Count of seats booked on each of the given N flights

Given an integer N denoting the number of flights and array bookings[][3] with each row of the form {a, b, K} denoting that there are K seats booked from flight a to flight b ( consider 1-based indexing), the task is to find the sequence of the number of seats booked in N flights.

Examples:

Input: bookings[][] = {{1, 2, 10}, {2, 3, 20}, {2, 5, 25}}
Output: 10 55 45 25 25
Explanation:
Initially, there are no seats booked in any of the flights. So the resultant sequence is {0, 0, 0, 0, 0}
Book 10 seats in flights 1 to 2. The sequence becomes {10, 10, 0, 0, 0}.
Book 20 seats in flights 2 to 3. The sequence becomes {10, 30, 20, 0, 0}.
Book 25 seats in flights 2 to 5. The sequence becomes {10, 55, 45, 25, 25}.

Input: bookings[][] = {{1, 3, 100}, {2, 6, 100}, {3, 4, 100}}
Output: 100 200 300 200 100 100

Naive Approach: Follow the steps below to solve the problem in simplest approach possible:

• Initialize an array seq[] of size N to store the count of allocated seats in each flight.
• Traverse the array bookings[].
• For each query {a, b, K}, add the element K in the array seq[] from the index a to b.
• After completing the above steps, print the array seq[] as the result.

Time Complexity: O(N²)
Auxiliary Space: O(N)

Efficient Approach: To optimize the above approach, the idea is to use the concept of Prefix Sum. Follow the steps below to solve the problem:

• Initialize an array seq[] of size (N + 2) to store all the allocated seats.
• Traverse the array bookings[].
• For each query {a, b, K}, increment the array seq[] at index (a – 1) by K and decrement the element at index (b + 1) by K.
• For the resulting sequence, find the prefix sum of the array seq[].
• After completing the above steps, print the array seq[] as the result.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to find the total of the
// seats booked in each of the flights
void corpFlightBookings(
    vector<vector<int> >& Bookings,
    int N)
{
    // Stores the resultant sequence
    vector<int> res(N, 0);

    // Traverse the array
    for (int i = 0;
         i < Bookings.size(); i++) {

        // Store the first booked flight
        int l = Bookings[i][0];

        // Store the last booked flight
        int r = Bookings[i][1];

        // Store the total number of
        // seats booked in flights [l, r]
        int K = Bookings[i][2];

        // Add K to the flight L
        res[l - 1] = res[l - 1] + K;

        // Subtract K from flight
        // number R + 1
        if (r <= res.size() - 1)
            res[r] = (-K) + res[r];
    }

    // Find the prefix sum of the array
    for (int i = 1; i < res.size(); i++)
        res[i] = res[i] + res[i - 1];

    // Print the total number of seats
    // booked in each flight
    for (int i = 0; i < res.size(); i++) {
        cout << res[i] << " ";
    }
}

// Driver Code
int main()
{
    // Given list of bookings
    vector<vector<int> > bookings{ { 1, 3, 100 },
                                   { 2, 6, 100 },
                                   { 3, 4, 100 } };
    int N = 6;

    // Function Call
    corpFlightBookings(bookings, N);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;

class GFG
{

// Function to find the total of the
// seats booked in each of the flights
static void corpFlightBookings(int [][]Bookings,
                               int N)
{

    // Stores the resultant sequence
    int res[] = new int[N];

    // Traverse the array
    for (int i = 0;
         i < Bookings.length; i++)
    {

        // Store the first booked flight
        int l = Bookings[i][0];

        // Store the last booked flight
        int r = Bookings[i][1];

        // Store the total number of
        // seats booked in flights [l, r]
        int K = Bookings[i][2];

        // Add K to the flight L
        res[l - 1] = res[l - 1] + K;

        // Subtract K from flight
        // number R + 1
        if (r <= res.length - 1)
            res[r] = (-K) + res[r];
    }

    // Find the prefix sum of the array
    for (int i = 1; i < res.length; i++)
        res[i] = res[i] + res[i - 1];

    // Print the total number of seats
    // booked in each flight
    for (int i = 0; i < res.length; i++)
    {
        System.out.print(res[i] + " ");
    }
}

// Driver Code
public static void main(String[] args)
{

    // Given list of bookings
    int bookings[][] = { { 1, 3, 100 },
                        { 2, 6, 100 },
                        { 3, 4, 100 } };
    int N = 6;

