LeetCode Challenge Day 40 — 1716. Calculate Money in LeetCode Bank

Hey folks

This is Day 40 of my LeetCode streak 🚀.
Today’s problem is 1716. Calculate Money in LeetCode Bank — a neat math/simulation task where deposits increase daily within each week and the whole week’s base amount also increases each new week.

📌 Problem Statement

You deposit money for n days:

• Week 1: deposit $1 on Monday, $2 on Tuesday, …, $7 on Sunday.
• Week 2: start from $2 on Monday, then $3, …, $8 on Sunday.
• And so on.

Return the total money after n days.

💡 Intuition

Split n into full weeks and leftover days.

• Each full week is an arithmetic sequence: the first week sums to 28, and each subsequent week adds 7 more (because each day’s deposit is +1 higher).
• Leftover days continue from the next week’s starting amount (weeks + 1).

🔑 Approach

1. Compute:
   • weeks = Math.floor(n / 7)
   • days = n % 7
2. Sum full weeks: week i contributes 28 + 7*i (0-indexed).
3. Sum leftover days: start from (weeks + 1) and add one per day.
4. Return weekTotal + dayTotal.

⏱️ Complexity Analysis

• Time complexity:
  We iterate through the number of full weeks (≈ n/7) and up to 6 leftover days → O(n) in the given implementation (can be O(1) with closed-form sums).

• Space complexity:
  Constant extra space → O(1).

🧑‍💻 Code (JavaScript)

/**
 * @param {number} n
 * @return {number}
 */
var totalMoney = function(n) {
    let weeks = Math.floor(n / 7);
    let days = n % 7;
    
    // total from full weeks
    let weekTotal = 0;
    for (let i = 0; i < weeks; i++) {
        weekTotal += (28 + 7 * i);  // sum of each week
    }
    
    // total from leftover days
    let dayTotal = 0;
    for (let d = 0; d < days; d++) {
        dayTotal += (weeks + 1 + d);
    }
    
    return weekTotal + dayTotal;
};

🧪 Example Walkthrough

If n = 10:

Full weeks: 1 week → 28

Leftover days: 3 days starting from 2 → 2 + 3 + 4 = 9

Total = 28 + 9 = 37 ✅

🎥 Reflections

A small problem with a clean structure. Recognizing the weekly pattern and breaking it into full weeks + leftover days makes the implementation straightforward. You can also derive closed-form formulas for both parts to make it O(1).

Happy Coding 👨‍💻