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authorjack <[email protected]>2024-06-14 13:13:15 -0600
committerjack <[email protected]>2024-06-14 13:13:15 -0600
commitd343a3b18dbaca9297d4f7b2280c4a16f0a5c8aa (patch)
tree96df922dae2a5073d9a50ea70c7aae6aa37e3ebe /count_good_numbers.c
downloadleetcode-d343a3b18dbaca9297d4f7b2280c4a16f0a5c8aa.tar.gz
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+// 1922. Count Good Numbers
+#include "leetcode.h"
+
+/*
+ * a digit string is good if the digits (0-indexed) at even indices are even and
+ * the digits at odd indices are prime (2,3,5,or 7). for example 2582 is good
+ * because the digits 2 and 8 at even positions are even and the digits 5 and 2
+ * at odd positions are prime. however, 3245 is not good because 3 is at an even
+ * index, but is not even. given an integer 'n', return the total number of good
+ * digit strings of length 'n'. since the answer may be large, return it modulo
+ * 1e9+7. a digit string is a string consisting of digits 0 through 9 that may
+ * contain leading zeros.
+ */
+
+const int MOD = 1e9 + 7;
+
+long long _pow(long long a, long long b) {
+ if (!b)
+ return 1;
+ return b % 2 ? a * _pow(a, b - 1) % MOD : _pow((a * a) % MOD, b / 2);
+}
+
+int countGoodNumbers(long long n) {
+ long long odd = n / 2, even = n - odd;
+ return _pow(20, odd) * ((n % 2) ? 5 : 1) % MOD;
+}
+
+int main() {
+ printf("%d\n", countGoodNumbers(1)); // expect: 5
+ printf("%d\n", countGoodNumbers(4)); // expect: 400
+ printf("%d\n", countGoodNumbers(50)); // expect: 564908303
+}