Minimum Waiting Time

Minimum Waiting Time

You're given a non-empty array of positive integers representing the amounts of time that specific queries take to execute. Only one query can be executed at a time, but the queries can be executed in any order.

A query's waiting time is defined as the amount of time that it must wait before its execution starts. In other words, if a query is executed second, then its waiting time is the duration of the first query; if a query is executed third, then its waiting time is the sum of the durations of the first two queries.

Write a function that returns the minimum amount of total waiting time for all of the queries. For example, if you're given the queries of durations [1, 4, 5], then the total waiting time if the queries were executed in the order of [5, 1, 4] would be (0) + (5) + (5 + 1) = 11. The first query of duration 5 would be executed immediately, so its waiting time would be 0, the second query of duration 1 would have to wait 5 seconds (the duration of the first query) to be executed, and the last query would have to wait the duration of the first two queries before being executed.

Note: you're allowed to mutate the input array.

Sample Input

queries = [3, 2, 1, 2, 6]

Sample Output

17

Solution 1

function minimumWaitingTime(queries) {
  let min = 0
  queries.sort((a,b) => a - b);
  for (let i = 0; i < queries.length; i++) {
    const duration = queries[i];
    const queriesLeft = queries.length - (i + 1);
    min += duration * queriesLeft;
  }
  return min;
}