Advent of Code 2019 Day 2 Intcode disassembly and analysis

01 Raw Input

"1,0,0,3,1,1,2,3,1,3,4,3,1,5,0,3,2,1,6,19,1,19,5,23,2,13,23,27,1,10,27,31,2,6,31,35,1,9,35,39,2,10,39,43,1,43,9,47,1,47,9,51,2,10,51,55,1,55,9,59,1,59,5,63,1,63,6,67,2,6,67,71,2,10,71,75,1,75,5,79,1,9,79,83,2,83,10,87,1,87,6,91,1,13,91,95,2,10,95,99,1,99,6,103,2,13,103,107,1,107,2,111,1,111,9,0,99,2,14,0,0"

02 Disassembled Code

  0: ADD( 1) 0 0 3 
  4: ADD( 1) 1 2 3 
  8: ADD( 1) 3 4 3 
 12: ADD( 1) 5 0 3 
 16: MUL( 2) 1 6 19 
 20: ADD( 1) 19 5 23 
 24: MUL( 2) 13 23 27 
 28: ADD( 1) 10 27 31 
 32: MUL( 2) 6 31 35 
 36: ADD( 1) 9 35 39 
 40: MUL( 2) 10 39 43 
 44: ADD( 1) 43 9 47 
 48: ADD( 1) 47 9 51 
 52: MUL( 2) 10 51 55 
 56: ADD( 1) 55 9 59 
 60: ADD( 1) 59 5 63 
 64: ADD( 1) 63 6 67 
 68: MUL( 2) 6 67 71 
 72: MUL( 2) 10 71 75 
 76: ADD( 1) 75 5 79 
 80: ADD( 1) 9 79 83 
 84: MUL( 2) 83 10 87 
 88: ADD( 1) 87 6 91 
 92: ADD( 1) 13 91 95 
 96: MUL( 2) 10 95 99 
100: ADD( 1) 99 6 103 
104: MUL( 2) 13 103 107 
108: ADD( 1) 107 2 111 
112: ADD( 1) 111 9 0 
116: HLT(99) 
117: MUL( 2) 14 0 0 

03 Analysis

NOTE: I'll call memory cell 0 "output", cell 1 "noun", and cell 2 "verb".
      Everything else is cNN (e.g. c3 or c107), based on their memory location.
NOTE 2: When an opcode parameter references a value that hasn't changed from its
        original value, I'll treat it as a constant.

c3 = 1 + 1
c3 = noun + verb
c3 = c3 + 1
c3 = 1 + 1
c19 = noun * 2
c23 = c19 + 1
c27 = 5 * c23
c31 = 4 + c27
c35 = 2 * c31
c39 = 3 + c35
c43 = 4 * c39
c47 = c43 + 3
c51 = c47 + 3
c55 = 4 * c51
c59 = c55 + 3
c63 = c59 + 1
c67 = c63 + 2
c71 = 2 * c67
c75 = 4 * c71
c79 = c75 + 1
c83 = 3 + c79
c87 = c83 * 4
c91 = c87 + 2
c95 = 5 + c91
c99 = 4 * c95
c103 = c99 + 2
c107 = 5 * c103
c111 = c107 + verb
output = c111 + 3

So it appears that the first several opcodes are dummies.  They exist to make
room for the inputs and output (memory cells 0-3) and for several numeric
constants (cells 4-15).  The calculation starts with the opcode at cell 16.

If we expand out the calculation, we get:

5 * (4 * (5 + (3 + 4 * (2 * (4 * (4 * (3 + 2 * (4 + 5 * (noun * 2 + 1))) + 3 + 3) + 3 + 1 + 2)) + 1) * 4 + 2) + 2) + verb + 3

Simplified, that turns into:

noun * 204800 + 234713 + verb

Since we know the output should be 19690720, that turns into:

204800 * noun + verb + 234713 = 19690720

Simplify:

204800 * noun + verb = 19456007

Move things around:

noun = 19456007 / 204800 - verb / 204800

Divide:

noun = 95 + 7 / 204800 - verb / 204800

From this, it's pretty clear that the noun is 95 and the verb is 7.

Pretty neat analysis. Was wondering if it was possible to analyze and mathematically determine day 2 part 2.