Grokking 75: Top Coding Interview Questions
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Solution: Number of Dice Rolls With Target Sum
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Problem Statement

You are given n dice, each dice having k faces numbered from 1 to k. You are also given target positive integer.

Return the number of ways you can roll the dice so that the sum of the face-up numbers equals the target sum. Since the answer may be too large, return it modulo 10<sup>9</sup> + 7.

Examples

Example 1

  • Input: n = 2, k = 4, target = 5
  • Expected Output: 4
  • Justification: The possible rolls are (1, 4), (2, 3), (3, 2), and (4, 1).

Example 2

  • Input: n = 3, k = 6, target = 8
  • Expected Output: 21

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