Planets Queries I - Implementation

Here is the solution:

function preprocess(f, n)
    jump[0][x] := f[x] for all x
    for i from 1 to log2(n)
        for x from 1 to n
            jump[i][x] := jump[i-1][jump[i-1][x]]

function query(x, k)
    for i from log2(k) down to 0
        if k has bit i set then
            x := jump[i][x]
    return x

Time: $O(n \log n)$ preprocessing, $O(\log k)$ per query. Space: $O(n \log n)$ for the table. The bit manipulation checks each bit of $k$ to decide which jumps to make.