Water and Jug Problem

Desicription

You are given two jugs with capacities x and y litres. There is an infinite amount of water supply available. You need to determine whether it is possible to measure exactly z litres using these two jugs.

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

Operations allowed:

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

Example 1: (From the famous “Die Hard” example)

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Input: x = 3, y = 5, z = 4
Output: True

Example 2:

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Input: x = 2, y = 6, z = 5
Output: False

Solution

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class Solution {
public:
bool canMeasureWater(int x, int y, int z) {
if(x + y < z) {
return false;
}

if(x == z || y == z || x + y == z) {
return true;
}

std::function<int(int, int)> gcd = [&](int a, int b) {
return b ? gcd(b, a % b) : a;
};

return z % gcd(x, y) == 0;
}
};