Given two positive integer n and k. n can be represented as the sum of 1s and 2s in many ways, using multiple numbers of terms. The task is to find the minimum number of terms of 1s and 2s use to make the sum n and also number of terms must be multiple of k. Print “-1”, if no such number of terms exists.
Input : n = 10, k = 2 Output : 6 10 can be represented as 2 + 2 + 2 + 2 + 1 + 1. Number of terms used are 6 which is multiple of 2. Input : n = 11, k = 4 Output : 8 10 can be represented as 2 + 2 + 2 + 1 + 1 + 1 + 1 + 1 Number of terms used are 8 which is multiple of 4.
Observe, the maximum number of terms used to represent n as the sum of 1s and 2s is n, when 1 are added n number of times. Also, the minimum number of terms will be n/2 times of 2s and n%2 times 1s are added. So, iterate from minimum number of terms to maximum number of terms and check if there is any multiple of k.
This article is contributed by Anuj Chauhan. 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.
- Count number of ways to divide a number in 4 parts
- Fifth root of a number
- Number of ways to calculate a target number using only array elements
- Happy Number
- Number of flips to make binary string alternate | Set 1
- Convert a number into negative base representation
- Minimum number of page turns to get to a desired page
- Minimum number of equal amount bags to collect at least M money
- Maximum number of groups of size 3 containing two type of items
- Count of Numbers in Range where the number does not contain more than K non zero digits
- Maths behind number of paths in matrix problem
- Sum of minimum difference between consecutive elements of an array
- Minimum steps to reach target by a Knight | Set 2
- Number of subsequences with negative product
- Find the node whose sum with X has minimum set bits