Is Find the N-th Value After K Seconds easy or hard?

The problem is rated Medium because the straightforward simulation is easy but recognizing the combinatorial pattern requires deeper insight. Identifying that the result equals C(n + k - 1, k) is the key step that leads to the optimal solution.

Find the N-th Value After K Seconds Python/Java solution

The dynamic programming solution iterates k times and updates an array using prefix sums. The optimal Python or Java solution computes C(n + k - 1, k) using a multiplicative combination formula with modulo arithmetic to avoid overflow.

How to solve Find the N-th Value After K Seconds in O(n)?

Recognize that repeated prefix sum operations produce values matching Pascal’s triangle. The final value becomes the binomial coefficient C(n + k - 1, k). Computing this combination with a multiplicative formula gives an O(n) solution without simulating each second.

What is the best approach for Find the N-th Value After K Seconds?

The most efficient approach uses a combinatorial formula. The value at index n-1 after k seconds equals C(n + k - 1, k). This avoids simulating all k prefix updates and reduces the complexity to O(n) or O(k) depending on the combination calculation method.

Is Find the N-th Value After K Seconds asked at Google/Amazon/Meta?

Problems involving prefix accumulation and combinatorial patterns frequently appear in interviews at companies like Google, Amazon, and Meta. Variants often test recognition of Pascal triangle patterns or converting dynamic programming transitions into mathematical formulas.

What data structure is used in Find the N-th Value After K Seconds?

The simulation approach uses a simple array to maintain running prefix sums. The optimized approach mainly relies on mathematical computation of binomial coefficients, so no advanced data structures are required.

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

The straightforward dynamic programming simulation runs in O(n * k) time because the array of size n is updated for k seconds. The optimized combinatorial solution computes a binomial coefficient and runs in O(n) or O(k) time with constant extra space.

Description Hints 1 Solution Video 7:51

3179. Find the N-th Value After K Seconds

Medium54.0% acceptance1 company

You are given two integers n and k.

Initially, you start with an array a of n integers where a[i] = 1 for all 0 <= i <= n - 1. After each second, you simultaneously update each element to be the sum of all its preceding elements plus the element itself. For example, after one second, a[0] remains the same, a[1] becomes a[0] + a[1], a[2] becomes a[0] + a[1] + a[2], and so on.

Return the value of a[n - 1] after k seconds.

Since the answer may be very large, return it modulo 10⁹ + 7.

Example 1:

Input: n = 4, k = 5

Output: 56

Explanation:

Second	State After
0	[1,1,1,1]
1	[1,2,3,4]
2	[1,3,6,10]
3	[1,4,10,20]
4	[1,5,15,35]
5	[1,6,21,56]

Example 2:

Input: n = 5, k = 3

Output: 35

Explanation:

Second	State After
0	[1,1,1,1,1]
1	[1,2,3,4,5]
2	[1,3,6,10,15]
3	[1,4,10,20,35]

Constraints:

1 <= n, k <= 1000

Asked at 1 company

Walmart Labs

Topics

Hints open one at a time

Hint 1

Calculate the prefix sum array of nums, k times.

7:51

Still stuck?Read 3 approaches, or watch a walkthrough.

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