如何在其他重叠的数字范围之间找到可用的数字范围

How to find free number ranges between other overlapping number ranges

本文关键字：范围 数字 之间 重叠 其他      更新时间：2023-09-26

我有n个数组。每个数组有m个元素。每个元素m由两个属性[数字]组成。

{
  start: x
  end: y
}

一个起始数字和一个结束数字，两者一起描述一个范围。所以每次开始都比结束小。我试图找到空闲的数字范围（同样是开始和结束），它们位于所有数组中的范围元素之间。另外，结果在一个范围内是有界的。

例如：

var boundary = {
    start: 0,
    end: 600
};
// for example i use two arrays with ranges, but in reality they are n (>= 1)
var numbersRanges1 = [
    {start: 100, end: 120},
    {start: 180, end: 200},
    {start: 400, end: 500}
];
var numbersRanges2 = [
    {start: 10, end: 80},
    {start: 150, end: 220},
    {start: 480, end: 500}
];
// result should look like
var expected = [
    {start: 0, end: 10},
    {start: 80, end: 100},
    {start: 120, end: 150},
    {start: 220, end: 400},
    {start: 500, end: 600}
];

这是我目前的工作解决方案（JS Bin）

var boundary = {
    start: 0,
    end: 600
};
// for example i use two arrays with ranges, but in reality they are n (>= 1)
var numbersRanges1 = [
    {start: 100, end: 120},
    {start: 180, end: 200},
    {start: 400, end: 500}
];
var numbersRanges2 = [
    {start: 10, end: 80},
    {start: 150, end: 220},
    {start: 480, end: 500}
];
// result should look like
var expected = [
    {start: 0, end: 10},
    {start: 80, end: 100},
    {start: 120, end: 150},
    {start: 220, end: 400},
    {start: 500, end: 600}
];
// merge arrays
var mergedRanges = numbersRanges1.concat(numbersRanges2);

// sort by start
function sortByStart(a, b){
    return a.start - b.start;
}
mergedRanges = mergedRanges.sort(sortByStart);
// group overlapping ranges
for(var i = 1; i < mergedRanges.length; i++){
    var range1 = mergedRanges[i-1];
    var range2 = mergedRanges[i];
    if((range1.start <= range2.end) && (range1.end >= range2.start)){
        range2.start = Math.min(range1.start, range2.start);
        range2.end = Math.max(range1.end, range2.end);
        mergedRanges.splice(i-1, 1);
    }
}
// go throw merged ranges and save ranges between in addition array
var freeRanges = [];
if(mergedRanges[0].start > boundary.start){
    freeRanges.push({
        start: boundary.start,
        end: mergedRanges[0].start
    });
}
for(var i = 1, mergedLen = mergedRanges.length; i <  mergedLen; i++){
    freeRanges.push({
        start: mergedRanges[i-1].end,
        end: mergedRanges[i].start
    });
}
if(mergedRanges[mergedLen-1].end < boundary.end){
    freeRanges.push({
        start: mergedRanges[mergedLen-1].end,
        end: boundary.end
    });
}
console.log(freeRanges);
console.log(expected);

该脚本在node.js服务器上运行。因为我们做了很多这样的并发计算，所以我试图找到一种资源高效且性能良好的算法。有更好的方法来实现这一点吗？我的代码中是否存在导致性能问题的陷阱？

这里有一个简化版本。

// for example i use two arrays with ranges, but in reality they are n (>= 1)
var numbersRanges1 = [
    {start: 100, end: 120},
    {start: 180, end: 200},
    {start: 400, end: 500}
];
var numbersRanges2 = [
    {start: 10, end: 80},
    {start: 150, end: 220},
    {start: 480, end: 500}
];
var boundary = {
    start: 0,
    end: 600
};
// merge arrays
var mergedRanges = numbersRanges1.concat(numbersRanges2);
// sort by start
function sortByStart(a, b){
    return a.start - b.start;
}
mergedRanges = mergedRanges.sort(sortByStart);
// go throw merged ranges and save ranges between in addition array
var freeRanges = [];
var start=0;
mergedRanges.forEach(function(one) {
  if(one.start<start) return;
  freeRanges.push({start:start,end:one.start});
  start=one.end;
});
if(start<boundary.end) {
  freeRanges.push({start:start,end:boundary.end});
}
console.log(JSON.stringify(freeRanges,null,2));
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