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author | Jack Sangdahl <[email protected]> | 2025-10-11 22:00:35 -0600 |
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committer | Jack Sangdahl <[email protected]> | 2025-10-11 22:00:35 -0600 |
commit | 34a6791c29e4c23dd299327a33247a77d39cc681 (patch) | |
tree | 385051502113e7b04e813a190cecc3f4123ba08e /find_sum_arr_product_seq.py | |
parent | a5f938a020f2ddb10668e8d10a146027ea1807cd (diff) | |
download | leetcode-master.tar.gz leetcode-master.zip |
Diffstat (limited to 'find_sum_arr_product_seq.py')
-rw-r--r-- | find_sum_arr_product_seq.py | 76 |
1 files changed, 76 insertions, 0 deletions
diff --git a/find_sum_arr_product_seq.py b/find_sum_arr_product_seq.py new file mode 100644 index 0000000..ebadb9f --- /dev/null +++ b/find_sum_arr_product_seq.py @@ -0,0 +1,76 @@ +# 3539. Find Sum of Array Product of Magical Sequences + +""" +you are given two integers 'm' and 'k', and an integer array 'nums'. a +sequence of integers 'seq' is called magical if 'seq' has a size of 'm', '0 +<= seq[i] < nums.len', and the binary representation of '2^seq[0] + 2^seq[1] ++ ...' has 'k' set bits. the array product of this sequence is defined as +'prod(seq) = (nums[seq[0]] nums[seq[1]] ...)'. return the sum of the +array products for all valid magical sequences. since the answer may be very +large, return it modulo 10^9+7. a set bit refers to a bit in the binary +represenation of a number that has a value of 1 +""" + + +class Solution(object): + def magicalSum(self, m, k, nums): + """ + :type m: int + :type k: int + :type nums: List[int] + :rtype: int + """ + mod = 10**9 + 7 + n = len(nums) + powtab = [[1] * (m + 1) for _ in range(n)] + for i in range(n): + for c in range(1, m + 1): + powtab[i][c] = powtab[i][c - 1] * nums[i] % mod + comb = [[0] * (m + 1) for _ in range(m + 1)] + for i in range(m + 1): + comb[i][0] = 1 + for j in range(1, i + 1): + comb[i][j] = (comb[i - 1][j - 1] + comb[i - 1][j]) % mod + dp = [[[0] * (k + 1) for _ in range(m + 1)] for __ in range(m + 1)] + dp[m][0][0] = 1 + for i in range(n): + next_dp = [[[0] * (k + 1) for _ in range(m + 1)] for __ in range(m + 1)] + pow_i = powtab[i] + for rem in range(m + 1): + for carry in range(m + 1): + row = dp[rem][carry] + if not any(row_elt for row_elt in row): + continue + for ones in range(k + 1): + base_val = row[ones] + if base_val == 0: + continue + for c in range(rem + 1): + t = c + carry + bit = t & 1 + ones2 = ones + bit + if ones2 > k: + continue + carry2 = t >> 1 + rem2 = rem - c + add = base_val + add = add * comb[rem][c] % mod + add = add * pow_i[c] % mod + next_dp[rem2][carry2][ones2] = ( + next_dp[rem2][carry2][ones2] + add + ) % mod + dp = next_dp + ans = 0 + for carry in range(m + 1): + extra = bin(carry).count("1") + need = k - extra + if 0 <= need <= k: + ans = (ans + dp[0][carry][need]) % mod + return ans % mod + + +if __name__ == "__main__": + obj = Solution() + print(obj.magicalSum(m=5, k=5, nums=[1, 10, 100, 10000, 1000000])) + print(obj.magicalSum(m=2, k=2, nums=[5, 4, 3, 2, 1])) + print(obj.magicalSum(m=1, k=1, nums=[28])) |