How should I practice Count Reachable Values by Halving and Decrementing?

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Problem · Breadth First Search

Count Reachable Values by Halving and Decrementing

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infosysNEW GRADOA

Problem statement

Start from the nonnegative integer num. From any current value you may perform either allowed operation:

If the value is even, replace it with half of itself.
If the value is positive, replace it with one less.

For this exercise, assume you may perform at most steps operations. Count the distinct nonnegative values that can appear across all valid operation sequences, including the initial value reached with zero operations.

Function

countReachableValues(num: int, steps: int) → int

Examples

Example 1

num = 6steps = 2return = 5

The reachable values are 6, 5, 3, 4, and 2.

Example 2

num = 0steps = 60return = 1

Halving zero returns zero and decrement is unavailable, so only zero is reachable.

Example 3

num = 5steps = 0return = 1

With no operation allowed, only the initial value is counted.

Constraints

0 <= num <= 10^9.
0 <= steps <= 60.
The answer fits in a signed 32-bit integer.