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Construct the Lexicographically Largest Valid Sequence

MediumArrayBacktracking
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Medium · dynamic programming solution for Construct the Lexicographically Largest Valid Sequence. Python, Go, and a step-by-step animation.

01

Problem

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

LeetCode 1718. Construct the Lexicographically Largest Valid Sequence. 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

Construct the Lexicographically Largest Valid Sequence — dynamic programming

Each answer is a combination of smaller answers already in the table. Built for LeetCode 1718. Construct the Lexicographically Largest Valid Sequence.

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 constructTheLexicographicallyLargestValidSequence(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 “Construct the Lexicographically Largest Valid Sequence — dynamic programming”. Edit the input, hit Run, then scrub.

Approach: Construct the Lexicographically Largest Valid Sequence — dynamic programming

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