You are given two positive integer n and k. You have to calculate the maximum possible XOR value of at most k-elements from 1 to n.
Note:k > 1
Input : n = 7, k = 3 Output : 7 Explanation : You can select 1, 2, 4 for maximum XOR-value Input : n = 7, k = 2 Output : 7 Explanation : You can select 3 and 4 for maximum value.
For any value of k we can select atleast two numbers from 1 to n and for the required result we have to take a closer look on the bit-representation of n. So lets understand it through an example. Suppose n = 6 and k = 2:
Bit representation of 6 = 110
Bit representation of 5 = 101
Bit representation of 4 = 100
Bit representation of 3 = 011
Bit representation of 2 = 010
Bit representation of 1 = 001
Now, you can see that after selecting as much numbers you want and selecting any of them you can not obtain XOR value greater than 111 i.e 7. So, for a given n and k >1 the maximum possible XOR value is 2log2(n)+1-1 (that is the value when all bits of n are turned to 1).
- Maximum XOR value in matrix
- Maximum XOR using K numbers from 1 to n
- Value in a given range with maximum XOR
- Maximum AND value of a pair in an array
- Maximum 0's between two immediate 1's in binary representation
- Maximum value of XOR among all triplets of an array
- Find the maximum subset XOR of a given set
- Find a value whose XOR with given number is maximum
- Maximum XOR value of a pair from a range
- Maximum XOR of Two Numbers in an Array
- Find the node whose xor with x gives maximum value
- Find a sub matrix with maximum XOR
- Maximum Bitwise AND pair from given range
- Find triplets in an array whose AND is maximum
- Maximum subset with bitwise OR equal to k
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.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.