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Minimum Time to Remove All Cars Containing Illegal Goods

HardStringDP
Solve on LeetCode

Hard · dynamic programming solution for Minimum Time to Remove All Cars Containing Illegal Goods. Python, Go, and a step-by-step animation.

01

Problem

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

LeetCode 2167. Minimum Time to Remove All Cars Containing Illegal Goods. 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

Minimum Time to Remove All Cars Containing Illegal Goods — dynamic programming

Each answer is a combination of smaller answers already in the table. Built for LeetCode 2167. Minimum Time to Remove All Cars Containing Illegal Goods.

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 minimumTimeToRemoveAllCarsContainingIllegalGoods(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 “Minimum Time to Remove All Cars Containing Illegal Goods — dynamic programming”. Edit the input, hit Run, then scrub.

Approach: Minimum Time to Remove All Cars Containing Illegal Goods — dynamic programming

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