Elementary sorts (selection, bubble, insertion)

O(n^2)

Sort with simple nested-loop passes: repeatedly pick the next-smallest element, swap adjacent out-of-order pairs, or insert each element into its sorted place among what came before.

Signals

n is small (tens or a few hundred)array is nearly sorted alreadysort in place with O(1) extra spaceteaching/interview question about how sorting worksstability matters and simplicity is fine

Template

function insertionSort(arr) {
    for (let i = 1; i < arr.length; i++) {
        const key = arr[i];
        let j = i - 1;
        while (j >= 0 && arr[j] > key) {
            arr[j + 1] = arr[j];
            j--;
        }
        arr[j + 1] = key;
    }
    return arr;
}

Looks similar, isn't

Fast sort (merge/quick): Elementary sorts are O(n^2), fine for small n or nearly-sorted input. Once n is large (thousands+) and unordered, the n^2 passes get too slow; you need an O(n log n) sort instead.

n small (roughly under a few hundred) or nearly sorted -> O(n^2) time is acceptable, O(1) space. Once the problem states n in the thousands or more, this stops being the answer.

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