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#include <iostream> #include <iomanip> #include <algorithm> #include <vector> #include <string> #include <cstring> #include <cmath> using namespace std; typedef long long ll; // DP Gimkit Solver // Developed by Ta180m // Initial conditions // Change these values to alter the initial state ll start = 0, goal = 1e10; // Start and end amounts int max_it = 150; // Number of iterations to solve int MPQ = 0, SB = 0, M = 0; // Initial upgrade status int D = 0, R = 0, B1 = 0, B2 = 0; // Initial power-up status // State: Iteration, Upgrade status, Power-up status // DP array stores maximum possible money for each state // pre array used to reconstruct optimal strategy ll DP[7200000], pre[7200000]; // Upgrade values double val[3][10] = { { 1, 5, 50, 100, 500, 2000, 5000, 10000, 250000, 1000000 }, { 2, 20, 100, 200, 1000, 4000, 10000, 50000, 1000000, 5000000 }, { 1, 1.5, 2, 3, 5, 8, 12, 18, 30, 100 } }; // Upgrade costs ll cost[2][3][10] = { { { 0, 10, 100, 1000, 10000, 75000, 300000, 1000000, 10000000, 100000000}, { 0, 15, 150, 1500, 15000, 115000, 450000, 1500000, 15000000, 200000000 }, { 0, 50, 300, 2000, 12000, 85000, 700000, 6500000, 65000000, 1000000000 } }, { { 0, 8, 75, 750, 7500, 56250, 225000, 750000, 7500000, 75000000 }, { 0, 12, 113, 1125, 11250, 86250, 337500, 1125000, 11250000, 150000000 }, { 0, 38, 225, 1500, 9000, 63750, 525000, 4875000, 48750000, 750000000 } } }; // Power-up costs int base[4] = { 250, 1000, 20, 50 }; double pcent[4] = { 0.16, 0.30, 0.03, 0.06 }; ll pcost(int i, ll x) { return 5 * ceil((double)(pcent[i] * x + base[i]) / 5); } // Utility function to format output string format(ll x) { string ret = to_string(x); int pos = ret.length() - 3; while (pos > 0) { ret.insert(pos, ","); pos -= 3; } return ret; } // Bottom-up DP algorithm int main() { // Initialize DP array memset(DP, -1, sizeof(DP)); // Calculate initial state int s = 3600 * MPQ + 360 * SB + 36 * M + 18 * D + 9 * R + 3 * B1 + B2; // Set initial value DP[s] = start; // Find the optimal solution int sol = 7200000; for (int i = 0; i < 36000 * max_it; i++) { if (DP[i] != -1) { if (i / 36000 > sol / 36000) break; if (DP[i] >= goal && (sol == 7200000 || DP[i] > DP[sol])) sol = i; // Calculate parameters int it = i / 36000; int MPQ = (i / 3600) % 10, SB = (i / 360) % 10, M = (i / 36) % 10; int D = (i / 18) % 2, R = (i / 9) % 2, B1 = (i / 3) % 3, B2 = i % 3; // Income per question ll inc = round((val[0][MPQ] + (i != 0 ? val[1][SB] : 0)) * val[2][M]); // Answer a question if (DP[i] + inc > DP[i + 36000]) { DP[i + 36000] = DP[i] + inc; pre[i + 36000] = i; } // Answer a question using the mini bonus if (B1 == 1 && DP[i] + 2 * inc > DP[i + 36003]) { DP[i + 36003] = DP[i] + 2 * inc; pre[i + 36003] = i; } // Answer a question using the mega bonus if (B2 == 1 && DP[i] + 5 * inc > DP[i + 36001]) { DP[i + 36001] = DP[i] + 5 * inc; pre[i + 36001] = i; } // Answer a question using both the mini bonus and the mega bonus if (B1 == 1 && B2 == 1 && DP[i] + 10 * inc > DP[i + 36004]) { DP[i + 36004] = DP[i] + 10 * inc; pre[i + 36004] = i; } // Upgrade money per question for (int j = MPQ + 1; j < 10 && DP[i] >= cost[D][0][j]; j++) { if (DP[i] - cost[D][0][j] > DP[i + 3600 * (j - MPQ)]) { DP[i + 3600 * (j - MPQ)] = DP[i] - cost[D][0][j]; pre[i + 3600 * (j - MPQ)] = i; } } // Upgrade streak bonus for (int j = SB + 1; j < 10 && DP[i] >= cost[D][1][j]; j++) { if (DP[i] - cost[D][1][j] > DP[i + 360 * (j - SB)]) { DP[i + 360 * (j - SB)] = DP[i] - cost[D][1][j]; pre[i + 360 * (j - SB)] = i; } } // Upgrade multiplier for (int j = M + 1; j < 10 && DP[i] >= cost[D][2][j]; j++) { if (DP[i] - cost[D][2][j] > DP[i + 36 * (j - M)]) { DP[i + 36 * (j - M)] = DP[i] - cost[D][2][j]; pre[i + 36 * (j - M)] = i; } } // Buy the discounter if (D == 0 && DP[i] - pcost(0, DP[i]) > DP[i + 18]) { DP[i + 18] = DP[i] - pcost(0, DP[i]); pre[i + 18] = i; } // Buy the