Given n, print the maximum number of composite numbers that sum up to n. First few composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, ………
Input: 90 Output: 22 Explanation: If we add 21 4's, then we get 84 and then add 6 to it, we get 90. Input: 10 Output: 2 Explanation: 4 + 6 = 10
Below are some important observations.
- If the number is less then 4, it won’t have any combinations.
- If the number is 5, 7, 11, it wont have any splitting.
- Since smallest composite number is 4, it makes sense to use maximum number of 4s.
- For numbers that don’t leave a composite remainder when divided by 4, we do following. If remainder is 1, we subtract 9 from it to get the number which is perfectly divisible by 4. If the remainder is 2, then subtract 6 from it to make n a number which is perfectly divisible by 4. If the remainder is 3, then subtract 15 from it to make n perfectly divisible by 4, and 15 can be made up by 9 + 6.
So the main observation is to make n such that is composes of maximum no of 4’s and the remaining can be made up by 6 and 9. We won’t need composite numbers more then that, as the composite numbers above 9 can be made up of 4, 6, and 9.
Below is the implementation of the above approach
Time complexity: O(1)
Auxiliary Space: O(1)
This article is contributed by Raja Vikramaditya. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
- Composite numbers with digit sum 1
- Product of all the Composite Numbers in an array
- Find a range of composite numbers of given length
- Sum and Product of all Composite numbers which are divisible by k in an array
- Sum and product of k smallest and k largest composite numbers in the array
- Generate a list of n consecutive composite numbers (An interesting method)
- Find the maximum number of composite summands of a number
- Split N^2 numbers into N groups of equal sum
- Maximum sum of distinct numbers such that LCM of these numbers is N
- Composite Number
- Composite XOR and Coprime AND
- Maximum sum of distinct numbers with LCM as N
- Maximum factors formed by two numbers
- Find maximum N such that the sum of square of first N natural numbers is not more than X
- Queries for maximum difference between prime numbers in given ranges
Improved By : vt_m