#1235 - Maximum Profit in Job Scheduling

Hard • View on LeetCode • View on GitHub

Array Dynamic Programming Sorting Binary Search

Problem Description

We have n jobs, where every job is scheduled to be done from startTime[i] to endTime[i], obtaining a profit of profit[i].

You're given the startTime, endTime and profit arrays, return the maximum profit you can take such that there are no two jobs in the subset with overlapping time range.

If you choose a job that ends at time X you will be able to start another job that starts at time X.

Solution

/**
 * @param {number[]} startTime
 * @param {number[]} endTime
 * @param {number[]} profit
 * @return {number}
 */
var jobScheduling = function(startTime, endTime, profit) {
  const jobCount = startTime.length;
  const indices = Array.from({ length: jobCount }, (_, i) => i)
    .sort((a, b) => startTime[a] - startTime[b]);

  const maxProfit = new Array(jobCount + 1).fill(0);

  for (let i = jobCount - 1; i >= 0; i--) {
    let left = i + 1;
    let right = jobCount - 1;
    const currentEnd = endTime[indices[i]];

    while (left <= right) {
      const mid = left + right >> 1;
      if (startTime[indices[mid]] < currentEnd) left = mid + 1;
      else right = mid - 1;
    }

    maxProfit[i] = Math.max(maxProfit[i + 1], profit[indices[i]] + maxProfit[left]);
  }

  return maxProfit[0];
};