2025-04-13 Daily Challenge

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In: DailyChallenge

Today I have done leetcode's April LeetCoding Challenge with cpp.

April LeetCoding Challenge 13

Description

Count Good Numbers

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 109 + 7.

A digit string is a string consisting of digits 0 through 9 that may contain leading zeros.

 

Example 1:

Input: n = 1
Output: 5
Explanation: The good numbers of length 1 are "0", "2", "4", "6", "8".

Example 2:

Input: n = 4
Output: 400

Example 3:

Input: n = 50
Output: 564908303

 

Constraints:

  • 1 <= n <= 1015

Solution

inline long long qpow(long long base, long long exp, long long mod) {
  long long result = 1;
  while(exp) {
    if(exp & 1) {
      result *= base;
      result %= mod;
    }
    base *= base;
    base %= mod;
    exp >>= 1;
  }
  return result;
}
class Solution {
  const int MOD = 1e9 + 7;
public:
  int countGoodNumbers(long long n) {
    return qpow(5, (1 + n) / 2, MOD) * qpow(4, n / 2, MOD) % MOD;
  }
};

// Accepted
// 166/166 cases passed (0 ms)
// Your runtime beats 100 % of cpp submissions
// Your memory usage beats 69.99 % of cpp submissions (7.9 MB)
Algorithm