Language With isZero Output Sequence | Dataford Interview Questions

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Problem

Study's learning interface uses a counter abstraction with only three operations: increment(), decrement(), and isZero(). Given a maximum digit and a repetition count, generate the repeating sequence 01234543210... without comparing counter values or using relational operators.

Return the generated digits as a string. Each repetition contains the values from 0 through maximum, followed by the values from maximum - 1 back to 0.

Formal Specification

Implement generate_wave(maximum, repetitions):

maximum is a non-negative integer specifying the peak digit.
repetitions is a non-negative integer specifying how many complete waves to emit.
Return a string containing all emitted digits.
Counter movement and loop termination must use only increment(), decrement(), and isZero().
Do not use <, >, <=, >=, equality checks, arithmetic on counter values, or conversion of a counter to an integer during the algorithm.

Constraints

0 <= maximum <= 1000
0 <= repetitions <= 1000
The output length is at most 2,001,000 characters
Counters are initialized with non-negative values
Counter control flow may use only increment(), decrement(), and isZero()

Function Signature

def generate_wave(maximum, repetitions):