googling

Data Structures and Algorithms

Tree:

• Tree representation in java
• BST find node (Recursive & Iterative)
• Min-Heap & Max-Heap (Heap & Heap)
• BFS & DFS
• Pre-order , In-order & Post-order Traversals (only recursive way till now)
• Height of a tree
• print nodes of BST in sorted order , use Inorder traversal

Dynamic Programming

Optimal substructure

It is when a problem is composed of subproblems of same type . Same type is the key here

Let's consider an example:

1. In this example
   we have to find the shortest path between A -> C . Now, this can be broken down into two subproblems ,i.e. shortest path from A -> B + shortest path from B -> C
   So, the problem can be said to be composed of subproblems of same tyoe i.e. both were of same nature of finiding the shortest

2. Now consider the below example:
   
   In this we have to find the longest distance between A -> D. The longest distance comes out to be 6KM via C, however we have to note that this is not a combination of longest distance between A -> C and longest distance between C -> D . Because in that case A -> C would had the value 3+2+4=9KM and C -> D would had 2+3+2=7KM, thus this problem cannot be said to be composed of subprolems of Same Type . They are not of same type i.e. find longest path of every subproblem, thus this example doesn't exhibit the property of Optimal subtructure

Overlapping Subproblems

This happens when the subproblems are calculating the problems which have been already calculated earlier by another subproblem.
Consider the example of Fibonacci (without any optimisation or memoization)when we calculate Fib(5) , then fib(3) gets calculated more than 1 time, so as fib(2) etc. Thus this problem of fibonacci can be said to have overlapping subproblems, because subproblems are overlapping or in other words going over the same problem which has been calculated earlier.