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Tested Python solution for LeetCode 1155 with 16 pytest cases. Generate a practice environment with lcpy.
lcpy gen -n 1155 # by problem number
lcpy gen -s number_of_dice_rolls_with_target_sum # by problem name
n dice, and each dice has k faces numbered from 1 to k.
Given three integers n, k, and target, return the number of possible ways (out of the k^n total ways) to roll the dice, so the sum of the face-up numbers equals target. Since the answer may be too large, return it modulo 10^9 + 7.
Input: n = 1, k = 6, target = 3
Output: 1
Explanation: You throw one die with 6 faces.
There is only one way to get a sum of 3.
Input: n = 2, k = 6, target = 7
Output: 6
Explanation: You throw two dice, each with 6 faces.
There are 6 ways to get a sum of 7: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1.
Input: n = 30, k = 30, target = 500
Output: 222616187
Explanation: The answer must be returned modulo 10^9 + 7.
1 <= n, k <= 301 <= target <= 1000class Solution:
# Time: O(n * k * target)
# Space: O(target)
def num_rolls_to_target(self, n: int, k: int, target: int) -> int:
mod = 10**9 + 7
dp = [1] + [0] * target
for _ in range(n):
ndp = [0] * (target + 1)
for t in range(1, target + 1):
for f in range(1, min(k, t) + 1):
ndp[t] = (ndp[t] + dp[t - f]) % mod
dp = ndp
return dp[target]
| Time | Space |
|---|---|
| O(n * k * target) | O(target) |