> For the complete documentation index, see [llms.txt](https://cs61b-2.gitbook.io/cs61b-textbook-fall-2026/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://cs61b-2.gitbook.io/cs61b-textbook-fall-2026/34.-radix-sorts/34.3-msd-radix-sort.md).
# 34.3 MSD Radix Sort
Basic idea: Just like LSD, but sort from leftmost digit towards the right.
Suppose we sort by topmost digit, then middle digit, then rightmost digit. Will we arrive at the correct result?
No, this will result in sorting the array by right most digit only as we are not saving the topmost and middle digit.
MSD Radix Sort (correct edition)
Notice first we sorted by leftmost digit. Then we grouped the data by the leftmost digit, so one group would start with a's, then the next group would start with b's, and so on and so forth. Then within our subgroups we would order by middle digit, and create newer subgroups. And finally we would break this up into further subgroups until we have all individual subproblems. This final result would be sorted.
### Runtimes
Best Case.
* We finish in one counting sort pass, looking only at the top digit: $$\Theta(N+R)$$
Worst Case.
* We have to look at every character, degenerating to LSD sort: $$\Theta(WN+WR)$$
### Summary of Runtimes
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