Given a 2D array arr[][], representing width of bricks of the same height present on a wall, the task is to find the minimum number of bricks that can be intersected by drawing a straight line from the top to the bottom of the wall.
Note: A line is said to intersect a brick if it passes through the brick and is non-intersecting if it is touching a brick’s boundary.
Examples:
Input: arr[][] = {{1, 2, 2, 1}, {3, 1, 2}, {1, 3, 2}, {2, 4}, {3, 1, 2}, {1, 3, 1, 1}}
Output: 2
Explanation: Considering the top left corner of the 2D array as the origin, the line is drawn at the coordinate x = 4 on the x-axis, such that it crosses the bricks on the 1st and 4th level, resulting in the minimum number of bricks crossed.Input: arr[][] = {{1, 1, 1}}
Output: 0
Explanation: The line can be drawn at x = 1 or x = 2 coordinate on the x-axis such that it does not cross any brick resulting in the minimum number of bricks crossed.
Naive Approach: The simplest approach is to consider straight lines that can be drawn on every possible coordinate on the x-axis, along the width of the wall, considering x = 0 at the top left corner of the wall. Then, calculate the number of bricks inserted in each case and print the minimum count obtained.
Time Complexity: O(N * M) where N is the total number of bricks and M is the total width of the wall
Auxiliary Space: O(1)
Approach: To optimize the above approach, the idea is to store the number of bricks ending at a certain width on the x-axis in a hashmap, and then find the line where the most number of bricks end. After getting this count, subtract it from the total height of the wall to get the minimum number of bricks crossed.
Follow the steps below to solve the problem:
- Initialize a hashmap, M to store the number of bricks ending at a certain width on the x-axis.
-
Traverse the array, arr using the variable i to store row index
- Initialize a variable, width as 0 to store the ending position.
- Store the size of the current row in a variable X.
-
Iterate in the range [0, X-2] using the variable j
- Increment the value of width by arr[i][j] and increment the value of width in M by 1.
- Also, keep track of the most number of bricks ending at a certain width and store it in a variable, res.
- Subtract the value of res from the overall height of the wall and store it in a variable, ans.
- Print the value of ans as the result.
Below is the implementation of the above approach:
// C++ program for the above approach #include <bits/stdc++.h> using namespace std;
// Function to find a line across a wall such // that it intersects minimum number of bricks void leastBricks(vector<vector< int > > wall)
{ // Declare a hashmap
unordered_map< int , int > map;
// Store the maximum number of
// brick ending a point on x-axis
int res = 0;
// Iterate over all the rows
for (vector< int > list : wall) {
// Initialize width as 0
int width = 0;
// Iterate over individual bricks
for ( int i = 0; i < list.size() - 1; i++) {
// Add the width of the current
// brick to the total width
width += list[i];
// Increment number of bricks
// ending at this width position
map[width]++;
// Update the variable, res
res = max(res, map[width]);
}
}
// Print the answer
cout << wall.size() - res;
} // Driver Code int main()
{ // Given Input
vector<vector< int > > arr{
{ 1, 2, 2, 1 }, { 3, 1, 2 },
{ 1, 3, 2 }, { 2, 4 },
{ 3, 1, 2 }, { 1, 3, 1, 1 }
};
// Function Call
leastBricks(arr);
return 0;
} |
// Java program for the above approach import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
public class GFG
{ // Function to find a line across a wall such
// that it intersects minimum number of bricks
static void leastBricks(ArrayList<ArrayList<Integer> > wall)
{
// Declare a hashmap
HashMap<Integer, Integer> map = new HashMap<>();
// Store the maximum number of
// brick ending a point on x-axis
int res = 0 ;
// Iterate over all the rows
for (ArrayList<Integer> list : wall) {
// Initialize width as 0
int width = 0 ;
// Iterate over individual bricks
for ( int i = 0 ; i < list.size() - 1 ; i++) {
// Add the width of the current
// brick to the total width
width += list.get(i);
// Increment number of bricks
