Problem
A standard die produces an integer from 1 through 6. Count all nonempty ordered sequences of outcomes whose sum is target. Different orders count separately. Return the count modulo 1,000,000,007.
Implement dice_combinations(target).
Input
target: The required sum of all rolls.
Output
Return the number of sequences modulo 1,000,000,007.
Constraints
1 ≤ target ≤ 1,000,000. Taking a count modulo 1,000,000,007 means returning its remainder after division by that number.
Examples
Input:
target = 2
Expected output:
expected = 2Input:
long long target = 2;
Expected output:
long long expected = 2;Input:
long target = 2;
Expected output:
long expected = 2;Explanation
The two sequences are [2] and [1, 1].
Input:
target = 4
Expected output:
expected = 8Input:
long long target = 4;
Expected output:
long long expected = 8;Input:
long target = 4;
Expected output:
long expected = 8;Explanation
The sequences are [4], [1,3], [3,1], [2,2], [1,1,2], [1,2,1], [2,1,1], and [1,1,1,1].
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
Think of smaller sums as building blocks for the target.
Hint 2
Use a running count for each sum based on the previous six sums.
Hint 3
Be careful to apply the modulo at every addition and handle sums below 1 separately.
Expected complexity
O(target) time, O(target) extra space
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.