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Pinduoduo·Software Engineer·Technical Phone Screen·Intermediate

IntermediateRejected
May 2026

Summary

Pinduoduo software engineer coding round that went sideways fast. The main question was a BFS/DP variant where you had to reconstruct the actual path, not just return the count, and I ran out of time badly enough that the interviewer tacked on an extra 30 minutes. Still couldn't crack it.

Questions Asked (1)

Q1

Given a positive integer n, find the minimum number of perfect squares that sum to n, and return the actual sequence of squares used, not just the count.

Algorithms & Data Structures
Author's notes

This is where it fell apart.

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AI HintsAI Generated

Suggested Approach

Use dynamic programming to compute the minimum number of perfect squares for all values up to n, then backtrack to reconstruct the sequence. Alternatively, apply BFS on the graph of remainders to find the shortest path, which naturally yields the sequence. Emphasize that the problem is a variant of the classic coin change problem with squares as coins.

Pro tip: Mention that while the mathematical Lagrange's four-square theorem guarantees the answer is at most 4, the actual sequence still requires computation. Also, note that BFS is often more efficient for finding the sequence because it stops as soon as the target is reached, unlike DP which computes all states.

1. Clarify the problem and constraints

Confirm that n is a positive integer, and that we need the actual squares, not just the count. Ask about the expected input size to choose the appropriate algorithm.

2. Choose an algorithm

Decide between dynamic programming and BFS. DP is straightforward for counting and can be adapted for sequence reconstruction; BFS finds the shortest path and naturally reconstructs the sequence.

3. Implement the solution

For DP: initialize an array dp of size n+1 with infinity, set dp[0]=0, and for each i from 1 to n, iterate over squares j^2 <= i, updating dp[i] = min(dp[i], dp[i - j^2] + 1). For BFS: use a queue starting from n, subtract squares until reaching 0, tracking the path.

4. Reconstruct the sequence

For DP: after filling dp, start from n and repeatedly find a square j^2 such that dp[n] = dp[n - j^2] + 1, appending j^2 and updating n. For BFS: during traversal, store the parent and the square used to reach each state, then backtrack from 0 to n.

5. Analyze complexity and optimize

Discuss time and space complexity: DP is O(n√n) time and O(n) space; BFS is O(n) time and space in the worst case. Mention possible optimizations like using a precomputed list of squares or pruning.

Key Points to Mention

  • Dynamic programming recurrence: dp[i] = min(dp[i - j^2] + 1) for all j where j^2 <= i.
  • BFS approach: treat each integer as a node, edges represent subtracting a perfect square, find shortest path from n to 0.
  • Sequence reconstruction: store parent pointers or choices during DP/BFS to backtrack and build the list of squares.
  • Lagrange's four-square theorem: every natural number is the sum of at most four squares, which bounds the answer.
  • Time and space complexity: DP O(n√n) time, O(n) space; BFS O(n) time and space.
  • Edge cases: n=1, n=0 (if allowed), and large n requiring memory optimization.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.