Minimum broadcast range required by M towers to reach N houses

Given an array a containing positions of N houses, and an array b containing positions of M radio towers, each placed along a horizontal line, the task is to find the minimum broadcast range such that each radio tower reaches every house.

Examples:

Input: a[] = {1, 5, 11, 20}, b[] = {4, 8, 15}
Output: 5
Explanation:
The minimum range required is 5, since that would be required for the tower at position 15 to reach the house at position 20

Input: a[] = {12, 13, 11, 80}, b[] = {4, 6, 15, 60}
Output: 20
Explanation:
The minimum range required is 20, since that would be required for the tower at position 60 to reach the house at position 80

Approach: Traverse both the arrays until the broadcast range for the last house is calculated. For every house, compare its distance from its left and right towers respectively and consider the minimum. Compare this minimum value with the maximum obtained so far and store the maximum.



Note: The distance of the left tower from the first house is considered Integer.MIN_VALUE. If we reach the end of towers, the distance of all remaining houses from the respective right tower is considered Integer.MAX_VALUE.

Below code implements the above approach:

C++

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// CPP program to implement the above approach
#include<bits/stdc++.h>
using namespace std;
  
int minBroadcastRange(int houses[], int towers[],int n,int m)
    {
        // Initialize distance of left
        // tower from first house
        int leftTower = INT_MIN;
  
        // Initialize distance of right
        // tower from first house
        int rightTower = towers[0];
  
        // j: Index of houses[]
        // k: Index of towers[]
        int j = 0, k = 0;
  
        // Store the minimum required range
        int min_range = 0;
  
        while (j < n) {
  
            // If the house lies between
            // left and right towers
            if (houses[j] < rightTower) {
  
                int left = houses[j] - leftTower;
                int right = rightTower - houses[j];
  
                // Compare the distance between the
                // left and right nearest towers
                int local_max = left < right ? left : right;
  
                if (local_max > min_range)
  
                    // updating the maximum value
                    min_range = local_max;
                j++;
            }
            else {
  
                // updating the left tower
                leftTower = towers[k];
  
                if (k < m - 1) {
  
                    k++;
                    // updating the right tower
                    rightTower = towers[k];
                }
                else
                    // updating right tower
                    // to maximum value after
                    // reaching the end of Tower array
                    rightTower = INT_MAX;
            }
        }
        return min_range;
    }
  
    // Driver code
    int main()
    {
        int a[] = { 12, 13, 11, 80 };
        int b[] = { 4, 6, 15, 60 };
        int n = sizeof(a)/sizeof(a[0]);
        int m = sizeof(b)/sizeof(b[0]);
        int max = minBroadcastRange(a, b,n,m);
        cout<<max<<endl;
    }
  
// This code is contributed by Surendra_Gangwar

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Java

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// Java program to implement the above approach
  
import java.io.*;
  
class GFG {
  
    private static int minBroadcastRange(
        int[] houses, int[] towers)
    {
  
        // Store no of houses
        int n = houses.length;
  
        // Store no of towers
        int m = towers.length;
  
        // Initialize distance of left
        // tower from first house
        int leftTower = Integer.MIN_VALUE;
  
        // Initialize distance of right
        // tower from first house
        int rightTower = towers[0];
  
        // j: Index of houses[]
        // k: Index of towers[]
        int j = 0, k = 0;
  
        // Store the minimum required range
        int min_range = 0;
  
        while (j < n) {
  
            // If the house lies between
            // left and right towers
            if (houses[j] < rightTower) {
  
                int left = houses[j] - leftTower;
                int right = rightTower - houses[j];
  
                // Compare the distance between the
                // left and right nearest towers
                int local_max = left < right ? left : right;
  
                if (local_max > min_range)
  
                    // updating the maximum value
                    min_range = local_max;
                j++;
            }
            else {
  
                // updating the left tower
                leftTower = towers[k];
  
                if (k < m - 1) {
  
                    k++;
                    // updating the right tower
                    rightTower = towers[k];
                }
                else
                    // updating right tower
                    // to maximum value after
                    // reaching the end of Tower array
                    rightTower = Integer.MAX_VALUE;
            }
        }
        return min_range;
    }
  
    // Driver code
    public static void main(String[] args)
    {
        int[] a = { 12, 13, 11, 80 };
        int[] b = { 4, 6, 15, 60 };
        int max = minBroadcastRange(a, b);
        System.out.println(max);
    }
}

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Python3

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# Python 3 program to implement the above approach
import sys
  
def minBroadcastRange( houses, towers, n, m):
  
    # Initialize distance of left
    # tower from first house
    leftTower = -sys.maxsize - 1
  
    # Initialize distance of right
    # tower from first house
    rightTower = towers[0]
  
    # j: Index of houses[]
    # k: Index of towers[]
    j , k = 0 , 0
  
    # Store the minimum required range
    min_range = 0
  
    while (j < n):
  
        # If the house lies between
        # left and right towers
        if (houses[j] < rightTower):
  
            left = houses[j] - leftTower
            right = rightTower - houses[j]
  
            # Compare the distance between the
            # left and right nearest towers
            if left < right :
                local_max = left 
            else:
                local_max = right
  
            if (local_max > min_range):
  
                # updating the maximum value
                min_range = local_max
            j += 1 
          
        else:
  
            # updating the left tower
            leftTower = towers[k]
  
            if (k < m - 1) :
  
                k += 1 
  
                # updating the right tower
                rightTower = towers[k]
              
            else:
                # updating right tower
                # to maximum value after
                # reaching the end of Tower array
                rightTower = sys.maxsize
    return min_range
  
# Driver code
if __name__ == "__main__":
      
    a = [ 12, 13, 11, 80 ]
    b = [ 4, 6, 15, 60 ]
    n = len(a)
    m = len(b)
    max = minBroadcastRange(a, b,n,m)
    print(max)
  
# This code is contributed by chitranayal

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C#

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// C# program to implement the above approach
 using System;
  
class GFG {
   
    private static int minBroadcastRange(
        int[] houses, int[] towers)
    {
   
        // Store no of houses
        int n = houses.Length;
   
        // Store no of towers
        int m = towers.Length;
   
        // Initialize distance of left
        // tower from first house
        int leftTower = int.MinValue;
   
        // Initialize distance of right
        // tower from first house
        int rightTower = towers[0];
   
        // j: Index of houses[]
        // k: Index of towers[]
        int j = 0, k = 0;
   
        // Store the minimum required range
        int min_range = 0;
   
        while (j < n) {
   
            // If the house lies between
            // left and right towers
            if (houses[j] < rightTower) {
   
                int left = houses[j] - leftTower;
                int right = rightTower - houses[j];
   
                // Compare the distance between the
                // left and right nearest towers
                int local_max = left < right ? left : right;
   
                if (local_max > min_range)
   
                    // updating the maximum value
                    min_range = local_max;
                j++;
            }
            else {
   
                // updating the left tower
                leftTower = towers[k];
   
                if (k < m - 1) {
   
                    k++;
                    // updating the right tower
                    rightTower = towers[k];
                }
                else
                    // updating right tower
                    // to maximum value after
                    // reaching the end of Tower array
                    rightTower = int.MaxValue;
            }
        }
        return min_range;
    }
   
    // Driver code
    public static void Main(String[] args)
    {
        int[] a = { 12, 13, 11, 80 };
        int[] b = { 4, 6, 15, 60 };
        int max = minBroadcastRange(a, b);
        Console.WriteLine(max);
    }
}
  
// This code is contributed by PrinciRaj1992

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Output:

20

Time complexity: O(M + N)

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