// ending at this width position
map.put(width,
map.getOrDefault(width, 0 ) + 1 );
// Update the variable, res
res = Math.max(res,
map.getOrDefault(width, 0 ));
}
}
// Print the answer
System.out.println(wall.size() - res);
}
// Driver code
public static void main(String[] args)
{
// Given Input
ArrayList<ArrayList<Integer> > arr
= new ArrayList<>();
arr.add( new ArrayList<>(Arrays.asList( 1 , 2 , 2 , 1 )));
arr.add( new ArrayList<>(Arrays.asList( 3 , 1 , 2 )));
arr.add( new ArrayList<>(Arrays.asList( 1 , 3 , 2 )));
arr.add( new ArrayList<>(Arrays.asList( 2 , 4 )));
arr.add( new ArrayList<>(Arrays.asList( 3 , 1 , 2 )));
arr.add( new ArrayList<>(Arrays.asList( 1 , 3 , 1 , 1 )));
// Function Call
leastBricks(arr);
}
} // This code is contributed by abhinavjain194 |
# Python 3 program for the above approach from collections import defaultdict
# Function to find a line across a wall such # that it intersects minimum number of bricks def leastBricks(wall):
# Declare a hashmap
map = defaultdict( int )
# Store the maximum number of
# brick ending a point on x-axis
res = 0
# Iterate over all the rows
for list in wall:
# Initialize width as 0
width = 0
# Iterate over individual bricks
for i in range ( len ( list ) - 1 ):
# Add the width of the current
# brick to the total width
width + = list [i]
# Increment number of bricks
# ending at this width position
map [width] + = 1
# Update the variable, res
res = max (res, map [width])
# Print the answer
print ( len (wall) - res)
# Driver Code if __name__ = = "__main__" :
# Given Input
arr = [
[ 1 , 2 , 2 , 1 ], [ 3 , 1 , 2 ],
[ 1 , 3 , 2 ], [ 2 , 4 ],
[ 3 , 1 , 2 ], [ 1 , 3 , 1 , 1 ]
]
# Function Call
leastBricks(arr)
# This code is contributed by ukasp.
|
// C# program for the above approach using System;
using System.Collections.Generic;
class GFG{
// Function to find a line across a wall such // that it intersects minimum number of bricks static void leastBricks(List<List< int >> wall)
{ // Declare a hashmap
Dictionary< int ,
int > map = new Dictionary< int ,
int >();
// Store the maximum number of
// brick ending a point on x-axis
int res = 0;
// Iterate over all the rows
foreach (List< int > subList in wall)
{
// Initialize width as 0
int width = 0;
for ( int i = 0; i < subList.Count - 1; i++)
{
// Add the width of the current
// brick to the total width
width += subList[i];
// Increment number of bricks
// ending at this width position
if (map.ContainsKey(width))
map[width]++;
else
map.Add(width, 1);
// Update the variable, res
res = Math.Max(res, map[width]);
}
}
// Print the answer
Console.Write(wall.Count-res);
} // Driver Code public static void Main()
{ // Given Input
List<List< int >> myList = new List<List< int >>();
myList.Add( new List< int >{ 1, 2, 2, 1 });
myList.Add( new List< int >{ 3, 1, 2 });
myList.Add( new List< int >{ 1, 3, 2 });
myList.Add( new List< int >{ 2, 4 });
myList.Add( new List< int >{ 3, 1, 2 });
myList.Add( new List< int >{ 1, 3, 1, 1 });
// Function Call
leastBricks(myList);
} } // This code is contributed by bgangwar59 |
<script> // JavaScript program for the above approach // Function to find a line across a wall such // that it intersects minimum number of bricks function leastBricks(wall) {
// Declare a hashmap
let map = new Map();
// Store the maximum number of
// brick ending a point on x-axis
let res = 0;
// Iterate over all the rows
for (let list of wall) {
// Initialize width as 0
let width = 0;
// Iterate over individual bricks
for (let i = 0; i < list.length - 1; i++) {
// Add the width of the current
// brick to the total width
width += list[i];
// Increment number of bricks
// ending at this width position
if (map.has(width)) {
map.set(width, map.get(width) + 1);
} else {
map.set(width, 1)
}
// Update the variable, res
res = Math.max(res, map.get(width));
}
}
// Print the answer
document.write(wall.length - res);
} // Driver Code // Given Input let arr = [ [1, 2, 2, 1], [3, 1, 2],
[1, 3, 2], [2, 4],
[3, 1, 2], [1, 3, 1, 1]
]; // Function Call leastBricks(arr); </script> |
2
Time Complexity: O(N) where N is the total number of bricks on the wall
Auxiliary Space: O(M) where M is the total width of the wall