From 62f9bf31f591e3fa66bc687a257dc43e6558533f Mon Sep 17 00:00:00 2001 From: oabrivard Date: Fri, 22 Dec 2023 14:39:35 +0100 Subject: [PATCH] Completed part 2 of Day 21 with the formula given in the reddit thread (I still not fully understand why the solution is the result of a quadratic equation) --- day21/day21.go | 39 +++ day21/day21_test.go | 10 + day21/input2.txt | 655 ++++++++++++++++++++++++++++++++++++++++++++ 3 files changed, 704 insertions(+) create mode 100644 day21/input2.txt diff --git a/day21/day21.go b/day21/day21.go index b6d484a..13ca39a 100644 --- a/day21/day21.go +++ b/day21/day21.go @@ -251,3 +251,42 @@ func Part1(lines []string, maxSteps int) int { return result } + +// Solved thanks to the post ox aexl on the reddit thread +// https://www.reddit.com/r/adventofcode/comments/18nevo3/2023_day_21_solutions/ +// It implies the creation of a specific input to have a grid large enough to simulate it is infinite +// for the 3 iterations. +/* +We need to figure out how many garden plots can be reached after 26501365 steps. +Note that 26501365 = 202300 * 131 + 65, where 131 is the side length of the input grid. +Store how many garden plots can be reached after 65, 65 + 131 and 65 + 2 * 131 steps, let's call these numbers r₁, r₂ and r₃. +Now it turns out that the number of garden plots that can be reached after x * 131 + 65 steps is a quadratic function p(x) = ax² + bx + c. +We know that +r₁ = p(0) = c +r₂ = p(1) = a + b + c +r₃ = p(2) = 4a + 2b + c +Solving this linear system of equations for the unknowns a, b and c gives +a = (r₃ + r₁ - 2r₂) / 2 +b = (4r₂ - 3r₁ - r₃) / 2 +c = r₁ +Finally, we just need to evaluate the polynomial p at 202300 +*/ +func Part2(lines []string) int64 { + + nbSteps := 26501365 + gridSize := 131 // from puzzle input + modulo := nbSteps % gridSize + leftOver := nbSteps / gridSize + + r1 := Part1(lines, modulo) + r2 := Part1(lines, modulo+gridSize) + r3 := Part1(lines, modulo+2*gridSize) + + a := (r3 + r1 - 2*r2) / 2 + b := (4*r2 - 3*r1 - r3) / 2 + c := r1 + + p := func(x int) int64 { return int64(a*x*x + b*x + c) } + + return p(leftOver) +} diff --git a/day21/day21_test.go b/day21/day21_test.go index 08b9376..3cbc520 100644 --- a/day21/day21_test.go +++ b/day21/day21_test.go @@ -62,3 +62,13 @@ func TestPart1WithInput(t *testing.T) { t.Fatalf("expected 3758, got %d", result) } } + +func TestPart2WithInput(t *testing.T) { + lines := utils.ReadLines("input2.txt") // tailored made input + + result := Part2(lines) + + if result != 621494544278648 { + t.Fatalf("expected 621494544278648, got %d", result) + } +} diff --git a/day21/input2.txt b/day21/input2.txt new file mode 100644 index 0000000..285cad9 --- /dev/null +++ b/day21/input2.txt @@ -0,0 +1,655 @@ 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