Given an array a, integer K and an integer X (which is initially initialized to 0). Our task is to find the minimum number of moves required to update the array such that each of its element is divisible by K by performing the following operations:
- Choose one index i from 1 to N and increase ai by X and then increase X by 1. This operation cannot be applied more than once to each element of the array
- Only increase the value of X by 1.
Input: K = 3, a = [1, 2, 2, 18]
Initially X = 0 hence update X to 1.
For X = 1 add X to the second element of array to make the array [1, 3, 2, 18] and increase X by 1.
For X = 2 add X to the first element of array [3, 3, 2, 18] and increase X by 1.
For X = 3 just increase X by 1.
For X = 4 add X to the third element of array to make the array [3, 3, 6, 18] and increase X by 1.
At last, the array becomes [3, 3, 6, 18] where all the elements are divisible by K = 3.
Input: K = 5, a = [15, 25, 5, 10, 20, 1005, 70, 80, 90, 100]
Here all elements are already divisible by 5.
Approach: The main idea is to find the maximum value of X that is needed to update the elements of the array to make it divisible by K.
- To do this we need to find the maximum value of (K – (ai mod K)) to add to the array elements to make it divisible by K.
- However, there can be equal elements so keep track of the number of such elements, using map data structures.
- When found another such element in the array then update the answer with (K – (ai mod K)) + (K * number of Equal Elements) because with every move we increase X by 1.
Below is the implementation of the above approach:
Time Complexity: O(N)
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