    // Function Call
    corpFlightBookings(bookings, N);
}
}

// This code is contributed by 29AjayKumar

Python3

# Python3 program for the above approach

# Function to find the total of the
# seats booked in each of the flights
def corpFlightBookings(Bookings, N):

    # Stores the resultant sequence
    res = [0] * N

    # Traverse the array
    for i in range(len(Bookings)):

        # Store the first booked flight
        l = Bookings[i][0]

        # Store the last booked flight
        r = Bookings[i][1]

        # Store the total number of
        # seats booked in flights [l, r]
        K = Bookings[i][2]

        # Add K to the flight L
        res[l - 1] = res[l - 1] + K

        # Subtract K from flight
        # number R + 1
        if (r <= len(res) - 1):
            res[r] = (-K) + res[r]

    # Find the prefix sum of the array
    for i in range(1, len(res)):
        res[i] = res[i] + res[i - 1]

    # Print total number of seats
    # booked in each flight
    for i in range(len(res)):
        print(res[i], end = " ")

# Driver Code
if __name__ == '__main__':

    # Given list of bookings
    bookings = [ [ 1, 3, 100 ],
               [ 2, 6, 100 ],
               [ 3, 4, 100 ] ]
    N = 6

    # Function Call
    corpFlightBookings(bookings, N)

# This code is contributed by mohit kumar 29

C#

// C# program for the above approach
using System;
class GFG
{

// Function to find the total of the
// seats booked in each of the flights
static void corpFlightBookings(int [,]Bookings,
                               int N)
{

    // Stores the resultant sequence
    int []res = new int[N];

    // Traverse the array
    for (int i = 0;
         i < Bookings.GetLength(0); i++)
    {

        // Store the first booked flight
        int l = Bookings[i,0];

        // Store the last booked flight
        int r = Bookings[i,1];

        // Store the total number of
        // seats booked in flights [l, r]
        int K = Bookings[i,2];

        // Add K to the flight L
        res[l - 1] = res[l - 1] + K;

        // Subtract K from flight
        // number R + 1
        if (r <= res.Length - 1)
            res[r] = (-K) + res[r];
    }

    // Find the prefix sum of the array
    for (int i = 1; i < res.Length; i++)
        res[i] = res[i] + res[i - 1];

    // Print the total number of seats
    // booked in each flight
    for (int i = 0; i < res.Length; i++)
    {
        Console.Write(res[i] + " ");
    }
}

// Driver Code
public static void Main(String[] args)
{

    // Given list of bookings
    int [,]bookings = { { 1, 3, 100 },
                        { 2, 6, 100 },
                        { 3, 4, 100 } };
    int N = 6;

    // Function Call
    corpFlightBookings(bookings, N);
}
}

// This code is contributed by shikhasingrajput

Javascript

<script>

// Javascript program for the above approach

// Function to find the total of the
// seats booked in each of the flights
function corpFlightBookings(Bookings, N)
{

    // Stores the resultant sequence
    let res = new Array(N).fill(0);

    // Traverse the array
    for(let i = 0;
            i < Bookings.length; i++)
    {

        // Store the first booked flight
        let l = Bookings[i][0];

        // Store the last booked flight
        let r = Bookings[i][1];

        // Store the total number of
        // seats booked in flights [l, r]
        let K = Bookings[i][2];

        // Add K to the flight L
        res[l - 1] = res[l - 1] + K;

        // Subtract K from flight
        // number R + 1
        if (r <= res.length - 1)
            res[r] = (-K) + res[r];
    }

    // Find the prefix sum of the array
    for(let i = 1; i < res.length; i++)
        res[i] = res[i] + res[i - 1];

    // Print the total number of seats
    // booked in each flight
    for(let i = 0; i < res.length; i++)
    {
        document.write(res[i] + " ");
    }
}

// Driver Code

// Given list of bookings
let bookings = [ [ 1, 3, 100 ],
                 [ 2, 6, 100 ],
                 [ 3, 4, 100 ] ];
let N = 6;

// Function Call
corpFlightBookings(bookings, N);

// This code is contributed by splevel62

</script>

Output:

100 200 300 200 100 100

Time Complexity: O(N)
Auxiliary Space: O(N)