diff options
Diffstat (limited to 'find_sum_arr_product_seq.c')
-rw-r--r-- | find_sum_arr_product_seq.c | 119 |
1 files changed, 119 insertions, 0 deletions
diff --git a/find_sum_arr_product_seq.c b/find_sum_arr_product_seq.c new file mode 100644 index 0000000..568eb09 --- /dev/null +++ b/find_sum_arr_product_seq.c @@ -0,0 +1,119 @@ +// 3539. Find Sum of Array Product of Magical Sequences +#include "leetcode.h" + +/* + * 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 + */ + +static int mod = 1e9 + 7; + +int magicalSum(int m, int k, int *nums, int numsSize) { + int **pow_tab = (int **)malloc(numsSize * sizeof(int *)); + for (int i = 0; i < numsSize; i++) { + pow_tab[i] = (int *)malloc((m + 1) * sizeof(int)); + pow_tab[i][0] = 1; + for (int j = 1; j <= m; j++) { + long long val = (1LL * pow_tab[i][j - 1] * nums[i]) % mod; + pow_tab[i][j] = (int)val; + } + } + int **cmb = (int **)malloc((m + 1) * sizeof(int *)); + for (int i = 0; i <= m; i++) { + cmb[i] = (int *)malloc((m + 1) * sizeof(int)); + memset(cmb[i], 0, (m + 1) * sizeof(int)); + } + for (int i = 0; i <= m; i++) { + cmb[i][0] = 1; + for (int j = 1; j <= i; j++) { + cmb[i][j] = cmb[i - 1][j - 1] + cmb[i - 1][j]; + if (cmb[i][j] >= mod) + cmb[i][j] -= mod; + } + } + int ***dp = (int ***)malloc((m + 1) * sizeof(int **)); + int ***next = (int ***)malloc((m + 1) * sizeof(int **)); + for (int i = 0; i <= m; i++) { + dp[i] = (int **)malloc((m + 1) * sizeof(int *)); + next[i] = (int **)malloc((m + 1) * sizeof(int *)); + for (int j = 0; j <= m; j++) { + dp[i][j] = (int *)calloc(k + 1, sizeof(int)); + next[i][j] = (int *)calloc(k + 1, sizeof(int)); + } + } + dp[m][0][0] = 1; + for (int i = 0; i < numsSize; i++) { + for (int j = 0; j <= m; j++) + for (int c = 0; c <= m; c++) + memset(next[j][c], 0, (k + 1) * sizeof(int)); + for (int rem = 0; rem <= m; rem++) { + for (int carry = 0; carry <= m; carry++) + for (int ones = 0; ones <= k; ones++) { + int base = dp[rem][carry][ones]; + if (!base) + continue; + for (int c = 0; c <= rem; c++) { + int tmp = c + carry; + int bit = tmp & 1; + int ones2 = ones + bit; + if (ones2 > k) + continue; + int carry2 = tmp >> 1; + int rem2 = rem - c; + long long add = base; + add = (add * cmb[rem][c]) % mod; + add = (add * pow_tab[i][c]) % mod; + int curr = next[rem2][carry2][ones2] + (int)add; + if (curr >= mod) + curr -= mod; + next[rem2][carry2][ones2] = curr; + } + } + } + int ***tmp = dp; + dp = next; + next = tmp; + } + long long ans = 0; + for (int carry = 0; carry <= m; carry++) { + int extra = __builtin_popcount(carry); + int need = k - extra; + if (need >= 0 && need <= k) { + ans += dp[0][carry][need]; + if (ans >= mod) + ans -= mod; + } + } + for (int i = 0; i < numsSize; i++) + free(pow_tab[i]); + free(pow_tab); + for (int i = 0; i <= m; i++) + free(cmb[i]); + free(cmb); + for (int rem = 0; rem <= m; rem++) { + for (int carry = 0; carry <= m; carry++) { + free(dp[rem][carry]); + free(next[rem][carry]); + } + free(dp[rem]); + free(next[rem]); + } + free(dp); + free(next); + return (int)(ans % mod); +} + +int main() { + int n1[] = {1, 10, 100, 10000, 1000000}; + int n2[] = {5, 4, 3, 2, 1}; + int n3[] = {28}; + printf("%d\n", magicalSum(5, 5, n1, ARRAY_SIZE(n1))); // expect: 991600007 + printf("%d\n", magicalSum(2, 2, n2, ARRAY_SIZE(n2))); // expect: 170 + printf("%d\n", magicalSum(1, 1, n3, ARRAY_SIZE(n3))); // expect: 28 +} |