Write an efficient C program to find the maximum average of contiguous elements inside an array of integers.

Example: [10, 4, -2, 7, 8, -1, -5] Maximum average of continuous elements 7+8=15/2 =7.5

Given a network of the employees of a company such that edges are between those employees who are friends to each other. Divide the employees into two teams such that no two people who are friends to each other are in the same team

You are Reciving the infinite number of stream , you to retun k random elemnts ,if you query at time t , in those k elements then proababilty of choosing should be 1 e.g. they should have equal probality

Find The Largest Binary Search Tree in GIven Tree . Its Should be the Subtree.

Very Faq. Asked Question All Tech Giants :) Will Post The Solution Soon :) Meanwhile You Can Try & Post the approach . 

Prerequisite  : Most Efficient Solution to Check if Given Tree is BST or not ? !st Try it or Search Archives :)

Basic Idea :

Traverse the tree. From each node to the parent, return the following
set of values.
1) If BST, size of the current BST or -1 if the tree is not.
2) Minval & Maxval of the subtree and maxbstsize seen so far (
probably using references)
So in each node check the following:

If( leftmax < node->data && node->data < rightmin)  // Means it is a BST
{
  new size = rightsize+leftsize+1
  update size if greater than max
  return size
}
else
{
  return -1;
} 

 Working Code:

 
/* Largest Binary search tree inside a binary tree -- O(n)*/

#include <stdlib.h>
#include <stdio.h>
using namespace std;

struct node
{
  int data;
  struct node* left;
  struct node* right;
};

struct node* insert_bst(struct node* root, int num){
  if(root == NULL){
    root = (struct node*)malloc(sizeof(struct node));
    root->data = num;
    root->left = NULL;
    root->right = NULL;
    return root;
  }else{
    if(num == root->data){
      return root;
    }

    if(num > root->data){
      root->right=insert_bst(root->right,num);
    }else{
      root->left=insert_bst(root->left,num);
    }
  }
  return root;
}

void inorder_traverse(struct node* root){
  if(root == NULL) return;

  inorder_traverse(root->left);
  printf("%d ",root->data);
  inorder_traverse(root->right);
}

struct node* bst_root = NULL;

int getmaxbst(struct node* root, int& subtreemin, int &subtreemax, int& max)
{
  if(root == NULL) return 0;

  int leftsubtreemin = -32767, rightsubtreemin = -32767;
  int leftsubtreemax = 32767, rightsubtreemax = 32767;
  int x,y;

  x = getmaxbst(root->left, leftsubtreemin, leftsubtreemax, max);
  y = getmaxbst(root->right, rightsubtreemin, rightsubtreemax, max);

  if(x==-1 || y ==-1)
    return -1;
  if(x==0) { leftsubtreemax = root->data; leftsubtreemin = root->data;}
  if(y==0) { rightsubtreemin = root->data; rightsubtreemax = root->data;}

  if(root->data < leftsubtreemax ||
     root->data > rightsubtreemin){
    return -1;
  }

  subtreemin = leftsubtreemin;
  subtreemax = rightsubtreemax;

  if(x+y+1 > max){
    max = x+y+1;
    bst_root = root;
  }

  return x+y+1;

}

int main()
{
  struct node* root=NULL;

  root=insert_bst(root,5);
  root=insert_bst(root,3);
  root=insert_bst(root,9);
  root=insert_bst(root,7);
  root=insert_bst(root,4);
  root=insert_bst(root,1);
  root=insert_bst(root,14);
  root=insert_bst(root,11);

  root->data = 0;

  int a,b,c,max=-32767;
  c = getmaxbst(root,a,b,max);
  printf("\nmax is %d\n",max);

  inorder_traverse(bst_root);
  return 1;
} 

TC O(N)

SC O(1) 

Find all the "maximal independent sets" in a given graph

Find the sum of contiguous subarray within a one-dimensional array of numbers which has the largest sum.

How do you find a shortest connection between two persons on Facebook(if the same exists)? You are provided with an API which returns the list of friends of a particular persons

Given an array of n integers having elements 1-n. By mistake one element repeated twice in the array and one element got missed. Need to find out the missing and repeated element. Time=O(n),space=O(1)

Devise an algorithm for maximizing the sum of the randomly selected elements from the k subarrays. Basically means that we will want to split the array in such way such that the sum of all the expected values for the elements selected from each subarray is maximum.

You have an array with *n* elements. The elements are either 0 or 1. You
want to *split the array into kcontiguous subarrays*. The size of each
subarray can vary between ceil(n/2k) and floor(3n/2k). You can assume that
k << n. After you split the array into k subarrays. One element of each
subarray will be randomly selected.

Devise an algorithm for maximizing the sum of the randomly selected
elements from the k subarrays. Basically means that we will want to split
the array in such way such that the sum of all the expected values for the
elements selected from each subarray is maximum.

You can assume that n is a power of 2.

Example:

Array: [0,0,1,1,0,0,1,1,0,1,1,0]
n = 12
k = 3
Size of subarrays can be: 2,3,4,5,6

Possible subarrays [0,0,1] [1,0,0,1] [1,0,1,1,0]
Expected Value of the sum of the elements randomly selected from the
subarrays: 1/3 + 2/4 + 3/5 = 43/30 ~ 1.4333333

Optimal split: [0,0,1,1,0,0][1,1][0,1,1,0]
Expected value of optimal split: 1/3 + 1 + 1/2 = 11/6 ~ 1.83333333


Source -> http://stackoverflow.com/questions/8189334/google-combinatorial-optimization-interview-problm

Given a set of numbers [1-N] . Find the number of subsets such that the sum of numbers in the subset is a prime number.

