Maximum Profit in Job Scheduling

Maximum Profit in Job Scheduling

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.

func jobScheduling(startTime []int, endTime []int, profit []int) int {
    // Initialize jobs array
    type Job struct {
        start, end, profit int
    }
    jobs := make([]Job, len(startTime))
    for i := 0; i < len(startTime); i++ {
        jobs[i] = Job{startTime[i], endTime[i], profit[i]}
    }
    // Sort it on start time
    sort.Slice(jobs, func(i, j int) bool { return jobs[i].start < jobs[j].start })

    nonConflictingJob := func(i int) int {
        left, right := i+1, len(jobs)-1
        for left <= right {
            mid := (left + right) / 2
            if jobs[mid].start >= jobs[i].end {
                left, right = left, mid-1
            } else {
                left, right = mid+1, right
            }
        }
        return left
    }

    memo := make(map[int]int) // Profit that can be made at position
    var dfs func(int) int
    dfs = func(pos int) int {
        // Exit condition
        if pos == len(jobs) {
            return 0
        }
        // Memoized branch
        if ans, ok := memo[pos]; ok {
            return ans
        }
        // Work branch
        var ans int
        ans += jobs[pos].profit
        ans += dfs(nonConflictingJob(pos))
        ans2 := dfs(pos+1)
        if ans < ans2 {
            ans = ans2
        }
        memo[pos] = ans
        return ans
    }

    return dfs(0)
}