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 the number of pairs (i, j) such that either arr[i] is divisible by arr[j] or arr[j] is divisible by arr[i]
- 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
- Count number of pairs in array having sum divisible by K | SET 2
- 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 rotations divisible by 4
- Count rotations divisible by 8
- Count pairs with Odd XOR
- Count pairs with given sum | Set 2
- Count numbers in range 1 to N which are divisible by X but not by Y
- Count the numbers divisible by 'M' in a given range
- Count sub-arrays whose product is divisible by k
- Count integers in the range [A, B] that are not divisible by C and D
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