Given n instance of item A and m instance of item B. Find the maximum number of groups of size 3 that can be formed using these items such that all groups contain items of both types, i.e., a group should not have either all items of type A or all items of type B.
Total number of items of type A in the formed groups must be less than or equal to n.
Total number of items of type B in the formed groups must be less than or equal to m.
Input : n = 2 and m = 6. Output : 2 In group 1, one item of type A and two items of type B. Similarly, in the group 2, one item of type A and two items of type B. We have used 2 (<= n) items of type A and 4 (<= m) items of type B. Input : n = 4 and m = 5. Output : 3 In group 1, one item of type A and two items of type B. In group 2, one item of type B and two items of type A. In group 3, one item of type A and two items of type B. We have used 4 (<= n) items of type A and 5 (<= 5) items of type B.
1. There will be n groups possible if m >= 2n. Or there will be m groups possible, if n >= 2m.
2. Suppose n = 3 and m = 3, so one instance of item A will make a group with the two instance of item B and one instance of item B will make a group with the two instance of item A. So, maximum two groups are possible. So find the total number of such conditions with given n and m by dividing m and m by 3. After this, there can be 0, 1, 2 instances of each type can be left. For finding the number of groups for the left instances:
a) If n = 0 or m = 0, 0 group is possible.
b) If n + m >= 3, only 1 group is possible.
Algorithm for solving this problem:
1. If n >= 2m, maximum number of groups = n.
2. Else if m >= 2n, maximum number of groups = m.
3. Else If (m + n) % 3 == 0, maximum number of group = (m + n)/3;
4. Else maximum number of group = (n + m)/3. And set n = n%3 and m = m%3.
a) If n != 0 && m != 0 && (n + m) >= 3, add one to maximum number of groups.
Below is implementation of the above idea :
This article is contributed by Anuj Chauhan(anuj0503). 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.
- Find the maximum distance covered using n bikes
- 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 area of triangle having different vertex colors
- Make n using 1s and 2s with minimum number of terms multiple of k
- 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 maximum elements of all possible sub-arrays of an array
- Number of ways an array can be filled with 0s and 1s such that no consecutive elements are 1