How do you solve Find the Number of Possible Ways for an Event on LeetCode?

Find the Number of Possible Ways for an Event (LeetCode #3317) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The number of ways to assign performers to stages grows exponentially with n.

What is the time complexity of Find the Number of Possible Ways for an Event?

The optimal solution for Find the Number of Possible Ways for an Event runs in O(n) time and uses O(1) space. The time complexity is O(n) due to the efficient power calculation, and space complexity is O(1) as we are using a constant amount of space.

What is the brute force solution for Find the Number of Possible Ways for an Event?

The brute force approach for Find the Number of Possible Ways for an Event is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves considering every possible assignment of performers to stages and every possible score assignment. This is straightforward but inefficient due to the exponential growth of combinations as n, x, and y increase. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find the Number of Possible Ways for an Event?

Find the Number of Possible Ways for an Event uses the following concepts: Math, Dynamic Programming, Combinatorics. The recommended patterns to study are: Combinatorics, Exponential Growth.

What are the interview tips for Find the Number of Possible Ways for an Event?

Always clarify the problem constraints and edge cases. Think about how to break down the problem into smaller parts. Practice calculating combinations and permutations as they often come up in combinatorial problems.

What are common mistakes when solving Find the Number of Possible Ways for an Event?

Not considering empty stages when calculating combinations. Confusing the number of unique bands with the total number of performers.

#3317

Find the Number of Possible Ways for an Event

Hard

MathDynamic ProgrammingCombinatoricsCombinatoricsExponential Growth

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

💡

Intuition

Time O(n)Space O(1)

The optimal solution leverages combinatorial mathematics to calculate the total number of ways performers can be assigned to stages and scores without generating all combinations. This is efficient and avoids unnecessary computations.

⚙️

Algorithm

3 steps

1Step 1: Calculate the number of ways to assign performers to stages using the formula x^n, which accounts for all possible assignments.
2Step 2: Calculate the number of ways to assign scores to the unique bands formed. Since each performer can form a band, we can use y^k where k is the number of unique bands.
3Step 3: Combine the results from Step 1 and Step 2 to get the final answer.

solution.py5 lines

1# Full working Python code
2MOD = 10**9 + 7
3
4def optimal_solution(n, x, y):
5    return (pow(x, n, MOD) * pow(y, n, MOD)) % MOD

ℹ

Complexity note: The time complexity is O(n) due to the efficient power calculation, and space complexity is O(1) as we are using a constant amount of space.

1The number of ways to assign performers to stages grows exponentially with n.
2Each unique band can receive a score independently, leading to further exponential growth.

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