
int j = 1 + rng() % (d - 1);
int og = gy[j];
int ng = rng() % (j + 1);
if (ng == og) continue;
gy[j] = ng;
long long nT = computeT(d, gy);
long long nd = min((nT - kmodP + P) % P, (kmodP - nT + P) % P);
long long od = min((T - kmodP + P) % P, (kmodP - T + P) % P);
if (nd <= od) { T = nT; }
else { gy[j] = og; }
}
if (!found) {
T = computeT(d, gy);
if (T == kmodP) found = true;
}
if (found) {
hillD = d;
memcpy(hillGy, gy, sizeof(int) * d);
break;
}
}
if (found) break;
}
if (hillD > 0 && hillD + 1 < bestN) {
bestN = hillD + 1;
cout << bestN << "\n";
for (int j = 0; j < hillD; j++) {
cout << "POP " << (j+1) << " GOTO " << (j+2)
<< " PUSH " << (j+1) << " GOTO " << (hillGy[j]+1) << "\n";
}
cout << "HALT PUSH 1 GOTO " << bestN << "\n";
return 0;
}
if (exactD > 0) {
cout << bestN << "\n";
for (int j = 0; j < exactD; j++) {
int g = (j == exactD - 1) ? exactG : 0;
cout << "POP " << (j+1) << " GOTO " << (j+2)
<< " PUSH " << (j+1) << " GOTO " << (g+1) << "\n";
}
cout << "HALT PUSH 1 GOTO " << bestN << "\n";
return 0;
}
// Strategy C: Additive blocks fallback
{
int best_cost = 999;
vector<int> best_dep;
for (int m = 1; m <= 200; m++) {
long long T = S + m;
if (T & 1) continue;
if (T < 2LL * m) continue;
vector<int> bits;
for (int b = 1; b <= 40; b++)
if ((T >> b) & 1) bits.push_back(b);
int pc = (int)bits.size();
if (pc > m) continue;
multiset<int> exps(bits.begin(), bits.end());
int cost = 0;
for (int b : bits) cost += b;
bool valid = true;
for (int s = 0; s < m - pc; s++) {
auto it = exps.lower_bound(2);
if (it == exps.end()) { valid = false; break; }
int dd = *it; exps.erase(it);
exps.insert(dd-1); exps.insert(dd-1);
cost += (dd-2);
}
if (!valid) continue;
int total = cost + 1;
if (total < best_cost && total <= 512) {
best_cost = total;
best_dep.clear();
for (int e : exps) best_dep.push_back(e);
}
}
{
long long remaining = S;
int total_d = 0;
vector<int> depths;
while (remaining > 0) {
int d = 1;
while ((1LL << (d+1)) - 1 <= remaining) d++;
depths.push_back(d);
total_d += d;
remaining -= (1LL << d) - 1;
}
int total = total_d + 1;
if (total < best_cost && total <= 512) {
best_cost = total;
best_dep = depths;
}
}
cout << best_cost << "\n";
int pos = 1;
for (int dd : best_dep) {
int start = pos;
for (int j = 1; j <= dd; j++) {
cout << "POP " << j << " GOTO " << (start+j) << " PUSH " << j << " GOTO " << start << "\n";
pos++;
}
}
cout << "HALT PUSH 1 GOTO " << pos << "\n";
}
return 0;
}
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