Junior Engineer Associate

You are given two water jugs with capacities X and Y litres respectively. Both the jugs are initially empty. There is an infinite amount of water supply available. The jugs do not have markings to measure smaller quantities.

The following operations are allowed:

• Fill any of the jugs entirely with water.
• Empty any of the jugs.
• Pour water from one jug into another till the other jug is full, or the first jug itself is empty.

You are required to tell whether it is possible to measure exactly ‘Z’ litres using both of the jugs.

If Z litres of water is measurable, you must have Z litres of water contained within one or both buckets by the end.

For example:

In order to measure 2 litres from jugs of 4 and 6 litres we can follow the following steps-

• Fill 6-litres jugs to its maximum capacity.
• Pour water from 6-litres jug to the jug with 4-litres capacity.
• Pour water from 6-litres jug to the jug with 4-litres capacity.

You are given a 2D matrix ‘ARR’ of size ‘N x 3’ having integers, where ‘N’ is the number of rows.

Your task is to find the smallest sum possible while taking one element from each row.

The rules for selecting elements are as follows-

1. In a row, after selecting an element at a given position, you cannot select the element directly below it
2. You can only select elements that are not directly below the previously selected element.

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