> For the complete documentation index, see [llms.txt](https://welchj.gitbook.io/cp-notes/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://welchj.gitbook.io/cp-notes/math/permutation.md).

# Permutation

## Generating Permutations

### 1. Recursion

At every point, loop through all future elements and make a decision if needs to include it or not.

```cpp
void search() {
    if (permutation.size() == n) {
        // process permutation
    } else {
        for (int i = 0; i < n; i++) {
            if (chosen[i]) continue;
            chosen[i] = true;
            permutation.push_back(i);
            search();
            chosen[i] = false;
            permutation.pop_back();
        }
    }
}
```