How do you solve Count Non Decreasing Arrays With Given Digit Sums on LeetCode?

Count Non Decreasing Arrays With Given Digit Sums (LeetCode #3883) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding digit sums helps in grouping valid numbers.

What is the time complexity of Count Non Decreasing Arrays With Given Digit Sums?

The optimal solution for Count Non Decreasing Arrays With Given Digit Sums runs in O(n) time and uses O(n) space. The complexity is linear due to the single pass through the digit sums and the DP array.

What is the brute force solution for Count Non Decreasing Arrays With Given Digit Sums?

The brute force approach for Count Non Decreasing Arrays With Given Digit Sums is Brute Force, with O(n²) time complexity and O(1) space complexity. Generate all possible arrays and filter out valid ones. This method is straightforward but inefficient due to the large search space. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Count Non Decreasing Arrays With Given Digit Sums?

Count Non Decreasing Arrays With Given Digit Sums uses the following concepts: Array, Dynamic Programming, Prefix Sum. The recommended patterns to study are: Dynamic Programming, Combinatorics.

What are the interview tips for Count Non Decreasing Arrays With Given Digit Sums?

Explain your thought process clearly. Discuss edge cases like empty arrays or maximum constraints. Practice similar DP problems to build intuition.

What are common mistakes when solving Count Non Decreasing Arrays With Given Digit Sums?

Not considering the non-decreasing condition. Overlooking the modulo operation for large numbers.

#3883

Count Non Decreasing Arrays With Given Digit Sums

Hard

ArrayDynamic ProgrammingPrefix SumDynamic ProgrammingCombinatorics

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(n)

Use dynamic programming to count valid arrays based on previously computed results, leveraging the properties of digit sums.

⚙️

Algorithm

3 steps

1Step 1: Precompute valid numbers grouped by digit sums.
2Step 2: Use a DP array to count combinations of valid numbers for each digit sum.
3Step 3: Accumulate results while ensuring non-decreasing order.

solution.py8 lines

1def countArrays(digitSum):
2    mod = 10**9 + 7
3    dp = [0] * (len(digitSum) + 1)
4    dp[0] = 1
5    for sum in digitSum:
6        for i in range(1, len(dp)):
7            dp[i] = (dp[i] + dp[i-1]) % mod
8    return dp[len(digitSum)]

ℹ

Complexity note: The complexity is linear due to the single pass through the digit sums and the DP array.

1Understanding digit sums helps in grouping valid numbers.
2Dynamic programming efficiently counts combinations without redundancy.

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