Skip to content
LEETFLIX

Count Non Decreasing Arrays With Given Digit Sums

HardArrayDPPrefix sum
Solve on LeetCode

Hard · dynamic programming solution for Count Non Decreasing Arrays With Given Digit Sums. Python, Go, and a step-by-step animation.

01

Problem

Read the prompt, flip through the examples, then steal the idea.

LeetCode 3883. Count Non Decreasing Arrays With Given Digit Sums. The copyrighted prompt is on LeetCode. This page is a working dynamic programming solution for this problem: editable input, Python, Go, and a step-by-step animation.

Constraints

  • —Player inputs are capped so the animation stays readable.
  • —Match LeetCode's own constraints when you submit there.

Examples

Input

n =
5

Output

8

Ways to climb 5 stairs with 1- or 2-steps: Fibonacci, 8.

02

Solution

Python and Go. The walkthrough below runs this same code.

Approach 1Optimal▶ Animated

Count Non Decreasing Arrays With Given Digit Sums — dynamic programming

Each answer is a combination of smaller answers already in the table. Built for LeetCode 3883. Count Non Decreasing Arrays With Given Digit Sums.

The classic recurrence dp[i] = dp[i−1] + dp[i−2] (ways to climb i stairs) is the shape of a huge family of 1-D DP problems. Fill left to right; two rolling variables are enough.

Algorithm

  1. Base: a, b = 1, 1 (ways to reach step 0 and 1).
  2. For i from 2 to n, a, b = b, a+b.
  3. Return b.
Time
O(n)
Space
O(1)
Solution.py
class Solution:    def countNonDecreasingArraysWithGivenDigitSums(self, n: int) -> int:        a, b = 1, 1        for _ in range(2, n + 1):            a, b = b, a + b        return b
Watch this run

03

Interactive walkthrough

Playing “Count Non Decreasing Arrays With Given Digit Sums — dynamic programming”. Edit the input, hit Run, then scrub.

Approach: Count Non Decreasing Arrays With Given Digit Sums — dynamic programming

Loading animation…