Dynamic Programming Questions at DoorDash: What to Expect

Dynamic Programming (DP) is a critical skill for DoorDash technical interviews because it directly tests a candidate's ability to optimize complex, real-world logistics problems. DoorDash's core business—coordinating deliveries, drivers, and orders across time and space—is built on optimization challenges. DP is the algorithmic framework for solving problems where the optimal solution can be constructed from optimal solutions to overlapping subproblems, making it perfect for scenarios like finding the most efficient delivery route, minimizing wait times, or maximizing order batching efficiency. Mastering DP demonstrates you can think recursively about a problem, break it down, and build an efficient, cached solution—a valuable skill for designing systems at scale.

What to Expect — Types of Problems

DoorDash's DP questions often fall into two main categories that mirror their business domain:

1. Knapsack & Resource Allocation Problems: These are highly prevalent. You might encounter problems about maximizing the number of deliveries a driver can complete given a time constraint (a 0/1 knapsack variant) or allocating orders to drivers to optimize for total value or shortest overall route. The "knapsack" is often time, capacity, or a number of tasks.
2. String/Sequence DP & Pathfinding: Questions involving comparing or transforming strings (e.g., order IDs, addresses) often use DP patterns like Longest Common Subsequence or Edit Distance. Grid-based pathfinding problems, while sometimes solved with BFS/DFS, can also be approached with DP to count unique paths or find minimum cost paths, analogous to navigating a city grid.

Expect the problems to have a clear optimal substructure. The interviewer will look for your ability to identify the state definition (e.g., dp[i][t] representing the maximum value for the first i orders with t remaining time), the recurrence relation, and the base cases.

How to Prepare — Study Tips with One Code Example

Start by internalizing the core patterns, not just memorizing solutions. Practice defining the state and transition in plain English before writing code. Always begin with a recursive brute-force solution, identify the overlapping subproblems, and then add memoization (top-down DP) before deriving the iterative (bottom-up) tabulation approach. This shows systematic thinking.

A fundamental pattern is the 0/1 Knapsack. Here’s a memoized (top-down) solution for a classic problem: given a set of items with weights and values, and a maximum weight capacity, determine the maximum total value you can carry.

def knapsack(weights, values, capacity):
    n = len(weights)
    memo = [[-1] * (capacity + 1) for _ in range(n)]

    def dfs(i, remaining_cap):
        if i == n or remaining_cap == 0:
            return 0
        if memo[i][remaining_cap] != -1:
            return memo[i][remaining_cap]

        # Option 1: Skip the item
        skip = dfs(i + 1, remaining_cap)

        # Option 2: Take the item if possible
        take = 0
        if weights[i] <= remaining_cap:
            take = values[i] + dfs(i + 1, remaining_cap - weights[i])

        memo[i][remaining_cap] = max(skip, take)
        return memo[i][remaining_cap]

    return dfs(0, capacity)

Recommended Practice Order

Build your DP skills progressively. First, master the foundational 1D DP problems like Climbing Stairs and House Robber. Then, move to core 2D patterns: 0/1 Knapsack, Unbounded Knapsack (Coin Change), and Longest Common Subsequence. These form the basis for most variations. Next, practice string transformation problems (Edit Distance) and interval DP. Finally, tackle DoorDash-specific problems by practicing questions tagged for the company, which will often dress these core patterns in domain-specific scenarios like task scheduling or route optimization.

Practice Dynamic Programming at DoorDash