Explain dynamic programming and when to apply it.
Interviewer Expectations for this Question
01
Core Competency
Assesses fundamental understanding of Data Structures & Algorithms conventions, runtime behavior, and memory/performance considerations.
02
Evaluation Criteria
Hiring managers look for precision, avoidance of ambiguous jargon, and ability to explain trade-offs under real production conditions.
Comprehensive Model Answer
Verified Solution
DP solves problems with overlapping subproblems and optimal substructure by storing results and reusing them. Two styles:
- Top-down memoisation: recursion plus a cache, easy to write from the recurrence.
- Bottom-up tabulation: fill a table iteratively, avoids recursion depth issues.
# Fibonacci, bottom-up, O(n) time O(1) space
def fib(n):
a, b = 0, 1
for _ in range(n):
a, b = b, a + b
return a
# 0/1 knapsack, O(n * capacity)
def knapsack(items, cap):
dp = [0] * (cap + 1)
for weight, value in items:
for c in range(cap, weight - 1, -1):
dp[c] = max(dp[c], dp[c - weight] + value)
return dp[cap]
Signals: count ways, min/max cost, "can you reach", subsequence problems. State definition and transition are the key interview skills.
Candidate Response Strategy & Interview Tips
- Start with a concise one-sentence summary: Deliver a direct, confident answer first before expanding into nuances.
- Demonstrate real-world trade-offs: Discuss where this approach excels and when you would avoid it in production systems.
- Discuss complexity & edge cases: Proactively explain time/space complexity or boundary conditions (null values, scale limits).
- Prepare for interviewer follow-ups: Technical hiring panels frequently probe deeper into concurrency, backward compatibility, or alternative libraries.