Sorting

Insertion sort vs Heap sort

Insertion sort and Heap sort both put an array in order, in different ways. Insertion sort: insert each value into a sorted prefix. Heap sort: build a max-heap in the array, then repeatedly move the largest value to the end. In the worst case heap sort takes O(n log n) while insertion sort takes O(n²), so heap sort scales better on large inputs.

At a glance

Property	Insertion sort	Heap sort
Technique	Insert each value into a sorted prefix	Build a max-heap in the array, then repeatedly move the largest value to the end
Best case time	O(n)	O(n log n)
Average case time	O(n²)	O(n log n)
Worst case time	O(n²)	O(n log n)
Extra space	O(1)	O(1)
Stable (equal values keep their order)	Yes	No
In place (no extra array)	Yes	Yes
Needs sorted input	No	No

Choose insertion sort when

the array is small or nearly sorted.

Avoid it when

the array is large and in random order.

Choose heap sort when

you need a guaranteed O(n log n) time and almost no extra memory.

Avoid it when

you need a stable sort, or the fastest sort on typical data.

The same inputs, counted

These numbers come from running both real implementations: operations (comparisons plus writes, a swap counting as two writes).

Input	Insertion sort	Heap sort
Mixed	30	43
Already sorted	12	53
Reversed	48	40
Nearly sorted	14	50
Duplicates	36	36

Insertion sort vs Heap sort

At a glance

Choose insertion sort when

Avoid it when

Choose heap sort when

Avoid it when

The same inputs, counted

See them run

More comparisons

Insertion sort vs Heap sort

At a glance

When to choose each

Choose insertion sort when

Avoid it when

Choose heap sort when

Avoid it when

The same inputs, counted

See them run

More comparisons