What is the time complexity of Direction Assignments with Exactly K Visible People?

The optimal solution for Direction Assignments with Exactly K Visible People runs in Unknown time and uses Unknown space.

What algorithm or data structure is used to solve Direction Assignments with Exactly K Visible People?

Direction Assignments with Exactly K Visible People uses the following concepts: Math, Combinatorics. The recommended patterns to study are: .

Direction Assignments with Exactly K Visible People — LeetCode #3881 (Medium)

Tags: Math, Combinatorics

Related patterns:

Brute Force approach

Time complexity: O(n²). Space complexity: O(1).

Generate all possible combinations of directions for n people and count how many configurations allow the person at index pos to see exactly k people. This is straightforward but inefficient.

The complexity arises from generating all combinations (2^n) and counting visible people (O(n)) for each combination.

Step 1: Generate all 2^n combinations of directions for n people.
Step 2: For each combination, count visible people for the person at index pos.
Step 3: Increment a counter if the count matches k.

Optimal Solution approach

Time complexity: Unknown. Space complexity: Unknown.

Use combinatorial counting to determine how many people can be assigned directions such that exactly k are visible. This avoids generating all combinations.

Step 1: Calculate the number of people to the left (a = pos) and to the right (b = n - pos - 1).
Step 2: Use combinatorial functions to count valid configurations for left and right based on k.
Step 3: Combine results from left and right configurations to get the total.

#3881

Direction Assignments with Exactly K Visible People

Medium

Math↗Combinatorics↗

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time UnknownSpace Unknown

Use combinatorial counting to determine how many people can be assigned directions such that exactly k are visible. This avoids generating all combinations.

⚙️

Algorithm

3 steps

1Step 1: Calculate the number of people to the left (a = pos) and to the right (b = n - pos - 1).
2Step 2: Use combinatorial functions to count valid configurations for left and right based on k.
3Step 3: Combine results from left and right configurations to get the total.

solution.py9 lines

1def countVisible(n, pos, k):
2    from math import comb
3    a, b = pos, n - pos - 1
4    total = 0
5    for left in range(max(0, k - b), min(a, k) + 1):
6        right = k - left
7        if 0 <= right <= b:
8            total += comb(a, left) * comb(b, right)
9    return total % (10**9 + 7)

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