Maximize count of planes that can be stopped per second with help of given initial position and speed
Given two arrays A[] and B[] consisting of N integers where A[i] represents the initial position of the ith plane and B[i] is the speed at which the plane is landing, the task is to print the number of the plane that can be stopped from landing by shooting an aircraft at every second.
Examples:
Input: A[] = {1, 3, 5, 4, 8}, B[] = {1, 2, 2, 1, 2}
Output: 4
Explanation:
- At second 1, shoot the plane at index 0, the positions of the planes are now A[] = {_, 1, 3, 3, 6}.
- At second 2, shoot the plane at index 1, the positions of the planes are now A[] = {_, _, 1, 2, 4}.
- At second 3, shoot the plane at index 2, the positions of the planes are now A[] = {_, _, _, 1, 2}.
- At second 4, shoot the plane at index 4 or 5, the positions of the planes are now A[] = {_, _, _, _, _}.
Therefore, a total of 4 planes can be stopped from landing.
Input: A[] = {2, 8, 2, 3, 1}, B[] = {1, 4, 2, 2, 2}
Output: 2
Approach: The given problem can be solved based on the following observations:
- It can be observed that the count of planes that can be stopped is the set of distinct times needed to land for each plane, as at the same time, only one plane can be destroyed.
- The time needed for a plane to land is A[i] / B[i] can be calculated using the formula: Time = Distance / Velocity
Follow the steps below to solve the problem:
- Initialize a Hash-Set, say S that stores the times needed for plane landing.
- Iterate over a range [0, N] using the variable i and perform the following tasks:
- Initialize a variable, say t as 1 if the value of A[i]%B[i] is greater than 0. Otherwise, update the variable t as 0.
- Add the value of A[i]/B[i] into the variable, say t.
- Add the value of t into the HashSet S.
- After performing the above steps, return the size of the HashSet as the resultant answer.
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 maximum number // of planes that can be stopped // from landing int maxPlanes( int A[], int B[], int N) { // Stores the times needed for // landing for each plane set< int > St; // Iterate over the arrays for ( int i = 0; i < N; i++) { // Stores the time needed for // landing of current plane int t = (A[i] % B[i] > 0) ? 1 : 0; // Update the value of t t += (A[i] / B[i]) + t; // Append the t in set St St.insert(t); } // Return the answer return St.size(); } // Driver Code int main() { int A[] = { 1, 3, 5, 4, 8 }; int B[] = { 1, 2, 2, 1, 2 }; int N = sizeof (A)/ sizeof (A[0]); cout << maxPlanes(A, B, N); return 0; } // This code is contributed by Dharanendra L V. |
Java
// Java program for the above approach import java.util.*; class GFG { // Function to find maximum number // of planes that can be stopped // from landing static int maxPlanes( int [] A, int [] B) { // Stores the times needed for // landing for each plane Set<Integer> St = new HashSet<>(); // Iterate over the arrays for ( int i = 0 ; i < A.length; i++) { // Stores the time needed for // landing of current plane int t = (A[i] % B[i] > 0 ) ? 1 : 0 ; // Update the value of t t += (A[i] / B[i]) + t; // Append the t in set St St.add(t); } // Return the answer return St.size(); } // Driver Code public static void main(String[] args) { int [] A = { 1 , 3 , 5 , 4 , 8 }; int [] B = { 1 , 2 , 2 , 1 , 2 }; System.out.println( maxPlanes(A, B)); } } |
Python3
# Python program for the above approach # Function to find maximum number # of planes that can be stopped # from landing def maxPlanes(A, B, N): # Stores the times needed for # landing for each plane St = set () # Iterate over the arrays for i in range (N): # Stores the time needed for # landing of current plane t = 1 if (A[i] % B[i] > 0 ) else 0 # Update the value of t t + = (A[i] / / B[i]) + t # Append the t in set St St.add(t) # Return the answer return len (St) # Driver Code A = [ 1 , 3 , 5 , 4 , 8 ] B = [ 1 , 2 , 2 , 1 , 2 ] N = len (A) print (maxPlanes(A, B, N)) # This code is contributed by shivanisinghss2110 |
C#
// C# program for the above approach using System; using System.Collections.Generic; public class GFG { // Function to find maximum number // of planes that can be stopped // from landing static int maxPlanes( int [] A, int [] B) { // Stores the times needed for // landing for each plane HashSet< int > St = new HashSet< int >(); // Iterate over the arrays for ( int i = 0; i < A.Length; i++) { // Stores the time needed for // landing of current plane int t = (A[i] % B[i] > 0) ? 1 : 0; // Update the value of t t += (A[i] / B[i]) + t; // Append the t in set St St.Add(t); } // Return the answer return St.Count; } // Driver code static public void Main (){ int [] A = { 1, 3, 5, 4, 8 }; int [] B = { 1, 2, 2, 1, 2 }; Console.WriteLine( maxPlanes(A, B)); } } // This code is contributed by Potta Lokesh |
Javascript
<script> // Function to find maximum number // of planes that can be stopped // from landing function maxPlanes(A, B) { // Stores the times needed for // landing for each plane let St = new Set(); // Iterate over the arrays for (let i = 0; i < A.length; i++) { // Stores the time needed for // landing of current plane let t = (A[i] % B[i] > 0) ? 1 : 0; // Update the value of t t += Math.floor(A[i] / B[i]) + t; // Append the t in set St St.add(t); } // Return the answer return St.size; } // Driver Code let A = [ 1, 3, 5, 4, 8 ]; let B = [ 1, 2, 2, 1, 2 ]; document.write( maxPlanes(A, B)); // This code is contributed by sanjoy_62. </script> |
Output:
3
Time Complexity: O(N*log(N))
Auxiliary Space: O(N)
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