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)

2 years ago · 62f9bf31f5
parent 3c98bec85a
commit 62f9bf31f5
3 changed files with 704 additions and 0 deletions
--- 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)
+}
--- 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)
+	}
+}
--- a/day21/input2.txt
+++ b/day21/input2.txt
@ -0,0 +1,655 @@
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