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:
- Find the sum of all multiples of 2 and 5 below N
- 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 all factorial numbers less than or equal to n
- Find three integers less than or equal to N such that their LCM is maximum
- Find a Number X whose sum with its digits is equal to N
- Find a number x such that sum of x and its digits is equal to given n.
- Sum of the multiples of two numbers below N
- Sum of multiples of a number up to N
- Find N distinct numbers whose bitwise Or is equal to K
- Find unique pairs such that each element is less than or equal to N
- Find four factors of N with maximum product and sum equal to N | Set-2
- Find four factors of N with maximum product and sum equal to N
- Find four factors of N with maximum product and sum equal to N | Set 3
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