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Add problem statements and inputs
author Jordi Gutiérrez Hermoso <jordigh@octave.org>
date Tue, 09 Jan 2018 21:51:44 -0500
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1 --- Day 18: Duet ---
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2
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3 You discover a tablet containing some strange assembly code labeled
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4 simply "Duet". Rather than bother the sound card with it, you decide
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5 to run the code yourself. Unfortunately, you don't see any
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6 documentation, so you're left to figure out what the instructions mean
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7 on your own.
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8
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9 It seems like the assembly is meant to operate on a set of registers
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10 that are each named with a single letter and that can each hold a
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11 single integer. You suppose each register should start with a value of
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12 0.
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13
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14 There aren't that many instructions, so it shouldn't be hard to figure
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15 out what they do. Here's what you determine:
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16
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17 snd X plays a sound with a frequency equal to the value of X.
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18
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19 set X Y sets register X to the value of Y.
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20
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21 add X Y increases register X by the value of Y.
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22
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23 mul X Y sets register X to the result of multiplying the value
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24 contained in register X by the value of Y.
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25
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26 mod X Y sets register X to the remainder of dividing the value
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27 contained in register X by the value of Y (that is, it sets X to
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28 the result of X modulo Y).
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29
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30 rcv X recovers the frequency of the last sound played, but only
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31 when the value of X is not zero. (If it is zero, the command does
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32 nothing.)
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33
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34 jgz X Y jumps with an offset of the value of Y, but only if the
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35 value of X is greater than zero. (An offset of 2 skips the next
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36 instruction, an offset of -1 jumps to the previous instruction,
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37 and so on.)
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38
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39
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40 Many of the instructions can take either a register (a single letter)
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41 or a number. The value of a register is the integer it contains; the
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42 value of a number is that number.
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43
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44 After each jump instruction, the program continues with the
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45 instruction to which the jump jumped. After any other instruction, the
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46 program continues with the next instruction. Continuing (or jumping)
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47 off either end of the program terminates it.
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48
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49 For example:
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50
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51 set a 1
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52 add a 2
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53 mul a a
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54 mod a 5
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55 snd a
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56 set a 0
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57 rcv a
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58 jgz a -1
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59 set a 1
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60 jgz a -2
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61
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62 The first four instructions set a to 1, add 2 to it, square it,
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63 and then set it to itself modulo 5, resulting in a value of 4.
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64
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65 Then, a sound with frequency 4 (the value of a) is played.
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66
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67 After that, a is set to 0, causing the subsequent rcv and jgz
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68 instructions to both be skipped (rcv because a is 0, and jgz
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69 because a is not greater than 0).
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70
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71 Finally, a is set to 1, causing the next jgz instruction to
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72 activate, jumping back two instructions to another jump, which
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73 jumps again to the rcv, which ultimately triggers the recover
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74 operation.
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75
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76
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77 At the time the recover operation is executed, the frequency of the
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78 last sound played is 4.
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79
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80 What is the value of the recovered frequency (the value of the most
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81 recently played sound) the first time a rcv instruction is executed
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82 with a non-zero value?
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83
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84 Your puzzle answer was 7071.
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85
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86 --- Part Two ---
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87
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88 As you congratulate yourself for a job well done, you notice that the
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89 documentation has been on the back of the tablet this entire time.
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90 While you actually got most of the instructions correct, there are a
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91 few key differences. This assembly code isn't about sound at all -
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92 it's meant to be run twice at the same time.
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93
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94 Each running copy of the program has its own set of registers and
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95 follows the code independently - in fact, the programs don't even
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96 necessarily run at the same speed. To coordinate, they use the send
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97 (snd) and receive (rcv) instructions:
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98
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99 snd X sends the value of X to the other program. These values wait
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100 in a queue until that program is ready to receive them. Each
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101 program has its own message queue, so a program can never receive
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102 a message it sent.
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103
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104 rcv X receives the next value and stores it in register X. If no
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105 values are in the queue, the program waits for a value to be sent
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106 to it. Programs do not continue to the next instruction until they
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107 have received a value. Values are received in the order they are
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108 sent.
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109
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110
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111 Each program also has its own program ID (one 0 and the other 1); the
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112 register p should begin with this value.
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113
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114 For example:
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115
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116 snd 1
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117 snd 2
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118 snd p
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119 rcv a
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120 rcv b
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121 rcv c
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122 rcv d
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123
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124 Both programs begin by sending three values to the other. Program 0
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125 sends 1, 2, 0; program 1 sends 1, 2, 1. Then, each program receives a
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126 value (both 1) and stores it in a, receives another value (both 2) and
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127 stores it in b, and then each receives the program ID of the other
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128 program (program 0 receives 1; program 1 receives 0) and stores it in
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129 c. Each program now sees a different value in its own copy of register
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130 c.
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131
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132 Finally, both programs try to rcv a fourth time, but no data is
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133 waiting for either of them, and they reach a deadlock. When this
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134 happens, both programs terminate.
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135
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136 It should be noted that it would be equally valid for the programs to
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137 run at different speeds; for example, program 0 might have sent all
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138 three values and then stopped at the first rcv before program 1
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139 executed even its first instruction.
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140
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141 Once both of your programs have terminated (regardless of what caused
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142 them to do so), how many times did program 1 send a value?
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143
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144 Your puzzle answer was 8001.
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145
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146 Both parts of this puzzle are complete! They provide two gold stars: **