Is there any efficient algorithm to find the number of iterations of any two values when the values are changing in a certain range? [closed]

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Main Codes

class NumIteration {
  input(num) {
     // do something
  }
  
  getIteration(num1, num2) {
    // do something
  }
}

Test Case:

const ni = new NumIteration()

ni.input(1)
ni.input(2) // 1 -> 2
ni.input(1) // 2 -> 1

ni.getIteration(1, 2) // return 1

ni.input(2) // 1 -> 2
ni.getIteration(1, 2) // return 2
ni.getIteration(2, 1) // return 1

ni.input(3) // 2 -> 3
ni.getIteration(2, 3) // return 1
ni.getIteration(1, 3) // return 1
ni.getIteration(1, 2) // return 2


ni.input(2) // 3 -> 2
ni.getIteration(3, 2) // return 1
ni.getIteration(2, 3) // return 1


ni.input(1) // 2 -> 1
ni.getIteration(2, 1) // return 2
ni.getIteration(3, 1) // return 1

ni.input(3) // 1 -> 3 Value changes may not be continuous
ni.getIteration(1, 3) // return 2
ni.getIteration(2, 3) // return 2
ni.getIteration(1, 2) // return 3
ni.getIteration(2, 1) // return 2

Requirements

Ensure memory usage as much as possible（the recording range shall not exceed the value change range）

As in the above example, you can store the following records in the input method:

class NumIteration {
  records = [
    { value: 1, ... },
    { value: 2, ... },
    { value: 3, ... },
  ]


  input(num) {
     // this.records....
  }
}