Given a range [L, R], the task is to find all possible co-prime pairs from the range such that an element doesn’t appear in more than a single pair.
Input : L=1 ; R=6 Output : 3 The answer is 3 [(1, 2) (3, 4) (5, 6)], all these pairs have GCD 1. Input : L=2 ; R=4 Output : 1 The answer is 1 [(2, 3) or (3, 4)] as '3' can only be chosen for a single pair.
Approach : The key observation of the problem is that the numbers with the difference of ‘1’ are always relatively prime to each other i.e. co-primes.
GCD of this pair is always ‘1’. So, the answer will be (R-L+1)/2 [ (total count of numbers in range) / 2 ]
- If R-L+1 is odd then there will be one element left which can not form a pair.
- If R-L+1 is even then all elements can form pairs.
Below is the implementation of the above approach:
- Finding a Non Transitive Coprime Triplet in a Range
- Find the number of distinct pairs of vertices which have a distance of exactly k in a tree
- Count Distinct Non-Negative Integer Pairs (x, y) that Satisfy the Inequality x*x + y*y < n
- Find a distinct pair (x, y) in given range such that x divides y
- Total distinct pairs from two arrays such that second number can be obtained by inverting bits of first
- Integers from the range that are composed of a single distinct digit
- Count of distinct remainders when N is divided by all the numbers from the range [1, N]
- Pairs with GCD equal to one in the given range
- Number of Co-prime pairs obtained from the sum of digits of elements in the given range
- Find unique pairs such that each element is less than or equal to N
- Count pairs in an array such that at least one element is prime
- Number which has the maximum number of distinct prime factors in the range M to N
- Composite XOR and Coprime AND
- Largest number less than or equal to N/2 which is coprime to N
- Replace the maximum element in the array by coefficient of range
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