Solution to the 10th problem

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The problem is solved by performing a recursive depth-first search (DFS) from each trailhead (height 0) across the topographic map. A valid hiking trail always moves orthogonally to neighboring positions with a height exactly 1 higher than the current position.

Problem A

For part A, the DFS keeps track of visited positions to avoid counting the same path multiple times. Whenever a trail reaches a height of 9, it contributes to the trailhead’s score. By summing these scores over all trailheads, the solution for the first part is obtained.

» cargo build -p aoc-24 --release && hyperfine ./target/release/aoc-24 -N --warmup 5
Benchmark 1: ./target/release/aoc-24
Time (mean ± σ):       6.2 ms ±   3.8 ms    [User: 1.4 ms, System: 1.1 ms]
Range (min … max):     3.7 ms …  37.4 ms    532 runs

Problem B

For part B, the visited tracking is disabled so that all distinct hiking trails are counted, even if they overlap at intermediate positions. The recursive DFS explores every valid path from each trailhead, incrementing the count whenever a trail reaches height 9. Summing these counts across all trailheads gives the total rating.

» cargo build -p aoc-24 --release && hyperfine ./target/release/aoc-24 -N --warmup 5
Benchmark 1: ./target/release/aoc-24
Time (mean ± σ):       8.2 ms ±   5.7 ms    [User: 1.4 ms, System: 1.2 ms]
Range (min … max):     4.1 ms …  40.7 ms    455 runs

This approach efficiently handles both parts of the problem by simply toggling whether visited positions are tracked, avoiding the need for more complex state management or memoization while remaining fast even for larger maps.

Code for this solution: d10.rs
Problem statement

Customize your input

Map

Once the map is rendered, the start points will be rendered in blue. The paths will be rendered with different colors, most of them overlapping.

Visualization

Configuration

Duration 50ms

Parallel items Iterative

Trails found: 0

Checking points (0):