|
| 1 | +from itertools import product |
| 2 | + |
| 3 | + |
| 4 | +class Solution: |
| 5 | + MOD = 10**9 + 7 |
| 6 | + |
| 7 | + def __multiply_matrices(self, mat1: list[list[int]], mat2: list[list[int]]) -> list[list[int]]: |
| 8 | + p, q, r = len(mat1), len(mat1[0]), len(mat2[0]) |
| 9 | + result = [[0] * r for _ in range(p)] |
| 10 | + for i, j in product(range(p), range(r)): |
| 11 | + temp = 0 |
| 12 | + for k in range(q): |
| 13 | + temp += mat1[i][k] * mat2[k][j] |
| 14 | + result[i][j] = temp % self.MOD |
| 15 | + return result |
| 16 | + |
| 17 | + def __power_matrix(self, matrix: list[list[int]], exp: int) -> list[list[int]]: |
| 18 | + n = len(matrix) |
| 19 | + result = [[int(i == j) for j in range(n)] for i in range(n)] |
| 20 | + while exp > 0: |
| 21 | + if exp & 1: |
| 22 | + result = self.__multiply_matrices(result, matrix) |
| 23 | + matrix = self.__multiply_matrices(matrix, matrix) |
| 24 | + exp >>= 1 |
| 25 | + return result |
| 26 | + |
| 27 | + def lengthAfterTransformations(self, s: str, t: int, nums: list[int]) -> int: |
| 28 | + transform = [[0] * 26 for _ in range(26)] |
| 29 | + for i in range(26): |
| 30 | + for shift in range(nums[i]): |
| 31 | + transform[i][(i + 1 + shift) % 26] += 1 |
| 32 | + transform = self.__power_matrix(transform, t) |
| 33 | + |
| 34 | + freqs = [[0] * 26] |
| 35 | + for ch in s: |
| 36 | + freqs[0][ord(ch) - ord('a')] += 1 |
| 37 | + freqs = self.__multiply_matrices(freqs, transform) |
| 38 | + return sum(freqs[0]) % self.MOD |
| 39 | + |
| 40 | + |
| 41 | +def main(): |
| 42 | + s = 'abcyy' |
| 43 | + t = 2 |
| 44 | + nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2] |
| 45 | + assert Solution().lengthAfterTransformations(s, t, nums) == 7 |
| 46 | + |
| 47 | + s = 'azbk' |
| 48 | + t = 1 |
| 49 | + nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] |
| 50 | + assert Solution().lengthAfterTransformations(s, t, nums) == 8 |
| 51 | + |
| 52 | + |
| 53 | +if __name__ == '__main__': |
| 54 | + main() |
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