File size: 6,574 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 | #include <iostream>
#include <vector>
#include <string>
#include <algorithm>
using namespace std;
struct Instruction {
string type; // "POP" or "HALT"
int a; // if POP: value to match. if HALT: unused
int x; // goto if match/halt
int b; // push value
int y; // goto else
};
vector<Instruction> program;
int add_instruction(string type, int a, int x, int b, int y) {
program.push_back({type, a, x, b, y});
return program.size();
}
const int UNKNOWN = -1;
struct Layer {
string type; // "Base", "Linear", "Double7", "Double9"
int val_in; // Value expected on stack
int val_aux; // Second value for Double
int val_garbage; // Garbage value
int entry_instr;
int return_target; // Where this layer returns to (in parent)
};
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
long long k;
if (!(cin >> k)) return 0;
if (k == 1) {
cout << "1\nHALT PUSH 1 GOTO 1\n";
return 0;
}
// We construct a program that executes Preamble + Body + Halt.
// Preamble takes 1 step. Halt takes 1 step.
// So Body needs to take t = k - 2 steps.
long long t = k - 2;
// Decompose t into layers
vector<string> layer_types;
// While t is large enough to use Double block (min cost 9)
while (t >= 9) {
// If t % 4 == 1, then (t - 7)/2 is odd. Use Double7.
// If t % 4 == 3, then (t - 9)/2 is odd. Use Double9.
if (t % 4 == 1) {
layer_types.push_back("Double7");
t = (t - 7) / 2;
} else {
layer_types.push_back("Double9");
t = (t - 9) / 2;
}
}
// Remaining t < 9. Must be odd.
// Use Linear blocks (+2 steps) to reduce to Base (1 step).
while (t > 1) {
layer_types.push_back("Linear");
t -= 2;
}
layer_types.push_back("Base");
// We want the vector to be [Base, Linear, ..., Outermost]
reverse(layer_types.begin(), layer_types.end());
// Assign values
int current_val = 1;
vector<Layer> layers(layer_types.size());
// Assign from Outermost to Innermost so values are consistent?
// Actually order doesn't matter as long as values are distinct.
for (int i = layer_types.size() - 1; i >= 0; --i) {
layers[i].type = layer_types[i];
layers[i].val_in = current_val++;
if (layers[i].type == "Double7" || layers[i].type == "Double9") {
layers[i].val_aux = current_val++;
layers[i].val_garbage = current_val++;
}
}
int next_instr = 1;
// Preamble
int preamble_idx = next_instr++;
add_instruction("HALT", 0, 0, 0, 0);
// Final Halt
int final_halt_idx = next_instr++;
add_instruction("HALT", 0, 0, 1, 1);
// Generate code for layers (Innermost first)
for (int i = 0; i < layers.size(); ++i) {
int child_entry = (i > 0) ? layers[i-1].entry_instr : -1;
if (layers[i].type == "Base") {
layers[i].entry_instr = next_instr++;
add_instruction("POP", layers[i].val_in, UNKNOWN, layers[i].val_in, UNKNOWN);
}
else if (layers[i].type == "Linear") {
int start_idx = next_instr++;
layers[i].entry_instr = start_idx;
// PUSH child_val GOTO Child_Entry
add_instruction("POP", layers[i].val_in, UNKNOWN, layers[i-1].val_in, child_entry);
int check_idx = next_instr++;
add_instruction("POP", layers[i].val_in, UNKNOWN, 1, 1);
program[start_idx-1].x = check_idx;
layers[i-1].return_target = check_idx;
}
else { // Double7 or Double9
int X = layers[i].val_in;
int Y = layers[i].val_aux;
int G = layers[i].val_garbage;
int child_val = layers[i-1].val_in;
int start_idx = next_instr++;
layers[i].entry_instr = start_idx;
int check_idx = next_instr++;
int swap_idx = next_instr++;
int pass2_idx = next_instr++;
int cleanup_idx = next_instr++;
int finish_idx = next_instr++;
int delay_idx = -1, restore_idx = -1;
if (layers[i].type == "Double9") {
delay_idx = next_instr++;
restore_idx = next_instr++;
}
int else_target = (layers[i].type == "Double9") ? delay_idx : cleanup_idx;
add_instruction("POP", Y, check_idx, child_val, child_entry); // Start
add_instruction("POP", X, swap_idx, G, else_target); // Check
add_instruction("HALT", 0, 0, Y, pass2_idx); // Swap
add_instruction("POP", X, 0, child_val, child_entry); // Pass2
add_instruction("POP", G, finish_idx, 0, 0); // Cleanup
add_instruction("POP", Y, UNKNOWN, 0, 0); // Finish
if (layers[i].type == "Double9") {
add_instruction("POP", G, restore_idx, 0, 0); // Delay
add_instruction("HALT", 0, 0, G, cleanup_idx); // Restore
}
layers[i-1].return_target = check_idx;
}
}
// Fix Preamble
int outer_layer_idx = layers.size() - 1;
program[preamble_idx-1].b = layers[outer_layer_idx].val_in;
program[preamble_idx-1].y = layers[outer_layer_idx].entry_instr;
// Fix Return Targets
for (int i = 0; i < layers.size(); ++i) {
int target = (i == layers.size() - 1) ? final_halt_idx : layers[i+1].return_target;
int instr_to_fix = -1;
if (layers[i].type == "Base") {
instr_to_fix = layers[i].entry_instr;
program[instr_to_fix-1].x = target;
} else if (layers[i].type == "Linear") {
instr_to_fix = layers[i].entry_instr + 1;
program[instr_to_fix-1].x = target;
} else {
instr_to_fix = layers[i].entry_instr + 5;
program[instr_to_fix-1].x = target;
}
}
cout << program.size() << "\n";
for (const auto& instr : program) {
if (instr.type == "HALT") {
cout << "HALT PUSH " << instr.b << " GOTO " << instr.y << "\n";
} else {
cout << "POP " << instr.a << " GOTO " << instr.x << " PUSH " << instr.b << " GOTO " << instr.y << "\n";
}
}
return 0;
} |