Shell Sort - Coursera Algorithms

Shell sort moves entries by more than one position at a time. It is basically insertion sort with a stride length h - it considers h interleaved sequences and sorts them using insertion sort. When the increment(h) is big, the sub-arrays are smaller and when the increment gets shorter in subsequent iterations, the array is already partially sorted. In both cases, insertion sort works great and hence, it's the best option here.

The optimal value for h is provided by Knuth as 3X+1, but no accurate model has been found for this algorithm yet.

It takes O(N3/2) compares in worst case. It's fast unless array size is large and it has less footprint for code. These make it a perfect choice for hardware sort prototype, linux/kernel, embedded systems etc.

Following is the program:

Related Posts: 

Insertion Sort

Insertion Sort - Coursera Algorithms

Insertion Sort swaps an element with a larger entry to it's left.

It take ~1/4 N2 compares and ~1/4 N2 exchanges.
Best case(already sorted) : N-1 compares and zero exchanges.
Worst case(reverse sorted):  ~1/2 N2 compares and ~1/2 N2 exchanges.
Partially sorted(when number of inversions <= cN): linear time as number of exchanges equal the number of inversions.

Following is the program, it also uses shuffle to make the order as random as possible. This is done by swapping each element with a random index r such that r is between 0 and iteration i. This takes linear time.

Selection Sort - Coursera Algorithms

Selection sort finds the minimum element and swaps it with the first element, till the complete array is sorted. It takes N²/2 compares and N exchanges.

Following is the program:

Decimal To Binary Conversion Using Stack

Stack can be used to convert a number into it's binary form.

1. Push the remainder into stack after dividing the number by 2.
2. Keep doing 1, till number>0.
3. Pop the binary remainders 1/0 to get the binary form.

 Following is the program:

 

Arithmetic Expression Evaluation Using Stack

Arithmetic expressions can be evaluated using two stacks - one for operands and other for numeric values.

Algorithm:

1. If element is numeric, push to numeric stack.
2. If element is operand, push to operand stack.
3. If element is "(", ignore. 
4. If element is ")", pop operand from operand stack and pop two numerics from numeric stack - perform the operation and push the result back into numeric stack. 

 Following is the program based on the generic stack implementation using arrays.

Generic Queue Using Resized Array And Iterator - Coursera Algorithms

To make the stack generic and to hide the internal representation of a queue from client, we can use Generics and Iterator.

Following is the program:

Generic Queue Using Linked List And Iterator - Coursera Algorithms

To make the stack generic and to hide the internal representation of a queue from client, we can use Generics and Iterator.

Following is the program: