CodingMediumcod-g644

Subject Combinatorial countingLevel Mid–Senior~22 minCommon in Algorithms & data structures interviewsIndustries Software development

Question

Count the number of ways to distribute n identical items into k distinct bins where each bin gets zero or more items (i.e. the number of non-negative integer solutions to x1+...+xk = n). This is the stars-and-bars count C(n+k-1, k-1), taken modulo 10^9+7. Constraints: 0 <= n <= 100000, 1 <= k <= 100000.

Implement

stars_and_bars(n: int, k: int) → int

Examples

in[3,2]out4

What a strong answer looks like

State your approach and its time/space complexity out loud before you optimize. Handle the edge cases (empty input, duplicates, overflow), and say why you chose this over the brute force. Green tests are the floor, not the grade.

Learn the concepts

Vibe coding: describe the solution in plain language (or narrate it) and the coach grades your approach. Generating runnable code from your description is coming next.

Run or narrate your approach, then ask the coach.