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Minimize time using elevator then climb stairs

Q: Minimize time using elevator then climb stairs

This question evaluates a candidate's ability to model and optimize a discrete decision under resource constraints, testing algorithmic optimization, numerical reasoning, handling of edge cases, and attention to integer/64-bit arithmetic.

Problem

You need to go up n floors (from floor 0 to floor n). You may:

Take the elevator first (at most once, only at the start) for k floors, where 0 ≤ k ≤ n .
- For each elevator floor traveled:
  - You gain e1 energy.
  - You spend t1 time.
- After riding k floors, your energy is E = k * e1 .
Then climb the remaining n - k floors by stairs .
- For each stair floor climbed:
  - If your current energy before climbing that floor is E , the time spent on that floor is:

$\lceil c / E \rceil$

 - After climbing that floor, your energy decreases by `e2`:
   
   `E := E - e2`

Energy must never become negative , meaning before every stair step you must have E ≥ e2 (so that after subtracting e2 you still have E ≥ 0 ).

Your task is to choose k to minimize the total travel time.

Input

Five integers:

n : number of floors to go up
e1 : energy gained per elevator floor
t1 : time per elevator floor
e2 : energy spent per stair floor
c : constant used in stair time formula

Output

Return the minimum possible total time to reach floor n.

If it is impossible to reach floor n for any k (i.e., you can’t complete the stair portion without energy going negative), return -1 .

Notes / Clarifications

The elevator can be taken only once and only before any stair climbing .
Stair time uses the current energy before spending e2 for that floor.
Use 64-bit arithmetic where appropriate.

Problem

You need to go up n floors (from floor 0 to floor n). You may:

Take the elevator first (at most once, only at the start) for k floors, where 0 ≤ k ≤ n .

For each elevator floor traveled:
- You gain e1 energy.
- You spend t1 time.
After riding k floors, your energy is E = k * e1 .

Then climb the remaining n - k floors by stairs .

For each stair floor climbed:
- If your current energy before climbing that floor is E , the time spent on that floor is:

\lceil c / E \rceil

- After climbing that floor, your energy decreases by `e2`: `E := E - e2`

Energy must never become negative , meaning before every stair step you must have E ≥ e2 (so that after subtracting e2 you still have E ≥ 0 ).

Your task is to choose k to minimize the total travel time.

Minimize time using elevator then climb stairs

Quick Overview

Problem

Input

Output

Notes / Clarifications

Comments (0)

Minimize time using elevator then climb stairs

Quick Overview

Problem

Input

Output

Notes / Clarifications

Comments (0)