
Asked in Amazon
Dice Throws Problem Statement
You are given D
dice, each having F
faces numbered from 1 to F
. The task is to determine the number of possible ways to roll all the dice such that the sum of the face-up numbers equals the given 'target' sum S
.
Example:
Input:
2
3 6 8
2 4 5
Output:
21
4
Explanation:
In the first test case, there are 3 dice each with 6 faces and the possible ways to roll them to get a sum of 8 are 21. In the second test case, there are 2 dice each with 4 faces, and there are 4 ways to roll them to reach the sum of 5.
Constraints:
1 ≤ T ≤ 5
1 ≤ D, F ≤ 50
1 ≤ S ≤ 10^3
Note:
As the result can be large, return your answer modulo 10^9 + 7
.
Follow Up:
Can you optimize the solution to use no more than O(S)
extra space?
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