Given two integers L and R, the task is to find the XOR of elements of the range [L, R].
Input: L = 4, R = 8
4 ^ 5 ^ 6 ^ 7 ^ 8 = 8
Input: L = 3, R = 7
Naive Approach: Intilialize answer as zero, Traverse all numbers from L to R and perform XOR of the numbers one by one with the answer. This would take O(N) time.
Efficient Approach: By following the approach discussed here, we can find the XOR of elements from the range [1, N] in O(1) time.
Using this approach, we have to find xor of elements from the range [1, L – 1] and from the range [1, R] and then xor the respective answers again to get the xor of the elements from the range [L, R]. This is because every element from the range [1, L – 1] will get XORed twice in the result resulting in a 0 which when XORed with the elements of the range [L, R] will give the result.
Below is the implementation of the above approach:
- Find numbers with n-divisors in a given range
- Find numbers with K odd divisors in a given range
- Find the number of divisors of all numbers in the range [1, n]
- Find a range of composite numbers of given length
- Find kth smallest number in range [1, n] when all the odd numbers are deleted
- Program to find count of numbers having odd number of divisors in given range
- Find the highest occurring digit in prime numbers in a range
- Sum of all even numbers in range L and R
- Sum of all even factors of numbers in the range [l, r]
- Sum of all odd factors of numbers in the range [l, r]
- Count of numbers having only 1 set bit in the range [0, n]
- Sum of all numbers divisible by 6 in a given range
- Check whether XOR of all numbers in a given range is even or odd
- Count Odd and Even numbers in a range from L to R
- Sum of all the prime numbers in a given range
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