LeetCode: Most Profit Assigning Work

Posted on February 22, 2018July 26, 2020 by braindenny

Most Profit Assigning Work

Similar Problems:

We have jobs: difficulty[i] is the difficulty of the ith job, and profit[i] is the profit of the ith job.

Now we have some workers. worker[i] is the ability of the ith worker, which means that this worker can only complete a job with difficulty at most worker[i].

Every worker can be assigned at most one job, but one job can be completed multiple times.

For example, if 3 people attempt the same job that pays $1, then the total profit will be $3. If a worker cannot complete any job, his profit is $0.

What is the most profit we can make?

Example 1:

Input: difficulty = [2,4,6,8,10], profit = [10,20,30,40,50], worker = [4,5,6,7]
Output: 100
Explanation: Workers are assigned jobs of difficulty [4,4,6,6] and they get profit of [20,20,30,30] seperately.

Notes:

1 <= difficulty.length = profit.length <= 10000
1 <= worker.length <= 10000
difficulty[i], profit[i], worker[i] are in range [1, 10^5]

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

// https://code.dennyzhang.com/most-profit-assigning-work
// Basic Ideas: dynamic programming + binarysearch
//
// Complexity: Time O(n*log(n)), Space O(n)
func maxProfitAssignment(difficulty []int, profit []int, worker []int) int {
    m := make(map[int]int)
    for i, d := range difficulty {
        v, status := m[d]
        if status == false {
            m[d] = profit[i]
        } else {
            if v<profit[i] {m[d]=profit[i]}
        }
    }

    sort.Ints(difficulty[:])
    for i := 0; i<len(profit); i++ {
        v, _ := m[difficulty[i]]
        profit[i] = v
    }

    // get most profit values
    dp := make([]int, len(difficulty))
    dp[0] = profit[0]
    for i, _ := range difficulty {
        if i == 0 { continue }
        dp[i] = profit[i]
        if dp[i] < dp[i-1] { dp[i] = dp[i-1] }
    }

    res := 0
    // binarysearch: find the first no smaller value
    for _, w := range worker{
        item := 0
        left, right := 0, len(difficulty)
        for left<right {
            mid := left + int((right-left)/2)
            if difficulty[mid] == w {
                item = dp[mid]
                break
            } else{
                if difficulty[mid] > w {
                   right = mid
                } else {
                    left = mid + 1
                }
            }
      }
      if item == 0 {
          if left != 0 { item = dp[left-1] }
      }
      res += item
    }
    return res
}

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