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insert_sorting.md

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Insertion Sort

Insertion-Sort(A, n) --> A[1...n]

for j <-- 2 to n
insert key A[j] into the already sorted sub-array A[1...j-1].
by pairwise key-swaps down to its right position

Example of insertion sort

original array : [8, 2, 4, 9, 3, 6]
step 1 : [2, 8, 4, 9, 3, 6]
step 2 : [2, 4, 8, 9, 3, 6]
step 3 : [2, 4, 8, 9, 3, 6]
step 4 : [2, 3, 4, 8, 9, 6]
step 5 : [2, 3, 4, 6, 8, 9]

Worst-case performance : O(n^2) comparisons and swaps
Best-case performance : O(n) comparisons, O(1) swaps
Average performance : O(n^2) comparisons and swaps
Worst-case space complexity : O(n) total, O(1) auxiliary

The insertion sort has several advantages:simple implementation,stable.