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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.
1#include <stdio.h>
2
3int totalMoney(int n) {
4 int total = 0;
5 int week = 0;
6 for (int i = 0; i < n; i++) {
7 if (i % 7 == 0) {
8 week++;
9 }
10 total += week + (i % 7);
11 }
12 return total;
13}
14
15int main() {
16 int n = 10;
17 printf("%d", totalMoney(n));
18 return 0;
19}
20This C solution uses a for loop to iterate through each day until n. It calculates the current 'week' number and the 'day of the week' using modulo arithmetic. It adds the appropriate amount for that day to a running total.
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).
1class In Java, the mathematical logic is implemented in the same manner, with static methods for quick and efficient computation. Weeks and remaining days are separately calculated and summed.