Formatted question description: https://leetcode.ca/all/1383.html
1383. Maximum Performance of a Team (Hard)
There are n
engineers numbered from 1 to n
and two arrays: speed
and efficiency
, where speed[i]
and efficiency[i]
represent the speed and efficiency for the i-th engineer respectively. Return the maximum performance of a team composed of at most k
engineers, since the answer can be a huge number, return this modulo 10^9 + 7.
The performance of a team is the sum of their engineers' speeds multiplied by the minimum efficiency among their engineers.
Example 1:
Input: n = 6, speed = [2,10,3,1,5,8], efficiency = [5,4,3,9,7,2], k = 2 Output: 60 Explanation: We have the maximum performance of the team by selecting engineer 2 (with speed=10 and efficiency=4) and engineer 5 (with speed=5 and efficiency=7). That is, performance = (10 + 5) * min(4, 7) = 60.
Example 2:
Input: n = 6, speed = [2,10,3,1,5,8], efficiency = [5,4,3,9,7,2], k = 3 Output: 68 Explanation: This is the same example as the first but k = 3. We can select engineer 1, engineer 2 and engineer 5 to get the maximum performance of the team. That is, performance = (2 + 10 + 5) * min(5, 4, 7) = 68.
Example 3:
Input: n = 6, speed = [2,10,3,1,5,8], efficiency = [5,4,3,9,7,2], k = 4 Output: 72
Constraints:
1 <= n <= 10^5
speed.length == n
efficiency.length == n
1 <= speed[i] <= 10^5
1 <= efficiency[i] <= 10^8
1 <= k <= n
Solution 1. Greedy
Intuition
For a given efficiency, we pick all works with the same or better efficiency. If the number of workers is greater than k
, we pick k
fastest workers.
Algorithm
We greedily try each engineer from the most efficient one to the least one.
For each engineer:
- first try adding him to the team and add his
speed[i]
to thesum
. - If after the addition there are more than
k
engineers in the team, pop the one with the leastspeed
, and deduct hisspeed
fromsum
. - try to update the answer using
sum * speed[i]
.
The idea behind
// OJ: https://leetcode.com/problems/maximum-performance-of-a-team/
// Time: O(NlogN)
// Space: O(N)
// Ref: https://leetcode.com/problems/maximum-performance-of-a-team/discuss/539687/JavaC%2B%2BPython-Priority-Queue
class Solution {
public:
int maxPerformance(int N, vector<int>& S, vector<int>& E, int K) {
vector<pair<int, int>> ps(N);
for (int i = 0; i < N; ++i) ps[i] = {E[i], S[i]};
sort(ps.begin(), ps.end());
long sum = 0, ans = 0;
priority_queue<int, vector<int>, greater<int>> pq;
for (int i = N - 1; i >= 0; --i) {
pq.push(ps[i].second);
sum += ps[i].second;
if (pq.size() > K) {
sum -= pq.top();
pq.pop();
}
ans = max(ans, sum * ps[i].first);
}
return ans % (int)(1e9+7);
}
};
Java
class Solution {
public int maxPerformance(int n, int[] speed, int[] efficiency, int k) {
final int MODULO = 1000000007;
int[][] speedEfficiencyArray = new int[n][2];
for (int i = 0; i < n; i++) {
speedEfficiencyArray[i][0] = speed[i];
speedEfficiencyArray[i][1] = efficiency[i];
}
Arrays.sort(speedEfficiencyArray, new Comparator<int[]>() {
public int compare(int[] speedEfficiency1, int[] speedEfficiency2) {
if (speedEfficiency1[1] != speedEfficiency2[1])
return speedEfficiency2[1] - speedEfficiency1[1];
else
return speedEfficiency2[0] - speedEfficiency1[0];
}
});
long maxPerformance = 0;
PriorityQueue<Integer> priorityQueue = new PriorityQueue<Integer>();
long speedSum = 0;
int minEfficiency = Integer.MAX_VALUE;
for (int i = 0; i < k; i++) {
int[] speedEfficiency = speedEfficiencyArray[i];
int curSpeed = speedEfficiency[0];
int curEfficiency = speedEfficiency[1];
priorityQueue.offer(curSpeed);
speedSum += curSpeed;
minEfficiency = Math.min(minEfficiency, curEfficiency);
long curPerformance = speedSum * (long) minEfficiency;
maxPerformance = Math.max(maxPerformance, curPerformance);
}
for (int i = k; i < n; i++) {
int prevSpeed = priorityQueue.poll();
speedSum -= prevSpeed;
int[] speedEfficiency = speedEfficiencyArray[i];
int curSpeed = speedEfficiency[0];
int curEfficiency = speedEfficiency[1];
priorityQueue.offer(curSpeed);
speedSum += curSpeed;
minEfficiency = Math.min(minEfficiency, curEfficiency);
long curPerformance = speedSum * (long) minEfficiency;
maxPerformance = Math.max(maxPerformance, curPerformance);
}
return (int) (maxPerformance % MODULO);
}
}