Size of the smallest subset with maximum Bitwise OR
Given an array of positive integers. The task is to find the size of the smallest subset such that the Bitwise OR of that set is Maximum possible.
Examples:
Input : arr[] = {5, 1, 3, 4, 2}
Output : 2
7 is the maximum value possible of OR,
5|2 = 7 and 5|3 = 7
Input : arr[] = {2, 6, 2, 8, 4, 5}
Output : 3
15 is the maximum value of OR and set
elements are 8, 6, 5
Source :Sprinklr on Campus Internship
Doing bitwise OR of a number with some value does not decrease its value. It either keeps the value same or increases. If we take a closer look at the problem we can notice that the maximum OR value that we can get is by doing bitwise OR of all array elements. But this includes all elements and here want to know the smallest subset. So we do the following.
I) Find bitwise OR of all array elements. This is the OR we are looking for.
II) Now we need to find the smallest subset with this bitwise OR. This problem is similar to subset sum provblem, We can solve it two ways :
- We recursively generate all subsets and return the smallest size with given OR
- We use Dynamic Programming to solve the problem. This solution is going to be very similar to Maximum size subset with given sum
The time complexity of the recursive solution is O(2^n) and time complexity of the Dynamic Programming solution is O(OR * n) where OR is OR of all array elements and n is size of input array.
Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.
Recommended Posts:
- Maximum subset with bitwise OR equal to k
- Maximum size subset with given sum
- Maximum size subset with given sum using Backtracking
- Find maximum subset sum formed by partitioning any subset of array into 2 partitions with equal sum
- Check if bitwise AND of any subset is power of two
- Check whether bitwise AND of a number with any subset of an array is zero or not
- Find subsequences with maximum Bitwise AND and Bitwise OR
- Smallest subset with sum greater than all other elements
- Find if there is any subset of size K with 0 sum in an array of -1 and +1
- Largest subset with M as smallest missing number
- Size of the largest divisible subset in an Array
- Smallest Greater (than S) String of length K whose letters are subset of S
- Find the smallest positive integer value that cannot be represented as sum of any subset of a given array
- Find smallest positive number Y such that Bitwise AND of X and Y is Zero
- Count of pairs having bit size at most X and Bitwise OR equal to X
- Maximum size of square such that all submatrices of that size have sum less than K
- Maximum subarray size, such that all subarrays of that size have sum less than k
- Find the maximum subset XOR of a given set
- Maximum sum of smallest and second smallest in an array
- Find subset with maximum sum under given condition
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.
- Count of substrings of length K with exactly K distinct characters
- Find if there is a path between two vertices in an undirected graph
- Longest subarray whose elements can be made equal by maximum K increments
- Shortest path in a directed graph by Dijkstra’s algorithm
- Finding Median of unsorted Array in linear time using C++ STL