Given an array seats[] where seat[i] is the number of vacant seats in the ith row in a stadium for a cricket match. There are N people in a queue waiting to buy the tickets. Each seat costs equal to the number of vacant seats in the row it belongs to. The task is to maximize the profit by selling the tickets to N people.
Examples:
Input: seats[] = {2, 1, 1}, N = 3
Output: 4
Person 1: Sell the seat in the row with
2 vacant seats, seats = {1, 1, 1}
Person 2: All the rows have 1 vacant
seat each, seats[] = {0, 1, 1}
Person 3: seats[] = {0, 0, 1}Input: seats[] = {2, 3, 4, 5, 1}, N = 6
Output: 22
Approach: In order to maximize the profit, the ticket must be for the seat in a row which has the maximum number of vacant seats and the number of vacant seats in that row will be decrement by 1 as one of the seats has just been sold. All the persons can be sold a seat ticket until there are vacant seats. This can be computed efficiently with the help of a priority_queue.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std; // Function to return the maximized profit int maxProfit(int seats[], int k, int n) { // Push all the vacant seats // in a priority queue priority_queue<int> pq; for (int i = 0; i < k; i++) pq.push(seats[i]); // To store the maximized profit int profit = 0; // To count the people that // have been sold a ticket int c = 0; while (c < n) { // Get the maximimum number of // vacant seats for any row int top = pq.top(); // Remove it from the queue pq.pop(); // If there are no vacant seats if (top == 0) break; // Update the profit profit = profit + top; // Push the updated status of the // vacant seats in the current row pq.push(top - 1); // Update the count of persons c++; } return profit; } // Driver code int main() { int seats[] = { 2, 3, 4, 5, 1 }; int k = sizeof(seats) / sizeof(int); int n = 6; cout << maxProfit(seats, k, n); return 0; } |
Java
// Java implementation of the approach import java.util.*; class GFG { // Function to return the maximized profit static int maxProfit(int seats[], int k, int n) { // Push all the vacant seats // in a priority queue PriorityQueue<Integer> pq; pq = new PriorityQueue<>(Collections.reverseOrder()); for(int i = 0; i < k; i++) pq.add(seats[i]); // To store the maximized profit int profit = 0; // To count the people that // have been sold a ticket int c = 0; while (c < n) { // Get the maximimum number of // vacant seats for any row int top = pq.remove(); // If there are no vacant seats if (top == 0) break; // Update the profit profit = profit + top; // Push the updated status of the // vacant seats in the current row pq.add(top - 1); // Update the count of persons c++; } return profit; } // Driver Code public static void main(String args[]) { int seats[] = { 2, 3, 4, 5, 1 }; int k = seats.length; int n = 6; System.out.println(maxProfit(seats, k ,n)); } } // This code is contributed by rutvik_56 |
Python3
# Python3 implementation of the approach # Function to return the maximized profit def maxProfit(seats, k, n) : # Push all the vacant seats # in a priority queue pq = []; for i in range(k) : pq.append(seats[i]); # for maintaining the property of max heap pq.sort(reverse = True); # To store the maximized profit profit = 0; # To count the people that # have been sold a ticket c = 0; while (c < n) : # for maintaining the property of max heap pq.sort(reverse = True); # Get the maximimum number of # vacant seats for any row top = pq[0]; # Remove it from the queue pq.pop(0); # If there are no vacant seats if (top == 0) : break; # Update the profit profit = profit + top; # Push the updated status of the # vacant seats in the current row pq.append(top - 1); # Update the count of persons c += 1; return profit; # Driver code if __name__ == "__main__" : seats = [ 2, 3, 4, 5, 1 ]; k = len(seats); n = 6; print(maxProfit(seats, k, n)); # This code is contributed by AnkitRai01 |
22
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