2483. Minimum Penalty for a Shop

Description

You are given the customer visit log of a shop represented by a 0-indexed string customers consisting only of characters 'N' and 'Y':

• if the ith character is 'Y', it means that customers come at the ith hour
• whereas 'N' indicates that no customers come at the ith hour.

If the shop closes at the jth hour (0 <= j <= n), the penalty is calculated as follows:

• For every hour when the shop is open and no customers come, the penalty increases by 1.
• For every hour when the shop is closed and customers come, the penalty increases by 1.

Return the earliest hour at which the shop must be closed to incur a minimum penalty.

Note that if a shop closes at the jth hour, it means the shop is closed at the hour j.

 

Example 1:

Input: customers = "YYNY"
Output: 2
Explanation: 
- Closing the shop at the 0th hour incurs in 1+1+0+1 = 3 penalty.
- Closing the shop at the 1st hour incurs in 0+1+0+1 = 2 penalty.
- Closing the shop at the 2nd hour incurs in 0+0+0+1 = 1 penalty.
- Closing the shop at the 3rd hour incurs in 0+0+1+1 = 2 penalty.
- Closing the shop at the 4th hour incurs in 0+0+1+0 = 1 penalty.
Closing the shop at 2nd or 4th hour gives a minimum penalty. Since 2 is earlier, the optimal closing time is 2.

Example 2:

Input: customers = "NNNNN"
Output: 0
Explanation: It is best to close the shop at the 0th hour as no customers arrive.

Example 3:

Input: customers = "YYYY"
Output: 4
Explanation: It is best to close the shop at the 4th hour as customers arrive at each hour.

 

Constraints:

• 1 <= customers.length <= 105
• customers consists only of characters 'Y' and 'N'.

 

Solutions

Solution: Prefix Sum

• Time complexity: O(n)
• Space complexity: O(1)

 

JavaScript

/**
 * @param {string} customers
 * @return {number}
 */
const bestClosingTime = function (customers) {
  const n = customers.length;
  let prefixPenalty = 0;
  let suffixPenalty = 0;
  let minPenalty = n;
  let result = -1;

  for (let index = 0; index < n; index++) {
    const penalty = customers[index] === 'Y' ? 1 : 0;

    suffixPenalty += penalty;
  }

  for (let index = 0; index <= n; index++) {
    const penalty = customers[index] === 'N' ? 1 : 0;
    const totalPenalty = prefixPenalty + suffixPenalty;

    if (totalPenalty < minPenalty) {
      result = index;
      minPenalty = totalPenalty;
    }

    prefixPenalty += penalty;
    suffixPenalty += penalty - 1;
  }

  return result;
};