求两个数之间的等差数列

Question

I have two numbers and I need to find an arithmetic progression between those two numbers in such a way it should always contain number zero .

Below is my code.

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]

Code works fine.

But if I change min = -7 , I get the [-7, -4.17, -1.33, 1.5, 4.33, 7.17, 10] which is missing zero .

Following is the situation

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

Answer 1

This task is not solvable

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.

Prove: numberOfPoints= 6 , min=-1000 and max=1 , you cant get arithmetic progression in 6 steps with zero, because in 6 steps minimum difference of step is 1001/6=166.86 , while if you include 0 , the maximum value of step must be 1 to not reach over the maximum.

Adding negative treshold does not matter as it only increase the value of step.

PS: I ignored this step in example above min is always negative max may or may not be negative. , because this step is even easier to prove that is not solvable. min=-10 , max=-9 , there is no zero between them and adding negative treshold does not change it.

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 */