← Bytedance Interview Insights
It's basically a stair-climbing DP variant.
Recognize this as a dynamic programming problem where the minimum cost to reach index i is the cost at i plus the minimum of the costs to reach i-1 and i-2. Start by defining the recurrence relation, then implement it with O(1) space by keeping only the last two values. Discuss time and space complexity and consider edge cases like empty or single-element arrays.
Pro tip: After presenting the optimal solution, mention that you can further optimize by using a greedy approach if the cost array has certain properties, but clarify that DP is the general solution. This shows you think about problem variations and constraints.
Confirm that you start at index 0 and must pay the cost at each index you stand on, including the last. Ask if the array can be empty or have one element, and whether costs are non-negative.
Let dp[i] be the minimum total cost to reach index i. The recurrence is dp[i] = cost[i] + min(dp[i-1], dp[i-2]) for i >= 2, with base cases dp[0] = cost[0] and dp[1] = cost[1].
Since dp[i] only depends on the previous two states, use two variables to store dp[i-1] and dp[i-2] and update them iteratively, achieving O(1) space.
Write clean code for the iterative solution, then walk through a small example (e.g., [10,15,20]) to verify correctness. Handle edge cases like empty array (return 0) and single element (return cost[0]).
State that the time complexity is O(n) and space complexity is O(1). Mention that this is optimal for the general case.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.