rebooter if (R == 0 && DP[i] - pcost(1, DP[i]) > DP[i - i % 36 + 9]) { DP[i - i % 36 + 9] = DP[i] - pcost(1, DP[i]); pre[i - i % 36 + 9] = i; } // Buy the mini bonus if (B1 == 0 && DP[i] - pcost(2, DP[i]) > DP[i + 2]) { DP[i + 3] = DP[i] - pcost(2, DP[i]); pre[i + 3] = i; } // Buy the mega bonus if (B2 == 0 && DP[i] - pcost(3, DP[i]) > DP[i + 1]) { DP[i + 1] = DP[i] - pcost(3, DP[i]); pre[i + 1] = i; } } } // Print output if (sol != 7200000) { vector<int> output; for (int i = sol; i != s; i = pre[i]) output.push_back(i); reverse(output.begin(), output.end()); cout << "Optimal strategy to reach $" << format(goal) << " from $" << format(start) << " in " << sol / 36000 << " iterations:" << endl; for (int i = 0; i < output.size(); i++) { int it = output[i] / 36000; int MPQ = (output[i] / 3600) % 10, SB = (output[i] / 360) % 10, M = (output[i] / 36) % 10; int D = (output[i] / 18) % 2, R = (output[i] / 9) % 2, B1 = (output[i] / 3) % 3, B2 = output[i] % 3; // Output iteration if (it != output[i - 1] / 36000) cout << right << setw(3) << it << ". "; else cout << " "; // Answer a question if (it != output[i - 1] / 36000 && B1 == (output[i - 1] / 3) % 3 && B2 == output[i - 1] % 3) { cout << "Answer 1 question, bringing your total up to $" << format(DP[output[i]]) << endl; } // Answer a question with the mini bonus else if (it != output[i - 1] / 36000 && B1 != (output[i - 1] / 3) % 3 && B2 == output[i - 1] % 3) { cout << "Answer 1 question using the mini bonus, bringing your total up to $" << format(DP[output[i]]) << endl; } // Answer a question using the mega bonus else if (it != output[i - 1] / 36000 && B1 == (output[i - 1] / 3) % 3 && B2 != output[i - 1] % 3) { cout << "Answer 1 question using the mega bonus, bringing your total up to $" << format(DP[output[i]]) << endl; } // Answer a question using both the mini and mega bonuses else if (it != output[i - 1] / 36000 && B1 != (output[i - 1] / 3) % 3 && B2 != output[i - 1] % 3) { cout << "Answer 1 question using both the mini and mega bonuses, bringing your total up to $" << format(DP[output[i]]) << endl; } // Upgrade money per question else if (MPQ != (output[i - 1] / 3600) % 10) { cout << "Buy the Level " << MPQ << " ($" << format(val[0][MPQ]) << ") money per question upgrade for $" << format(cost[D][0][MPQ]) << ", making your total $" << format(DP[output[i]]) << endl; } // Upgrade streak bonus else if (SB != (output[i - 1] / 360) % 10) { cout << "Buy the Level " << SB << " ($" << format(val[1][SB]) << ") streak bonus upgrade for $" << format(cost[D][1][SB]) << ", making your total $" << format(DP[output[i]]) << endl; } // Upgrade multiplier else if (M != (output[i - 1] / 36) % 10) { cout << "Buy the Level " << M << " (x" << format(val[2][M]) << ") multiplier for $" << format(cost[D][2][M]) << ", making your total $" << format(DP[output[i]]) << endl; } // Buy the rebooter else if (R != (output[i - 1] / 9) % 2) { cout << "Buy and use the rebooter for $" << format(pcost(1, DP[output[i - 1]])) << ", making your total $" << format(DP[output[i]]) << endl; } // Buy the discounter else if (D != (output[i - 1] / 18) % 2) { cout << "Buy and use the discounter for $" << format(pcost(0, DP[output[i - 1]])) << ", making your total $" << format(DP[output[i]]) << endl; } // Buy the mini bonus else if (B1 != (output[i - 1] / 3) % 3) { cout << "Buy the mini bonus for $" << format(pcost(2, DP[output[i - 1]])) << ", making your total $" << format(DP[output[i]]) << endl; } // Buy the mega bonus else if (B2 != output[i - 1] % 3) { cout << "Buy the mega bonus for $" << format(pcost(3, DP[output[i - 1]])) << ", making your total $" << format(DP[output[i]]) << endl; } // Error else cout << "Error: Something went wrong" << endl; } } else cout << "No strategy to reach $" << format(goal) << " from $" << format(start) << " in " << max_it << " iterations could be found" << endl; }

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