如何将一组重叠范围划分为非重叠范围?

2022-01-24 00:00:00 python algorithm math range rectangles

问题描述

假设您有一组范围:

  • 0 - 100: 'a'
  • 0 - 75:'b'
  • 95 - 150: 'c'
  • 120 - 130:'d'

显然，这些范围在某些点重叠.您将如何剖析这些范围以生成不重叠范围的列表，同时保留与其原始范围相关的信息(在本例中为范围后面的字母)?

Obviously, these ranges overlap at certain points. How would you dissect these ranges to produce a list of non-overlapping ranges, while retaining information associated with their original range (in this case, the letter after the range)?

例如上面运行算法后的结果是:

For example, the results of the above after running the algorithm would be:

  • 0 - 75:'a'、'b'
  • 76 - 94: 'a'
  • 95 - 100:'a'、'c'
  • 101 - 119:'c'
  • 120 - 130:'c'、'd'
  • 131 - 150:'c'

解决方案

我在编写混合(部分重叠)音频样本的程序时遇到了同样的问题.

I had the same question when writing a program to mix (partly overlapping) audio samples.

我所做的是将开始事件"和停止事件"(针对每个项目)添加到列表中，按时间点对列表进行排序，然后按顺序处理.你可以做同样的事情，除了使用整数点而不是时间，而不是混合声音，你将添加符号到与范围相对应的集合中.是生成空范围还是忽略它们都是可选的.

What I did was add an "start event" and "stop event" (for each item) to a list, sort the list by time point, and then process it in order. You could do the same, except using an integer point instead of a time, and instead of mixing sounds you'd be adding symbols to the set corresponding to a range. Whether you'd generate empty ranges or just omit them would be optional.

编辑也许一些代码...

# input = list of (start, stop, symbol) tuples
points = [] # list of (offset, plus/minus, symbol) tuples
for start,stop,symbol in input:
    points.append((start,'+',symbol))
    points.append((stop,'-',symbol))
points.sort()

ranges = [] # output list of (start, stop, symbol_set) tuples
current_set = set()
last_start = None
for offset,pm,symbol in points:
    if pm == '+':
         if last_start is not None:
             #TODO avoid outputting empty or trivial ranges
             ranges.append((last_start,offset-1,current_set))
         current_set.add(symbol)
         last_start = offset
    elif pm == '-':
         # Getting a minus without a last_start is unpossible here, so not handled
         ranges.append((last_start,offset-1,current_set))
         current_set.remove(symbol)
         last_start = offset

# Finish off
if last_start is not None:
    ranges.append((last_start,offset-1,current_set))

显然，完全未经测试.

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