Longest First

The classic crossword construction approach: long words become the structural backbone of the grid, and shorter words fill in around them.

Long words have more letters, which means more potential crossing points. By placing them first, every subsequent shorter word has a wider variety of intersection options to choose from.

This strategy tends to produce grids shaped around one or two long anchor words. In benchmarks, it often yields favorable compactness ratios (grid area per placed word) since long anchors define a tight bounding box that shorter words pack into. However, it may place fewer total words than connectivity-aware strategies because word ordering ignores the compatibility graph.

How It Works

1. 1

   Sort words by length descending

   Word lengths from longest to shortest. Among words of equal length, the order is randomized across attempts to produce different layouts.

2. 2

   Place words greedily in order

   Place the longest word horizontally at origin. For each subsequent word, find the placement that maximizes intersections with already-placed words. Long words placed early give later words more options.

Pseudocode

function longestFirstOrder(words):
    return sort(words, by length descending,
                ties broken randomly per attempt)

function placeWords(orderedWords):
    place orderedWords[0] horizontally at (0, 0)
    for word in orderedWords[1:]:
        bestPlacement = null
        for placedWord in placed:
            for sharedLetter in word ∩ placedWord:
                p = perpendicularPlacement(word, placedWord, sharedLetter)
                if isValid(p):
                    score = countIntersections(p)
                    if score > bestScore:
                        bestPlacement = p
        if bestPlacement:
            place(word, bestPlacement)

Complexity

Sort: O(W log W). Placement: O(W² × L²) for the greedy search. Total: O(W² × L²) per attempt.

★ Best across all four strategies on this scenario. Reproducible via scripts/benchmark-strategies.ts.

Metric Definitions

Each benchmark run executes 16 randomized attempts of the strategy and returns up to 4 distinct layouts, sorted by quality. This process is repeated 3 times to reduce variance. The metrics below describe how each column is derived from those runs.

Best ×

The highest intersection count from the top-ranked layout across 3 independent runs. An intersection is a grid cell shared by two words (one across, one down). Higher is better.

Avg ×

The mean intersection count across all returned layouts (up to 4 per run), averaged over 3 runs. This includes second- through fourth-best layouts, so it reflects consistency rather than peak performance.

Placed

The most words placed on the grid in any top-ranked layout. For Adjacency-Aware, this includes dictionary fill words from Phase 2, so it can exceed the input word count. Shown as placed/input.

Compactness

Grid bounding-box area (rows times columns) divided by the number of placed words. Lower values indicate denser packing. Note that this measures the full bounding box, which includes empty cells between words. Adjacency-Aware's denominator is inflated by fill words.

2-Letter Frags

The number of 2-letter contiguous letter runs in the best grid that are not covered by any placed word in that direction. These are perpendicular fragments left behind by parallel placements that Phase 2 could not extend into complete dictionary words. Only applicable to adjacency strategies; always 0 for other strategies since they never place words in parallel.

Fill Words

The number of dictionary words added in Phase 2 to extend 2-letter gaps into complete words. These are not from the user's word list. Capped at max(3, 75% of user word count). Only applicable to adjacency strategies.

Time

Wall-clock time for one run (16 randomized attempts), averaged across 3 runs. Measured in single-threaded JavaScript without Web Workers. Includes ordering, candidate enumeration, validation, and (for Adjacency-Aware) Phase 2 gap filling.

When to Use This

• •You have one or two long themed entries you want prominently displayed
• •Your word list has high length variance (mix of 3-letter and 8+ letter words)
• •You prefer a more traditional, anchor-driven crossword aesthetic

Other Strategies