How to reach a common number by adding a number k, to an array of numbers arr[]?

Question

I am stuck with an algorithm problem since days. If we have an array of numbers, lets say, arr[2,4,9] and a var k, lets say k=7.

Is there a common number possible which can be reached by adding k to each of the elements inside the arr[] ?

EDIT:

WHen i say common number i mean a number X=(n_ikarr[i]) where n is a positive integer which could be different for each i, k is a positive integer provided to us, arr is the array of numbers. So it is basically to find an n for which n_ikarr[i] = a common number for all i.

I had a hunch of using LCM concept here but was not able to figure out the algorithim all the way through. A lead will be highly appreciated.

Clearly adding `k` to each of the elements in the array `arr` would yield `9, 11, 16` which is possible (but I don't think that's what you mean)... what result would you like? — Elliott Frisch, Jan 04 '19 at 04:36
No, it is not possible, even if you add different multiples of `7` to each element. — Jai, Jan 04 '19 at 04:38
Question in the last part , "we have to add a variable K" to make elements of array equal, i think it needs more clarification. — Vishwa Ratna, Jan 04 '19 at 05:14

score 2 · Accepted Answer · answered Jan 04 '19 at 04:39

2

If you can add multiples of k to each element, then each element of the array can take on a value of the form

value := arr[i] + j * k

for some integer value j. Thus, they can only obtain the same value if all elements are initially some multiple of k difference from each other.

Alternatively, you can view this problem in terms of modular arithmetic. Only if all elements reduce to the same value modulo k will you be able to obtain a common value between them by adding multiples of k

forall e in arr ->  e mod k == c; for some constant c

answered Jan 04 '19 at 04:39

Dillon Davis

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That is too wary imo. OP asked a variable K and not its multiple. The Question is really absurd and needs more clarification. – Vishwa Ratna Jan 04 '19 at 05:11
If we interpreted OP's question literally, if would be equivalent to asking if for array `[a, b, c]`, are `[a + k, b + k, c + k]` equal. I feel that OP's mention of LCM is enough to clarify that we can add `k` multiple times to each element. – Dillon Davis Jan 04 '19 at 05:16
1

Yeah, LCM is just fine, Appreciate your response :) – Vishwa Ratna Jan 04 '19 at 05:18
@Dillin You are correct sir. We can indeed have multiples of k. Edits provided. – Adarsh Singh Jan 05 '19 at 14:34

score 0 · Answer 2 · answered Jan 04 '19 at 05:18

Super easy.

    List<Integer> l = Arrays.asList(1, 6, 11);
    int k = 5;

    int min = l.stream().mapToInt(x -> x).min().getAsInt();
    boolean result = l.stream().mapToInt(x -> x)
            .map(x -> x - min)
            .allMatch(x -> x % k == 0);

    System.out.println("result = " + result);

How to reach a common number by adding a number k, to an array of numbers arr[]?

EDIT:

2 Answers2