The hyehwa930-albums-2015 from choyongjoon

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Code snippet for rearrange albums

greedy approach from left to right. assume sorted.

if collision occurs,
if we can handle with moving two items
1) move last merged item to left
2) move new item to right
else we push new item to notMerged

notMerged will be processed with themselves only.
(increase top value of notMerged items after rearrange (not in this code))
repeat until notMerged.length == 0

var items = [
  {left: 2, width: 4}, // 2~6
  {left: 7, width: 4}, // 7~11 
  {left: 8, width: 4}  // 8~12
];
console.log(items);

var items2 = items;

var margin = 0;
var limit = 3;

var notMerged = [];

do {
  var merged = {}
  merged.left = items[0].left;
  merged.width = items[0].width;
  merged.lastLimit = Math.min(items[0].left, limit);
  merged.size = 1;

  for (var i = 1; i < items.length; ++i) {
    var a = items[i];
    var gap = gapBetween(merged, a);
    if (gap < 0) {
      var overlap = -gap;
      if (overlap <= limit + merged.lastLimit) {
        // can merge
        // first, move last merged to left
        if (overlap < merged.lastLimit) {
          items[merged.size - 1].left -= overlap;
          merged.width -= overlap;
        } else {
          items[merged.size - 1].left -= merged.lastLimit;
          merged.width -= merged.lastLimit;
          a.left += (overlap - merged.lastLimit);
        }
        var newGap = gapBetween(merged, a);
        merged = merge(merged, a, newGap);
      } else {
        // can't merge
        notMerged.push(a);
      }
    } else {
      merged = merge(merged, a, gap);
    }
  }
  items = notMerged;
} while(items.length > 0)

console.log(items2);

function merge(merged, a, gap) {
  merged.width = a.left + a.width - merged.left;
  merged.lastLimit = Math.min(limit, gap);
  merged.size++;
  return merged;
}

function gapBetween(a, b) {
  return b.left - (a.left + a.width + margin);
}

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