求两个数之间的等差数列

Question

我有两个数字，我需要在这两个数字之间找到一个等差数列，它应该始终包含数字零。

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 ， [-7, -4.17, -1.33, 1.5, 4.33, 7.17, 10]得到缺少零的[-7, -4.17, -1.33, 1.5, 4.33, 7.17, 10] 。

以下是情况

1. numberOfPoints是固定的min和max变化。
2. min始终为负max可能是也可能不是负值。
3. 可以将A negative threshold value添加到min以获得其中包含数字零的等差数列。

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 ，你不能在 6 步中得到 0 的arithmetic progression ，因为在 6 步中，步长的最小差异是1001/6=166.86 ，而如果你包括0 ，则最大值of step 必须为1才能不超过最大值。

添加负阈值无关紧要，因为它只会增加步长的值。

PS：我在上面的例子中忽略了这一步min is always negative max may or may not be negative. ，因为这一步更容易证明不可解。 min=-10 , max=-9 ，它们之间没有零并且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 an 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 */