Water Jug Problem Statement

You have two water jugs with capacities X and Y liters respectively, both initially empty. You also have an infinite water supply. The goal is to determine if it is possible to measure exactly Z liters using these two jugs and the operations outlined below.

Operations Allowed:

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

Input:

The input consists of multiple test cases. The first line contains an integer 'T' representing the number of test cases. The next T lines each contain three space-separated integers X, Y, and Z indicating the capacities of both jugs and the target measurement, respectively.

Output:

For each test case, output 'True' if it's possible to measure exactly Z liters, otherwise output 'False'. Each result should be on a new line.

Example:

To measure 2 liters using jugs with capacities 4 and 6 liters:

Fill the 6-liter jug completely.

Transfer from the 6-liter jug to the 4-liter jug until the latter is full.

Repeat the transfer from the 6-liter jug to the 4-liter jug.

Constraints:

1 ≤ T ≤ 5 * 10⁴

0 ≤ X, Y, Z ≤ 5 * 10⁴

Time Limit: 1 second

Note:

You do not need to print anything; the printing is handled externally. Simply implement the required function.

Question

Water Jug Problem Statement

You have two water jugs with capacities X and Y liters respectively, both initially empty. You also have an infinite water supply. The goal is to determine if it is possible to measure exactly Z liters using these two jugs and the operations outlined below.

Operations Allowed:

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

Input:

The input consists of multiple test cases. The first line contains an integer 'T' representing the number of test cases. The next T lines each contain three space-separated integers X, Y, and Z indicating the capacities of both jugs and the target measurement, respectively.

Output:

For each test case, output 'True' if it's possible to measure exactly Z liters, otherwise output 'False'. Each result should be on a new line.

Example:

To measure 2 liters using jugs with capacities 4 and 6 liters:

Fill the 6-liter jug completely.
Transfer from the 6-liter jug to the 4-liter jug until the latter is full.
Repeat the transfer from the 6-liter jug to the 4-liter jug.

Constraints:

1 ≤ T ≤ 5 * 10⁴
0 ≤ X, Y, Z ≤ 5 * 10⁴
Time Limit: 1 second

Note:

You do not need to print anything; the printing is handled externally. Simply implement the required function.

Accepted Answer

The problem is to determine whether it is possible to measure a specific amount of water using two jugs with given capacities.

The jugs can be filled, emptied, and water can be poured from one jug to another.
If the target measure is achievable, there must be exactly Z liters of water in one or both jugs.
We can solve this problem using the concept of the greatest common divisor (GCD) of the jug capacities.
If Z is divisible by the GCD of X and Y, then it is possible to measure Z liters of water.