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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 <iostream>
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 std::cout << totalMoney(n);
18 return 0;
19}
20This C++ solution mimics the C solution, using a standard for loop and modular arithmetic to increment the total based on weekly and daily increments. This is a straightforward port from C with adjustments for C++ I/O.
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).
1function
JavaScript solution effectively applies optimized formulas for weekly and daily calculations without repetition, embracing the language's mathematical strengths.