'Rounded number to a best suitable nearest number so that i can calculate the interval thats are factor of 2, 5 or 10

There can be any specified number, then I want to write a function to return the best upper limit number to calculate the interval.

To divide the number into 5 intervals, the best numbers are

  1. if less than or equal 5 = divide into 1, 2, 3, 4, 5
  2. if 10 => divide into 2, 4, 6, 8, 10
  3. if 25 => divide into 5, 10, 15, 20, 25
  4. if 50 => divide into 10, 20, 30, 40, 50
  5. if 100 => divide into 20, 40, 60, 80, 100
  6. if 125 => divide into 25, 50, 75, 100, 125
  7. If 500 => divide into 100, 200, 300, 400, 500

But the input number, cannot be that 5, 10, 25, 50, 100, 125, 500, ...

So I would like to write a function that can return the best bold number, but i am stuck now. I want to calculate on the fly. No predefined values as I don't know what would be the input number. For less than or equal to 10, i can add additional to handle, but greater than 10, I want to get through by some formula calculation.

input output
8 10
13 25
110 125
456 500
1601 2000
53194 60000

Is there any formula to calculate so that I can write the function that takes the above input and return the output? Thanks a lot.

The reason not to split 110 into 22, 44, 66, 88, 110, these numbers are not suitable to appear in the chart axis except 2, 4, 6, 8 , 10.

javascriptalgorithmmath


Solution 1:[1]

I suggest defining your interval in some way like this:

For a positive input number n, find the minimum interval i such that 5i >= n and i is one of the following forms: 10^k, 2(10^k), 5(10^k), or 25(10^k), where k is a non-negative integer

You can then solve the resulting inequalities by taking logarithms, and take the minimum viable solution to find the interval.

function interval(n, steps=5) {

  // Find the minimum x such that x = a*b^k >= n / steps, where k is an integer 
  const solve = (a, b) => a * b ** Math.ceil(Math.log((n / steps) / a) / Math.log(b));

  // Return the lowest of the possible solutions    
  return Math.min(
    solve(1, 10),
    solve(2, 10),
    solve(5, 10),
    solve(25, 10)
  ); 
}
// alternatively const interval = (n, steps=5) => Math.min(...[1, 2, 5, 25].map(a => a * 10 ** Math.ceil(Math.log10((n / steps) / a))));
const inputs = [5, 8, 13, 110, 456, 1601, 53194];
console.log("input\t int\t limit");
for (const n of inputs) {
  console.log(n, '\t', interval(n), '\t', 5 * interval(n));
}

This does not match your suggested output in all cases, but does provide sensible and consistent values. You could adjust the forms that are allowed if you want to tweak this.

Sources

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Source: Stack Overflow

Solution Source
Solution 1

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