Check if all 3 Candy bags can be emptied by removing 2 candies from any one bag and 1 from the other two repeatedly
Given 3 integers a, b and c indicating number of candies present in three bags. You need to find whether we can empty all the bags by performing a specific operation where in each operation, you can eat 2 candies from one bag and 1 candy each from the other 2 bags. It is not permittable to skip any bag i.e either 1 or 2 candies must be eaten from each bag in each operation. Return true if possible else return false.
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.
Input: 4, 2, 2
Operation 1: you can eat 2 candies from bag1 and 1 from bag2 and bag3 each.
Candies left after operation 1
bag1 = 2, bag2 = 1, bag3 = 1
Operation 2: you can eat 2 candies from bag1 and 1 from each bag2 and bag3 each
Candies left after operation 2
bag1 = 0, bag2 = 0, bag3 = 0
Hence it is possible to empty all the bags
Input: 3, 4, 2
Naive Approach: Iterate through the variables until all three does not become 0. At every iteration reduce the maximum element by 2 and remaining variables by 1.
Time Complexity: O(N), where N is value of maximum variable of a, b and c
Efficient Approach: The given problem can be solved with the efficient approach by making the following observations:
- In each operation we’ll pick 1+2+1=4 candies, hence the sum of all the candies in bag1, bag2, and bag3 must be divisible by 4.
- Number of operations required to empty all the bags would be (sum of all candies)/4.
- We have to pick either 1 or 2 candies from a bag at any operation, hence the minimum candies present of the 3 bags must be greater than or equal to the number of operations.
Time Complexity: O(1)
Space Complexity: O(1)