How do you solve Water and Jug Problem on LeetCode?

Water and Jug Problem (LeetCode #365) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(log(min(x, y))) time complexity and O(1) space complexity. Key insight: The target must be less than or equal to the sum of the jug capacities.

What is the time complexity of Water and Jug Problem?

The optimal solution for Water and Jug Problem runs in O(log(min(x, y))) time and uses O(1) space. The time complexity is O(log(min(x, y))) due to the GCD calculation, which is efficient and does not require exploring all states.

What is the brute force solution for Water and Jug Problem?

The brute force approach for Water and Jug Problem is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach explores all possible states of the jugs by simulating every operation. This means we will try every combination of filling, emptying, and pouring until we either reach the target or exhaust all possibilities. The optimal Optimal Solution approach improves this to O(log(min(x, y))).

What algorithm or data structure is used to solve Water and Jug Problem?

Water and Jug Problem uses the following concepts: Math, Depth-First Search, Breadth-First Search. The recommended patterns to study are: Graph Traversal (BFS/DFS), Mathematical Properties (GCD).

What are the interview tips for Water and Jug Problem?

Always start with a brute force approach to understand the problem better. Look for mathematical properties that can simplify the problem. Practice explaining your thought process clearly, as it helps in interviews.

What are common mistakes when solving Water and Jug Problem?

Forgetting to check if the target is greater than the sum of the jug capacities. Not considering the mathematical properties of the problem, leading to unnecessary simulations.

#365

Water and Jug Problem

Medium

MathDepth-First SearchBreadth-First SearchGraph Traversal (BFS/DFS)Mathematical Properties (GCD)

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(log(min(x, y)))
Space	O(1)	O(1)

💡

Intuition

Time O(log(min(x, y)))Space O(1)

The optimal solution leverages the mathematical properties of the problem, specifically the greatest common divisor (GCD). If the target can be expressed as a combination of the two jug capacities, we can reach the target without simulating every possible state.

⚙️

Algorithm

3 steps

1Step 1: Check if the target is greater than the sum of the jug capacities; if so, return false.
2Step 2: Calculate the GCD of the two jug capacities.
3Step 3: Check if the target is a multiple of the GCD and less than or equal to the sum of the capacities.

solution.py6 lines

1import math
2
3def canMeasureWater(x, y, target):
4    if target > x + y:
5        return False
6    return target % math.gcd(x, y) == 0

ℹ

Complexity note: The time complexity is O(log(min(x, y))) due to the GCD calculation, which is efficient and does not require exploring all states.

1The target must be less than or equal to the sum of the jug capacities.
2The target must be a multiple of the GCD of the two jug capacities.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.