How do relatively modern languages such as ruby/python/js etc may store multiple data types in arrays and are still able to access any element from the array using its index in O(1) time?
As far as I understand, we do simple mathematics to determine the memory address pointing to any element, and we do so by the index multiplied by the size of each element of the array.
Firstly, neither the Ruby Language Specification nor the Python Language Specification nor the ECMAScript Language Specification prescribe any particular implementation strategy for arrays (or lists as they are called in Python). Every implementor is free to implement them however they wish.
Secondly, lumping them all together doesn't make much sense. For example, in ECMAScript, arrays are really just objects with numeric properties, and actually, those numeric properties aren't even really numeric, they are strings.
Third, they don't really store multiple data types. E.g. Ruby only has one data type: objects. Since everything is an object, everything has the same type, so there is no problem storing objects in arrays.
Fourth, at least the Ruby Language Specification does not actually guarantee that array access is O(1). It is highly likely that a Ruby Implementation which does not provide O(1) access would be rejected by the community, but it would not violate any spec.
Now, of course, any implementor is allowed to be as clever as they want to be. E.g. V8 detects when all values of an array are numbers and then stores the array differently. But that is a private internal implementation detail of V8.
In memory, a heterogeneous array is an array of pointers. Every array element stores the memory address of the item at that position in the array.
Since memory addresses are all the same size, you can find the address of each address by multiplying the array index by the address size, and adding it to the base address of the array.
