Algorithms Set 8

Given two integers L and R, write a program that finds the count of numbers having prime number of set bits in their binary representation in the range [L, R].

Example 1:

Example 2:

Your Task:  
You dont need to read input or print anything. Complete the function primeSetBits() which takes L and R as input parameter and returns the count of numbers having prime number of set bits in their binary representation.

Expected Time Complexity: O(nlog(n)sqrt(n))
Expected Auxiliary Space: O(1)

Constraints:
1 <= L <= R <=1000

Given a number N, print all its unique prime factors and their powers in N.

N = 100
Factor Power
  2      2
  5      2

N = 35
Factor  Power
  5      1
  7      1

Input:
The first line of input contains an integer T denoting the number of test cases.The first line of each test case is N.

Output:
Print all prime factors and their powers separated by spaces.  The output should be printed in increasing order of prime factors.

Constraints:
1 ≤ T ≤ 200
2 ≤ N ≤ 10000

Example:

Given a number N, the task is to find the largest prime factor of that number.
 

Example 1:

Example 2:

Your Task:
You don't need to read input or print anything. Your task is to complete the function largestPrimeFactor() which takes an integer N as input parameters and returns an integer, largest prime factor of N.
 

Expected Time Complexity: O(sqrt(N))
Expected Space Complexity: O(1)
 

Constraints:
1 <= N <= 10⁵