Problem: Compute the Eddington Number

Given a list of positive integers distances, where distances[i] represents the distance traveled on day i, your task is to compute the cyclist’s Eddington number E.

Definition of Eddington Number E

E is defined as the largest integer such that there are at least E days with a distance traveled greater than or equal to E.

Examples

• distances = [1, 3, 3, 5, 6] → E = 3 (Explanation: Three days have a distance ≥ 3: 3, 3, 5, 6. If E=4, only 5, 6 are ≥ 4, which is 2 days, not 4. So E=3 is the largest.)
• distances = [10, 8, 5, 4, 3] → E = 4 (Explanation: Four days have a distance ≥ 4: 10, 8, 5, 4. If E=5, only 10, 8, 5 are ≥ 5, which is 3 days, not 5. So E=4 is the largest.)
• distances = [1, 1, 1] → E = 1

Constraints

• 1 <= n <= 2e5 (where n is the number of days/length of distances array)
• 1 <= distances[i] <= 1e9

Requirement

Aim for an efficient solution.