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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.
1function totalMoney(n) {
2 let total = 0;
3 let week = 0;
4 for (let i = 0; i < n; i++) {
5 if (i % 7 === 0) {
6 week++;
7 }
8 total += week + (i % 7);
9 }
10 return total;
11}
12
13console.log(totalMoney(10));
14In this JavaScript solution, a loop iterates over each day, checking modulus to start a new week, and adds the proper daily value. JavaScript's flexibility with integers simplifies this direct approach.
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).
1#include <iostream>
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;
}
int main() {
int n = 10;
std::cout << totalMoney(n);
return 0;
}
Following the same arithmetic approach, this C++ code makes use of formulae to sum up weeks and extra days without calling iterative loops.