Build Array Where You Can Find The Maximum Exactly K Comparisons Python/Java solution

Python and Java implementations typically follow the same DP formulation. Python solutions often use recursion with functools.lru_cache for memoization, while Java implementations commonly use iterative 3D arrays for bottom-up DP. Both approaches maintain states defined by index, current maximum, and search cost.

What is the best approach for Build Array Where You Can Find The Maximum Exactly K Comparisons?

The most efficient approach uses dynamic programming with a 3D state and prefix sum optimization. The state dp[i][j][c] represents arrays of length i where j is the current maximum and c is the search cost. Prefix sums allow fast computation of transitions where a new maximum is introduced. This reduces the complexity to O(n * m * k) time and O(n * m * k) space.

Is Build Array Where You Can Find The Maximum Exactly K Comparisons asked at Google/Amazon/Meta?

Dynamic programming problems involving state transitions and counting combinations appear frequently in interviews at companies like Google, Amazon, and Meta. Variants of this problem test the ability to define multi-dimensional DP states and optimize transitions using prefix sums or cumulative aggregates.

What data structure is used in Build Array Where You Can Find The Maximum Exactly K Comparisons?

The core data structure is a 3D dynamic programming table, typically implemented as a nested array or vector. Prefix sum arrays are used to accelerate transitions that sum values across ranges of maximums. Hash maps may also be used in memoized recursion to cache computed states.

What is the time complexity of Build Array Where You Can Find The Maximum Exactly K Comparisons?

The optimized dynamic programming solution runs in O(n * m * k) time with O(n * m * k) space. A naive DP version that iterates through all smaller maximum values adds an extra factor of m, leading to O(n * m^2 * k). Memoized recursion also achieves O(n * m * k) because each state is computed once.

Description Hints 2 Solution Video 32:13

1420. Build Array Where You Can Find The Maximum Exactly K Comparisons

Q: Is Build Array Where You Can Find The Maximum Exactly K Comparisons easy or hard?

LeetCode classifies this problem as Hard because it requires designing a three-dimensional dynamic programming state and optimizing transitions using prefix sums. Candidates must carefully reason about how the maximum value evolves while building the array and how the search cost changes.

Q: How to solve Build Array Where You Can Find The Maximum Exactly K Comparisons in O(n)?

Solving this problem strictly in O(n) is not feasible because the state depends on three parameters: array length n, value range m, and cost k. The optimal practical complexity is O(n * m * k) using dynamic programming with prefix sums. Each state transition is computed in constant time after prefix precomputation.

Hard65.3% acceptance2 companies

You are given three integers n, m and k. Consider the following algorithm to find the maximum element of an array of positive integers:

You should build the array arr which has the following properties:

arr has exactly n integers.
1 <= arr[i] <= m where (0 <= i < n).
After applying the mentioned algorithm to arr, the value search_cost is equal to k.

Return the number of ways to build the array arr under the mentioned conditions. As the answer may grow large, the answer must be computed modulo 10⁹ + 7.

Example 1:

Input: n = 2, m = 3, k = 1
Output: 6
Explanation: The possible arrays are [1, 1], [2, 1], [2, 2], [3, 1], [3, 2] [3, 3]

Example 2:

Input: n = 5, m = 2, k = 3
Output: 0
Explanation: There are no possible arrays that satisfy the mentioned conditions.

Example 3:

Input: n = 9, m = 1, k = 1
Output: 1
Explanation: The only possible array is [1, 1, 1, 1, 1, 1, 1, 1, 1]

Constraints:

1 <= n <= 50
1 <= m <= 100
0 <= k <= n

Asked at 2 companies

Dunzo

Google

Topics

Dynamic Programming Prefix Sum

Hints open one at a time

Hint 1

Use dynamic programming approach. Build dp table where dp[a][b][c] is the number of ways you can start building the array starting from index a where the search_cost = c and the maximum used integer was b.

Hint 2

Recursively, solve the small sub-problems first. Optimize your answer by stopping the search if you exceeded k changes.

32:13

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1class Solution:
2    def numOfArrays(self, n: int, m: int, k: int) -> int:
3        

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Input

2
3
1

Input

5
2
3

Input

9
1
1

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