Citadel·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jun 2026

Summary

Citadel software engineer interview with a combinatorics/DP problem dressed up in a Grace Hopper theme. Pretty focused, just the one algorithmic question from what I remember.

Questions Asked (1)

Given n processes and m time intervals, count the number of ways to assign exactly one process to each interval such that no process appears in two consecutive intervals. Return the result modulo 10^9+7.

Algorithms & Data Structures

Author's notes

The Grace Hopper framing threw me for a second, felt like a trick.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Model the problem as a dynamic programming over intervals, where the state tracks the process assigned to the previous interval. Use a recurrence that sums over all processes except the previous one, and optimize with prefix sums to achieve O(mn) time. Handle the base case for the first interval and return the sum of valid assignments for the last interval modulo 10^9+7.

Pro tip: Clarify edge cases upfront (e.g., n=1 and m>1 yields 0 ways) and mention that the DP can be optimized to O(m) space by keeping only the previous row. This shows attention to both correctness and efficiency.

1. Define DP state

Let dp[i][j] be the number of valid assignments for the first i intervals where the i-th interval is assigned process j. Initialize dp[1][j] = 1 for all j.

2. Formulate recurrence

For i > 1, dp[i][j] = sum_{k != j} dp[i-1][k]. This ensures no process appears in two consecutive intervals.

3. Optimize with prefix sums

Compute total = sum_k dp[i-1][k] and prefix sums to get dp[i][j] = total - dp[i-1][j] in O(1) per state, reducing time to O(mn).

4. Handle modulo and base cases

Apply modulo 10^9+7 at each addition/subtraction. If n=1 and m>1, return 0; if m=1, return n.

5. Compute final answer

After filling the DP table, the answer is sum_j dp[m][j] modulo 10^9+7. Optionally, reduce space to O(n) by keeping only the previous row.

Key Points to Mention

Dynamic programming with state representing the process assigned to the current interval.
Recurrence relation that excludes the previous process to enforce the non-consecutive constraint.
Optimization using prefix sums or total sum to achieve O(mn) time complexity.
Modulo arithmetic to handle large numbers and avoid overflow.
Edge cases: n=1 with m>1, m=1, and large constraints.
Space optimization to O(n) by storing only the previous DP row.

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