Quick Select - Coursera Algorithms

Quick select finds k^th smallest element by partitioning. It takes linear time and O(N²) in worst case.

Following is the program:

Quick Sort - Coursera Algorithms

Quick Sort uses a partition element, such that the there are no larger entries to it's left and no smaller entries to it's right. It is in place, but not a stable sort.

Time complexity: O(NlgN)
Worst case : O(N²)

Following is the program:

Merge Sort - Coursera Algorithms

Merge sort uses divide and conquer approach to sort the elements. It takes at most NlgN compares and 6NlgN array accesses with total running time of NlgN.

Following is an optimized merge sort - it uses insertion sort for less number of elements. Please see Insertion Sort for the insertion sort algorithm. It also has a method for bottom up merge sort which is not as efficient as the recursive merge sort.

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Insertion Sort

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:

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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:

Generic Stack Using Resized Array And Iterator - Coursera Algorithms

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

Following is the program:

Generic Stack Using Linked List And Iterator - Coursera Algorithms

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

Following is the program:

Queue Using Array Resizing - Coursera Algorithms

Queues follow FIFO standard. To implement, we need to maintain two indices to first and last elements of the array, for enqueue and dequeue operations.

Following is the program:

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Queue Using Linked List - Coursera Algorithms

Queue Using Linked List - Coursera Algorithms

Queues follow FIFO standard. To implement, we need to maintain two pointers to first and last nodes of linked list, as we insert at the end of the list and removed the first element of the list for enqueue and dequeue operations.

Following is the program:

Stack Using Array Resizing - Coursera Algorithms

When implementing stacks using arrays, we may run into overflow and underflow problems. We can resize the array on need basis by doubling the array in push op when the array has reached it's limit and by halving the array in pop op when the array is just 25% utilized. 

This will result in constant amortized time operations, but ~N in worst case.

Linked list on the other hand has constant time even in worst case. But still, linked list may take more time and memory because of the links. 

If occasional slow ops are bearable, then arrays would be a better option than linked lists. 

Following is the complete program:

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Stack Using Linked List - Coursera Algorithms

Stack Using Array - Coursera Algorithms

Stack Using Array - Coursera Algorithms

Stack works in a LIFO order. It supports insert, remove, iteration and test for empty operations.

They can be represented using array. An initial capacity for this array is taken as input. We manipulate an index variable for push and pop, instead of actually deleting items from stack.

If using objects in stack, avoid loitering(holding references to objects and preventing GC) by using following code in pop operation:

public String pop() { String item = s[--N]; s[N] = null; return item; } 

Following is the complete program:

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Stack Using Linked List - Coursera Algorithms

Stack Using Linked List - Coursera Algorithms

Stack works in a LIFO order. It supports insert, remove, iteration and test for empty operations.

They can be represented using linked list. Push and pop operations are done on the first element. This takes constant time for any operation and about ~36N Bytes for N stack items - 16B overhead + 8B inner Node class + 8B reference to Node object + 4B for integer values.

Following is the program: