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The iterative approach involves simulating each day in a loop, tracking both the weeks and individual days. We'll add the appropriate amount of money for each day based on the rules provided. This approach leverages basic looping constructs and conditionally increments the sums based on the day of the week.
Time Complexity: O(n), where n is the number of days. Each day is processed once.
Space Complexity: O(1), only a constant amount of space is used.
1def totalMoney(n: int) -> int:
2 total = 0
3 week = 0
4 for i in range(n):
5 if i % 7 == 0:
6 week += 1
7 total += week + (i % 7)
8 return total
9
10print(totalMoney(10))The Python solution also follows an iterative paradigm, looping through days and using modulo to adjust for week changes.
The mathematical approach seeks to minimize iterations by using formulae to directly compute sums based on weeks, leveraging arithmetic series properties. This method is typically more efficient and concise.
Time Complexity: O(1).
Space Complexity: O(1).
1using System;
public class Solution {
public int TotalMoney(int n) {
int weeks = n / 7;
int days = n % 7;
int total = (28 + 7 * weeks) * weeks / 2 + (weeks + 1) * days + days * (days - 1) / 2;
return total;
}
public static void Main() {
Solution sol = new Solution();
Console.WriteLine(sol.TotalMoney(10));
}
}
C# follows the established pattern of using mathematical formulas to avoid unnecessary iterations, leading to a constant time computation.