查找两个数字之间的算术级数

Question

我有两个数字，我需要找到这两个数字之间的算术级数，以使它始终包含数字zero。

下面是我的代码。

var numberOfPoints = 6;
var min = -5;   
var max = 10;
var step = (max - min) / numberOfPoints;
var pointsArray = [min];
var point = min;
for (var i = 0; i < numberOfPoints; i++) {
   point = point + step;
   pointsArray.push(+point.toFixed(2));
}
console.log(pointsArray); //[-5, -2.5, 0, 2.5, 5, 7.5, 10]

代码工作正常。

但是如果我更改min = -7，则会得到缺少zero的[-7, -4.17, -1.33, 1.5, 4.33, 7.17, 10]。

以下情况

1. [numberOfPoints是固定的min，并且max有所不同。
2. [min始终为负max可以为负，也可以不为负。
3. A negative threshold value可以加到min上以获得数字为[[zero的算术级数。

Answer 1

此任务无法解决

Following is the situation

- numberOfPoints is fixed min and max varies.
- min is always negative max may or may not be negative.
- A negative threshold value can be added to min to get an arithmetic progression having number zero in it.

证明：numberOfPoints= 6，min=-1000和max=1不能以零为单位在6步中获得arithmetic progression，因为在6步中步的最小差为1001/6=166.86，而如果包括0，则步的最大值必须为1以不超过最大值。
添加负阈值并不重要，因为它只会增加step的值。
PS：在min is always negative max may or may not be negative.以上的示例中，我忽略了此步骤，因为此步骤甚至更容易证明是不可解决的。 min=-10，max=-9之间没有零，添加负阈值不会改变它。

Answer 2

/*

min and max must have opposite signs, because there's no zero between two negative numbers
but they cannot be arbitrary, they have to satisfy a condition

if the k-th term of the progression is zero then min + k * step = 0 or 
min + k * (max - min) / numberOfPoints = 0 
from which k = - numberOfPoints * min / (max - min)
the condition is that - numberOfPoints * min / (max - min) must be a positive integer 
in the interval [1, numberOfPoints]
otherwise there's no solution

in the first example that you have (-6) * (-5) / (10 - (-5)) = 3
but in the second (-6) * (-7) / (10 - (-7)) = 2.470588235294118
(-4, 2), (-3, 3), (-2, 4) will all work, but (-2, 3) won't

*/