题目描述：
On an infinite number line (x-axis), we drop given squares in the order they are given.
The i-th square dropped (positions[i] = (left, side_length)) is a square with the left-most point being positions[i][0] and sidelength positions[i][1].
The square is dropped with the bottom edge parallel to the number line, and from a higher height than all currently landed squares. We wait for each square to stick before dropping the next.
The squares are infinitely sticky on their bottom edge, and will remain fixed to any positive length surface they touch (either the number line or another square). Squares dropped adjacent to each other will not stick together prematurely.
Return a list ans of heights. Each height ans[i] represents the current highest height of any square we have dropped, after dropping squares represented by positions[0], positions[1], ..., positions[i].
Example 1:
Input: [[1, 2], [2, 3], [6, 1]] Output: [2, 5, 5] Explanation:
After the first drop of positions[0] = [1, 2]: _aa _aa ------- The maximum height of any square is 2. After the second drop of positions[1] = [2, 3]: __aaa __aaa __aaa _aa__ _aa__ -------------- The maximum height of any square is 5. The larger square stays on top of the smaller square despite where its center of gravity is, because squares are infinitely sticky on their bottom edge. After the third drop of positions[1] = [6, 1]: __aaa __aaa __aaa _aa _aa___a -------------- The maximum height of any square is still 5. Thus, we return an answer of [2, 5, 5].
Example 2:
Input: [[100, 100], [200, 100]] Output: [100, 100] Explanation: Adjacent squares don't get stuck prematurely - only their bottom edge can stick to surfaces.
Note:
1 <= positions.length <= 1000.1 <= positions[0] <= 10^8.1 <= positions[1] <= 10^6.
题目大意：
给定一组正方形箱子的坐标（left, side_length），表示左侧位置和箱子的边长。
将箱子从无限高的空中投掷到x轴，边有交集的箱子会堆叠（边界相接不算交集），查询每个箱子投掷后的最大堆叠高度。
解题思路：
离散化
将箱子的左、右边界离散化为dmap，利用数组maxs保存离散化后的坐标的最大值
Python代码：
class Solution(object):
def fallingSquares(self, positions):
"""
:type positions: List[List[int]]
:rtype: List[int]
"""
pset = set()
for left, width in positions:
pset.add(left + 0.5)
pset.add(left + width)
dmap = {val : idx + 1 for idx, val in enumerate(sorted(pset))}
maxs = collections.defaultdict(int)
maxt = 0
size = len(dmap)
ans = []
for left, width in positions:
ll, rr = dmap[left + 0.5], dmap[left + width]
maxn = max(maxs[x] for x in range(ll, rr + 1))
for k in range(ll, rr + 1): maxs[k] = maxn + width
maxt = max(maxn + width, maxt)
ans.append(maxt)
return ans
本文链接：http://bookshadow.com/weblog/2017/10/15/leetcode-falling-squares/
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