- Now, we take a more complex problem called sorting.
- Problem Definition: Sort given n numbers by non-descending order.
- There are many sorting algorithm. Insertion sort is a simple algorithm.
- Insertion Sort: We can assume up to first number is sorted. Then sort up to two numbers. Next, sort up to three numbers. This process continue till we sort all n numbers.
- Consider the following example of five integer:
79 43 39 58 13 : Up to first number, 79, is sorted.
43 79 39 58 13 : Sorted up to two numbers.
39 43 79 58 13 : Sorted up to three numbers.
39 43 58 79 13 : Sorted up to four numbers.
13 39 43 58 79 : Sorted all numbers. - That is, if first (i-1) numbers are sorted then insert ith number into its correct position. This can be done by shifting numbers right one number at a time till a position for ith number is found.
- That is, shift number at (i-1)th position to ith position, number in (i-2)th position to (i-1)th position, and so on, till we find a correct position for the number in ith position. This method is depicted in the figure on right side.
Sort