Given two integers N and K where N, K > 0, the task is to find the total number of pairs (a, b) where 1 ≤ a, b ≤ N such that a % b = K.
Input: N = 4, K = 2
Only valid pairs are (2, 3) and (2, 4).
Input: N = 11, K = 5
Naive approach: Run two loop from 1 to n and count all the pairs (i, j) where i % j = K. The time complexity of this approach will be O(n2).
Efficient approach: Initially total count = N – K because all the numbers from the range which are > K will give K as the remainder after dividing it. After that, for all i > K there are exactly (N – K) / i numbers which will give remainder as K after getting divided by i.
Below is the implementataion of the above approach:
- Find number of pairs in an array such that their XOR is 0
- Find the number of pairs such that their gcd is equals to 1
- Find the maximum cost of an array of pairs choosing at most K pairs
- Find all pairs (a, b) in an array such that a % b = k
- Find sum of a[i]%a[j] for all valid pairs
- Find the maximum possible value of a[i] % a[j] over all pairs of i and j
- Find the sum of all possible pairs in an array of N elements
- Given two unsorted arrays, find all pairs whose sum is x
- Find all pairs (a,b) and (c,d) in array which satisfy ab = cd
- Number of pairs with Bitwise OR as Odd number
- Find two non-overlapping pairs having equal sum in an Array
- Find k pairs with smallest sums in two arrays
- Find k pairs with smallest sums in two arrays | Set 2
- Count number of pairs (i, j) such that arr[i] * arr[j] > arr[i] + arr[j]
- Number of pairs with maximum sum
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