Devise a small memory streaming algorithm to determine if |A| = 1.

For a stream of insertions and deletions, recall that x[j] = #insertions - #deletions of element j.
Given such a stream satisfying x[j] >= 0 for all elements j, let

A = { j : x[j] > 0 }

Determining whether A is empty is easy: just check if the sum of all x[j]'s equals 0 (which is easily doable in a stream).

Problem: devise a small memory streaming algorithm to determine if |A| = 1.

Extensions: What about higher sizes of A? What if the promise is not satisfied and we define A to be the set of j's with x[j] not equal to 0.

Given a string of lowercase characters, reorder them such that the same characters are at least distance d from each other.

Input: { a, b, b }, distance = 2

Output: { b, a, b }

Given Table of Cities , Find Minimum Number of Hopes Required to Fly From One to Other City

There is a very Primitive Database and it has a table say "Travel". The content of table is as follows:

Source | Dest
--------------


Sea | LA
LA | FL
LA | MA
FL | Sea
Sea | FL

The ask is to find out all routes between (Sea) to (FL) with mininum hop.
the Result would be:
1. Sea -> FL
2. Sea -> LA - > FL

You have to write a Middle tier function to achieve above result. You can assume there is DBAPI that return the Destination city if you provide the source city.

Given two bst, print the output that would come if two bsts are merged and then an inorder traversal is performed. Of, course you can't merge trees here.

PS:Heard From One of The My Friend :

Provide an efficient algorithm to solve the question "Can I buy N items?

 A shop sells an item in packets of 6, 9, and 17. A customer can buy any number of packets, but a packet cannot be broken up. Provide an efficient algorithm to solve the question "Can I buy N items?". For example, is it possible to buy 29 items? What about 19? Your algorithm simply needs to return true or false.

Design Data Structure For Students-Courses Realtionship

In a university, students can enroll in different courses. A student may enroll for more than one course. Both students and courses can be identified by IDs given to them. Design a data structure to store students, courses, and the student-course relationships. You can use arrays, lists, stacks, trees, graphs, etc. or come up with your own data structures. Give the running times, in Big O notation, for the following operations for your data structure and justify the answers: a) Return all students in a list. b) Return all courses in a list. c) Return all courses in a list for a given student. d) Return all students in a list for a given course.

Given two words of equal length that are in a dictionary, write a method to transform one word into another word by changing only one letter at a time. The new word you get in each step must be in the dictionary

Numbers are randomly generated and passed to a method. Write a program to find and maintain the median value as new values are generated.

Given an Array of Strings . Write a program to find the longest word made of other words efficiently ?

Find the smallest number expressible as the sum of cubes of two numbers in two different ways. Indeed, 10^3 + 9^3 =12^3+1^3=1729 , Do It Efficiently

Problem:
A mathematician G. H. Hardy was on his way to visit his collaborator S. Ramanujan an who was in the hospital. Hardy remarked to Ramanujan that he traveled in taxi cab number 1729 which seemed a dull one and he hoped it was not a bad omen. To this, Ramanujan replied that 1729 was a very interesting number-it was the smallest number expressible as the sum of cubes of two numbers in two different ways. Indeed,
103 + 93 =123 + 1 3 二1729.

Hint: This problem is very similar to another very popular problem that is asked in interviews. You are given a  η ×η matrix in which both rows and columns are sorted in ascending order and you are supposed
to find a given number in the matrix.


Algorithm:
In this case, we are essentially looking for an implicit matrix A such that A(i,j) =i^3十j^3. In our case, the matrix will have n^1/3 rows and columns and this matrix of size n^1/3 * n^1/3 we try to search k=i^3+j^3 isn't it  ans algorithms for searching for a number in such a matrix that are linear in the number of rows.

One approach is to start by comparing x to An,1. If  x = An ,l , stop.Otherwise, there are two cases:
- x < A1,n in which case x is less than element at Column n at 1,n position. which mean we can escape whole row itself . we decrement column pointer to left.e.g. previous column.
- x > A1,n , in which case if x > a[1][n] is greater than it will be greater then all elements in Row 1.. we increment the row pointer to next row.


Efficient Solution:
Here is the Pseudo Code For The Same.
int IsNumberEqualstoSumeTwoCubes(int n)
{
       int row=Ceil(Pow(n,1/3));// Pow Has Complexity of O(logn) Ceil(1729)=577
       int column=row;
       int i=0;int j=column;
      while(i<row && j>=0)
     {
               int m=i*i*i+j*j*j;
               if(m==n)
                   return 1; // print i^3 and j^3 these are two such numbers
              else if ( m < n)
               i++;
              else
               j--;
      }
return 0; //such number DNE
}

Complexity Analysis:
In either case, we have a matrix with η fewer elements to search. In each iteration, we remove a row or a column, which means we inspect 2η-1 elements.


We claim that our algorithm that solves the matrix search problem will have to compare x with each of the 2n-l elements shown (i.e the diagonal elements (in case of column element matching )and  the elements immediately below them (in case of row elements matching )and this is obvious just draw a diagram in which both row & column are in sorted order & try to run the above algorithm ).
Call these elemmts the # elements..
Comparing x with any other elements in matrix does not eliminate the any of the # elements.we can easily Proof this by Contradiction:Suppose X algorithm doesn't compare x with  any of the above # elements.
then we could make that element x ( instead of x-1 got to prev. column  or x+1 go to next row.).hence we will get wrong result.

Above Algorithm Really Requires Deep Understanding of Young_tableau :)

Time Complexity O(row+column)=O(N^1/3+N^1/3)=O(2*N^1/3)=O(N^1/3)
Space Complexity O(1)