Sparse Table - Building

For $k = 0$, set st[i][0] = tourDepth[i] (minimum over range of length $1$). For larger $k$, use the recurrence: st[i][k] = min(st[i][k-1], st[i + 2^(k-1)][k-1]). This works because a range of length $2^k$ splits into two ranges of length $2^{k-1}$. The first half starts at $i$, the second half starts at $i + 2^{k-1}$.

You compute this bottom-up: first all ranges of length $1$, then length $2$, then length $4$, and so on. Each entry depends only on smaller powers, so the DP order is correct. Time: $O(n \log n)$ because you fill a table of size $n \times \log n$, and each entry takes $O(1)$ time to compute.