Given n, m, A and B. The task is to count the number of pairs of integers (x, y) such that 1 x n and 1 y m and (x+y) mod A and (x+y) mod B both equals to 0.
Input: n = 60, m = 90, A = 5, B = 10 Output: 540 Input: n = 225, m = 452, A = 10, B = 15 Output: 3389
Approach: If (x+y) is divisible by both A and B then basically LCM of A and B is the smallest divisor of (x+y). So we calculate all numbers that is less than or equal to m and divisible by LCM of them and when iterating with the loop then we check if the present number is divisible by LCM of A and B.
Below is the implementation of the above approach:
Time Complexity: O(n)
- Count of pairs from 1 to a and 1 to b whose sum is divisible by N
- Count pairs in array whose sum is divisible by K
- Count pairs of numbers from 1 to N with Product divisible by their Sum
- Print k numbers where all pairs are divisible by m
- Number of pairs from the first N natural numbers whose sum is divisible by K
- Count pairs with Odd XOR
- Count of pairs (x, y) in an array such that x < y
- Count pairs (a, b) whose sum of cubes is N (a^3 + b^3 = N)
- Count number of pairs (A <= N, B <= N) such that gcd (A , B) is B
- Count of pairs of (i, j) such that ((n % i) % j) % n is maximized
- Count pairs (a, b) whose sum of squares is N (a^2 + b^2 = N)
- Count rotations divisible by 4
- Count rotations divisible by 8
- Count pairs with sum as a prime number and less than n
- Count pairs with Bitwise AND as ODD number
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