Last Updated: 12 Apr, 2021
Money in the bank
Easy
Harshit wants to save money for his first car. He puts money in the Ninja bank every day.
He starts by putting in ‘1’ rupee on Monday, the first day. Every day from Tuesday to Sunday, he will put in ‘1’ rupee more than the day before. On every subsequent Monday, he will put in ‘1’ rupee more than the previous Monday.
You are given ‘N’, your task is to return the total amount of money he will have in the Ninja bank at the end of the ‘N’th day.
For example:
Given ‘N’ = 2
On Day 1 = 1
On Day 2 = 2
Total Amount = 1 + 2 = 3.
Therefore the answer is 3.
Input format :
The first line of input contains an integer ‘T’ denoting the number of test cases.
The first and the only line of each test case contains a single integer ‘N’,that is the number of days.
Output format :
For each test case, print the total amount of money after N days.
The output of each test case will be printed in a separate line.
Constraints:
1 <= T <= 10
1 <= N <= 5000
Where ‘T’ is the total number of test cases, and N is the number of days.
Time limit: 1sec.
Approaches
The main idea is to loop from 1 to ‘N’ and add 1 coin more than we did yesterday and every time we complete a week, set the coin value to the number of weeks that have passed.
- Maintain a variable ‘DAY’ and loop from 1 to ‘N’
- For every ‘DAY’ increase the value of ‘COIN’ by 1.
- If the ‘DAY’ % 7 is 0, set the value of ‘COIN’ to ‘DAY’/7.
- Maintain a variable ‘RES’ and add the value of ‘COIN’ for every ‘DAY’
- Return ‘RES’ as the final answer.
The main idea is to observe that for every fullweek we complete we add an extra rupee than we did last monday.Therefore formulate the problem as taught below:
- We have ‘FULLWEEK’ = ‘N’ / 7 full weeks.
- The first week we deposit (1 + 7) * 7 / 2 = 28 rupees.
- The ‘Wth’ week we deposit (W + W + 6) * 7 / 2 = (W + 3) * 7 rupees, the (W + 1)th week we deposit 7 rupees more.
- So the money we deposit each week is also an arithmetic sequence, whose sum is (28 + 28 + 7 * (‘FULLWEEK’ - 1)) * ‘FULLWEEK’ / 2 = (49 + 7 * ‘FULLWEEK’) * ‘FULLWEEK’ / 2.
- The last non-full week has ‘REMAININGDAYS’ = ‘N’ % 7 days.
- We deposit ‘FULLWEEK’ + 1 rupees on its Monday, so we deposit (‘FULLWEEK’ + 1 + (‘FULLWEEK’ + 1 + ‘REMAININGDAYS’ - 1)) * ‘REMAININGDAYS’ / 2 = (2 * ‘FULLWEEK’ + ‘REMAININGDAYS’ + 1) * ‘REMAININGDAYS’ / 2 rupees for this week.
- So the final answer is (49 + 7 * ‘FULLWEEK’) *‘FULLWEEK’ / 2 + (2 * ‘FULLWEEK’ + ‘REMAININGDAYS’ + 1) * ‘REMAININGDAYS’ / 2.