This is the partition problem; its application to photo galleries is discussed in this blog post by Johannes Treitz. The suggested solution is:
- To find k, the number of rows needed, scale the photos to half the window's height, sum up their widths, divide by the window's width, and then round.
- The photos' aspect ratios then serve as a set S of weights. Find the optimal distribution of S over k using an existing linear partition algorithm.
The blog post includes the following CoffeeScript to build the gallery:
viewport_width = $(window).width()
ideal_height = parseInt($(window).height() / 2)
summed_width = photos.reduce ((sum, p) -> sum += p.get('aspect_ratio') * ideal_height), 0
rows = Math.round(summed_width / viewport_width)
if rows < 1
# (2a) Fallback to just standard size
photos.each (photo) -> photo.view.resize parseInt(ideal_height * photo.get('aspect_ratio')), ideal_height
else
# (2b) Distribute photos over rows using the aspect ratio as weight
weights = photos.map (p) -> parseInt(p.get('aspect_ratio') * 100)
partition = linear_partition(weights, rows)
# (3) Iterate through partition
index = 0
row_buffer = new Backbone.Collection
_.each partition, (row) ->
row_buffer.reset()
_.each row, -> row_buffer.add(photos.at(index++))
summed_ratios = row_buffer.reduce ((sum, p) -> sum += p.get('aspect_ratio')), 0
row_buffer.each (photo) -> photo.view.resize parseInt(viewport_width / summed_ratios * photo.get('aspect_ratio')), parseInt(viewport_width / summed_ratios)
The linear_partition
function is implemented as follows (see github):
# Linear partition
# Partitions a sequence of non-negative integers into k ranges
# Based on Óscar López implementation in Python (http://stackoverflow.com/a/7942946)
# Also see http://www8.cs.umu.se/kurser/TDBAfl/VT06/algorithms/BOOK/BOOK2/NODE45.HTM
# Dependencies: UnderscoreJS (http://www.underscorejs.org)
# Example: linear_partition([9,2,6,3,8,5,8,1,7,3,4], 3) => [[9,2,6,3],[8,5,8],[1,7,3,4]]
linear_partition = (seq, k) =>
n = seq.length
return [] if k <= 0
return seq.map((x) -> [x]) if k > n
table = (0 for x in [0...k] for y in [0...n])
solution = (0 for x in [0...k-1] for y in [0...n-1])
table[i][0] = seq[i] + (if i then table[i-1][0] else 0) for i in [0...n]
table[0][j] = seq[0] for j in [0...k]
for i in [1...n]
for j in [1...k]
m = _.min(([_.max([table[x][j-1], table[i][0]-table[x][0]]), x] for x in [0...i]), (o) -> o[0])
table[i][j] = m[0]
solution[i-1][j-1] = m[1]
n = n-1
k = k-2
ans = []
while k >= 0
ans = [seq[i] for i in [(solution[n-1][k]+1)...n+1]].concat ans
n = solution[n-1][k]
k = k-1
[seq[i] for i in [0...n+1]].concat ans