Cut and Paste - Analysis

To move $[l, r]$ to the end:

$1.$ Split at $l$: get $[0, l-1]$ and $[l, n-1]$

$2.$ Split the second part at $r-l+1$: get $[l, r]$ and $[r+1, n-1]$

$3.$ Merge: $[0, l-1] + [r+1, n-1] + [l, r]$

Each split and merge is $O(\log n)$. With $2$ splits and $2$ merges, total time per operation is $O(\log n)$. This pattern (split, rearrange, merge) handles many sequence manipulation problems.