LeetCode-in-Java
2327. Number of People Aware of a Secret
Medium
On day 1, one person discovers a secret.
You are given an integer delay, which means that each person will share the secret with a new person every day, starting from delay days after discovering the secret. You are also given an integer forget, which means that each person will forget the secret forget days after discovering it. A person cannot share the secret on the same day they forgot it, or on any day afterwards.
Given an integer n, return the number of people who know the secret at the end of day n. Since the answer may be very large, return it modulo 109 + 7.
Example 1:
Input: n = 6, delay = 2, forget = 4
Output: 5
Explanation:
Day 1: Suppose the first person is named A. (1 person)
Day 2: A is the only person who knows the secret. (1 person)
Day 3: A shares the secret with a new person, B. (2 people)
Day 4: A shares the secret with a new person, C. (3 people)
Day 5: A forgets the secret, and B shares the secret with a new person, D. (3 people)
Day 6: B shares the secret with E, and C shares the secret with F. (5 people)
Example 2:
Input: n = 4, delay = 1, forget = 3
Output: 6
Explanation:
Day 1: The first person is named A. (1 person)
Day 2: A shares the secret with B. (2 people)
Day 3: A and B share the secret with 2 new people, C and D. (4 people)
Day 4: A forgets the secret. B, C, and D share the secret with 3 new people. (6 people)
Constraints:
2 <= n <= 10001 <= delay < forget <= n
Solution
public class Solution {
public int peopleAwareOfSecret(int n, int delay, int forget) {
long[][] dp = new long[n + forget][3];
// 0: people who currently know the secret (includes [1] below)
// 1: people who start sharing the secret on this day
// 2: people who forget on this day
long mod = (long) 1e9 + 7;
dp[0][0] = dp[delay][1] = dp[forget][2] = 1;
for (int i = 1; i < n; i++) {
// dp[i][1] was originally just the i - delay newcomers
dp[i][1] = (dp[i][1] + dp[i - 1][1] - dp[i][2] + mod) % mod;
// these people forget on i + forget day
dp[i + forget][2] = dp[i][1];
// these people start sharing on i + delay day
dp[i + delay][1] = dp[i][1];
// today's total people who know the secret
dp[i][0] = (dp[i - 1][0] + dp[i][1] - dp[i][2] + mod) % mod;
}
return (int) dp[n - 1][0];
}
}