Given an integer . The task is to count all such numbers that are less than or equal to N which are divisible by any of 2 or 3 or 5.
Note: If a number less than N is divisible by both 2 or 3, or 3 or 5, or all of 2,3 and 5 then also it should be counted only once.
Input : N = 5 Output : 4 Input : N = 10 Output : 8
Simple Approach: A simple approach is to traverse from 1 to N and count multiple of 2, 3, 5 which are less than equal to N. To do this, iterate up to N and just check whether a number is divisible by 2 or 3 or 5. If it is divisible, increment the counter and after reaching N, print the result.
Time Complexity: O(N).
Efficient Approach: An efficient approach is to use the concept of set theory. As we have to find numbers that are divisible by 2 or 3 or 5.
Now the task is to find n(a),n(b),n(c),n(ab), n(bc), n(ac), and n(abc). All these terms can be calculated using Bit masking. In this problem we have taken three numbers 2,3, and 5. So, the bit mask should be of 2^3 bits i.e 8 to generate all combination of 2,3, and 5.
Now according to the formula of set union, all terms containing odd numbers of (2,3,5) will add into the result and terms containing even number of (2,3,5) will get subtracted.
Below is the implementation of the above approach:
- Count of Multiples of A ,B or C less than or equal to N
- Find the sum of all multiples of 2 and 5 below N
- Find numbers which are multiples of first array and factors of second array
- Sum of multiples of A and B less than N
- Sum of all the multiples of 3 and 7 below N
- Multiples of 3 or 7
- Find a Number X whose sum with its digits is equal to N
- Find all factorial numbers less than or equal to n
- Find a number x such that sum of x and its digits is equal to given n.
- Find three integers less than or equal to N such that their LCM is maximum
- Find the first N integers such that the sum of their digits is equal to 10
- Find an N x N grid whose xor of every row and column is equal
- Nth number in a set of multiples of A , B or C
- Sum of the multiples of two numbers below N
- Sum of multiples of a number up to N
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