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Diffstat (limited to 'count_num_ideal_arr.c')
-rw-r--r-- | count_num_ideal_arr.c | 36 |
1 files changed, 36 insertions, 0 deletions
diff --git a/count_num_ideal_arr.c b/count_num_ideal_arr.c new file mode 100644 index 0000000..298b1da --- /dev/null +++ b/count_num_ideal_arr.c @@ -0,0 +1,36 @@ +// 2338. Count the Number of Ideal Arrays +#include "leetcode.h" + +/* + * you are given two integers 'n' and 'maxValue' which are used to describe an + * ideal array. a 0-indexed integer array 'arr' of length 'n' is considered + * ideal if the following conditions hold true: every 'arr[i]' is a value from 1 + * to 'maxValue' for '0 <= i < n', and every 'arr[i]' is divisble by 'arr[i - + * 1]'. return the number of distinct ideal arrays of length 'n'. since the + * answer may be very large, return it modulo 10^9+7. + */ + +int idealArrays(int n, int maxValue) { + int cmb[10001][14] = {1}, cnt[10001][14] = {}, mod = 1e9 + 7; + if (!cmb[1][1]) { + for (int i = 1; i <= 10000; ++i) + for (int j = 0; j < 14; ++j) + cmb[i][j] = !j ? 1 : (cmb[i - 1][j - 1] + cmb[i - 1][j]) % mod; + for (int i = 1; i <= 10000; ++i) { + ++cnt[i][0]; + for (int j = 2 * i; j <= 10000; j += i) + for (int k = 0; cnt[i][k]; ++k) + cnt[j][k + 1] += cnt[i][k]; + } + } + int ans = 0; + for (int i = 1; i <= maxValue; ++i) + for (int j = 0; j < fmin(14, n) && cnt[i][j]; ++j) + ans = (1LL * cnt[i][j] * cmb[n - 1][j] + ans) % mod; + return ans; +} + +int main() { + printf("%d\n", idealArrays(2, 5)); // expect: 10 + printf("%d\n", idealArrays(5, 3)); // expect: 11 +} |