1716. Calculate Money in Leetcode Bank

Easy

題目描述

Description

Hercy wants to save money for his first car. He puts money in the Leetcode bank every day.

He starts by putting in $1 on Monday, the first day. Every day from Tuesday to Sunday, he will put in$1 more than the day before. On every subsequent Monday, he will put in $1 more than the previous Monday.

Given n, return the total amount of money he will have in the Leetcode bank at the end of the nth day.

Example 1:

Input: n = 4
Output: 10
Explanation:
After the 4th day, the total is 1 + 2 + 3 + 4 = 10.

Example 2:

Input: n = 10
Output: 37
Explanation:
After the 10th day, the total is (1 + 2 + 3 + 4 + 5 + 6 + 7) + (2 + 3 + 4) = 37. Notice that on the 2nd Monday, Hercy only puts in $2.

Example 3:

Input: n = 20
Output: 96
Explanation:
After the 20th day, the total is (1 + 2 + 3 + 4 + 5 + 6 + 7) + (2 + 3 + 4 + 5 + 6 + 7 + 8) + (3 + 4 + 5 + 6 + 7 + 8) = 96.

Constraints:

• 0 <= n <= $10^6$

解答

Solution

/**
 * @param {number} n
 * @return {number}
 */
var totalMoney = function (n) {
  const totalWeeks = Math.floor(n / 7);
  const days = n % 7;

  let result = ((28 + (28 + 7 * (totalWeeks - 1))) * totalWeeks) / 2;

  result += (days * (days + 1)) / 2 + days * totalWeeks;

  return result;
};

解題思路

先算出目前天數等於幾週又幾天

const totalWeeks = Math.floor(n / 7); // 總週數
const days = n % 7; // 其餘天數

再用等差數列公式算出題目要求的結果

等差數列的和 = (首項 + 末項) * 項數 / 2

所以假設有 totalWeeks 週
首項會是 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28
末項會是 28 + 7 * (totalWeeks - 1)

-1 是因為第一週不變是 28
第二週 = 28 + 7 * (2 - 1) = 35
第三週 28 + 7 * (3 - 1) = 42
以此類推

項數就是 totalWeeks
套用公式就會變成 ((28 + (28 + 7 * (totalWeeks - 1))))* totalWeeks / 2

let result = ((28 + (28 + 7 * (totalWeeks - 1))) * totalWeeks) / 2;

算完週的部分再把其餘天數算出來並加起來，就是答案了

result += (days * (days + 1)) / 2 + days * totalWeeks;
return result;

心得

酷酷數學