How do you solve Find the N-th Value After K Seconds on LeetCode?

Find the N-th Value After K Seconds (LeetCode #3179) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * k) time complexity and O(n) space complexity. Key insight: The problem can be viewed as a prefix sum problem.

What is the time complexity of Find the N-th Value After K Seconds?

The optimal solution for Find the N-th Value After K Seconds runs in O(n * k) time and uses O(n) space. This complexity arises because we fill a 2D array of size (k+1) x n, and for each second, we iterate through n elements.

What is the brute force solution for Find the N-th Value After K Seconds?

The brute force approach for Find the N-th Value After K Seconds is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach simulates the process of updating the array for each second. We directly compute the new values based on the previous state of the array, which is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n * k).

What algorithm or data structure is used to solve Find the N-th Value After K Seconds?

Find the N-th Value After K Seconds uses the following concepts: Array, Math, Simulation, Combinatorics, Prefix Sum. The recommended patterns to study are: Prefix Sum, Dynamic Programming.

What are the interview tips for Find the N-th Value After K Seconds?

Always clarify the constraints and edge cases before diving into coding. Think about the mathematical properties of the problem, especially for simulation problems. Practice explaining your thought process as you code.

What are common mistakes when solving Find the N-th Value After K Seconds?

Not considering the modulo operation, leading to overflow. Confusing the update rules for the array elements.

#3179

Find the N-th Value After K Seconds

Medium

ArrayMathSimulationCombinatoricsPrefix SumPrefix SumDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n * k)Space O(n)

Instead of simulating each second, we can recognize that the problem can be solved using combinatorial mathematics. The value at a[n-1] after k seconds corresponds to the number of ways to select elements from the previous states.

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Algorithm

4 steps

1Step 1: Initialize a 2D array 'dp' where dp[i][j] represents the value at index j after i seconds.
2Step 2: Set dp[0][j] = 1 for all j from 0 to n-1 (initial state).
3Step 3: For each second from 1 to k, compute each dp[i][j] as the sum of all dp[i-1][m] for m from 0 to j.
4Step 4: Return dp[k][n - 1] modulo 10^9 + 7.

solution.py15 lines

1# Full working Python code
2
3def find_nth_value_optimal(n, k):
4    MOD = 10**9 + 7
5    dp = [[0] * n for _ in range(k + 1)]
6    for j in range(n):
7        dp[0][j] = 1
8    for i in range(1, k + 1):
9        for j in range(n):
10            dp[i][j] = dp[i][j - 1] if j > 0 else 0
11            dp[i][j] = (dp[i][j] + dp[i - 1][j]) % MOD
12    return dp[k][n - 1]
13
14# Example usage
15print(find_nth_value_optimal(4, 5))  # Output: 56

ℹ

Complexity note: This complexity arises because we fill a 2D array of size (k+1) x n, and for each second, we iterate through n elements.

1The problem can be viewed as a prefix sum problem.
2The final value can be derived from combinatorial principles.

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