Algorithms in a Nutshell

Insertion Sort

In the card game Bridge, each player is dealt 13 cards, all face down. One way to arrange a hand is to pick up the cards one at a time and insert each card into the hand. The invariant to maintain is that the cards in the hand are always sorted by suit and then by rank within the same suit. Start by picking up a single card to form a hand that is (trivially) already sorted. For each card picked up, find the correct place to insert the card into the hand, thus maintaining the invariant that the cards in the hand are sorted. When all the cards are placed, the invariant establishes that the algorithm works. When you hold cards in your hand, it is easy to insert a card into its proper position because the other cards are just pushed aside a bit to accept the new card. When the collection is stored in memory, however, a sorting algorithm must do more work to manually move information, in order to open up space for an element to be inserted.

The pseudocode in Figure 4-6 describes how Insertion Sort repeatedly invokes the insert helper function to ensure that A[0,i] is properly sorted; eventually, i reaches the rightmost element, sorting A entirely. Figure 4-7 shows how Insertion Sort operates on a small, unordered collection A of size n=16. The 15 rows that follow depict the state of A after each pass. A is sorted "in place" by incrementing pos=1 up to n−1 and inserting the element A[pos] into its rightful position in the growing sorted region A[0,pos], demarcated on the ...