Minimum Numbers of cells that are connected with the smallest path between 3 given cells
Given coordinates of 3 cells (X1, Y1), (X2, Y2) and (X3, Y3) of a matrix. The task is to find the minimum path which connects all three of these cells and print the count of all the cells that are connected through this path.
Note: Only possible moves are up, down, left and right.
Examples:
Input: X1 = 0, Y1 = 0, X2 = 1, Y2 = 1, X3 = 2 and Y3 = 2
Output: 5
(0, 0), (1, 0), (1, 1), (1, 2), (2, 2) are the required cells.Input: X1 = 0, Y1 = 0, X2 = 2, Y2 = 0, X3 = 1 and Y3 = 1
Output: 4
Approach: First sort the cells from the one with minimum row number at first to one with maximum row number at last. Also, store minimum column number and maximum column number among these three cells in variable MinCol and MaxCol respectively.
After that, store row number of the middle cell(from sorted cells) in variable MidRow and mark all the cells of this MidRow from MinCol to MaxCol.
Now our final step will be to mark all the column number of 1st and 3rd cell till they reach MidRow.
Here, marking means we will store the required cells coordinate in a set. Thus, our answer will be size of this set.
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 minimum cells that are // connected via the minimum length path int Minimum_Cells(vector<pair<int, int> > v) { int col[3], i, j; for (i = 0; i < 3; i++) { int column_number = v[i].second; // Array to store column number // of the given cells col[i] = column_number; } sort(col, col + 3); // Sort cells in ascending // order of row number sort(v.begin(), v.end()); // Middle row number int MidRow = v[1].first; // Set pair to store required cells set<pair<int, int> > s; // Range of column number int Maxcol = col[2], MinCol = col[0]; // Store all cells of middle row // within column number range for (i = MinCol; i <= Maxcol; i++) { s.insert({ MidRow, i }); } for (i = 0; i < 3; i++) { if (v[i].first == MidRow) continue; // Final step to store all the column number // of 1st and 3rd cell upto MidRow for (j = min(v[i].first, MidRow); j <= max(v[i].first, MidRow); j++) { s.insert({ j, v[i].second }); } } return s.size(); } // Driver Function int main() { // vector pair to store X, Y, Z vector<pair<int, int> > v = { { 0, 0 }, { 1, 1 }, { 2, 2 } }; cout << Minimum_Cells(v); return 0; } |
chevron_right
filter_none
Python3
# Python3 implementation of the approach # Function to return the minimum cells that # are connected via the minimum length path def Minimum_Cells(v) : col = [0] * 3 for i in range(3) : column_number = v[i][1] # Array to store column number # of the given cells col[i] = column_number col.sort() # Sort cells in ascending order # of row number v.sort() # Middle row number MidRow = v[1][0] # Set pair to store required cells s = set() # Range of column number Maxcol = col[2] MinCol = col[0] # Store all cells of middle row # within column number range for i in range(MinCol, int(Maxcol) + 1) : s.add((MidRow, i)) for i in range(3) : if (v[i][0] == MidRow) : continue; # Final step to store all the column # number of 1st and 3rd cell upto MidRow for j in range(min(v[i][0], MidRow), max(v[i][0], MidRow) + 1) : s.add((j, v[i][1])); return len(s) # Driver Code if __name__ == "__main__" : # vector pair to store X, Y, Z v = [(0, 0 ), ( 1, 1 ), ( 2, 2 )] print(Minimum_Cells(v)) # This code is contributed by Ryuga |
chevron_right
filter_none
Output:
5
Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.
Recommended Posts:
- Count of cells in a matrix whose adjacent cells's sum is prime Number
- Min number of moves to traverse entire Matrix through connected cells with equal values
- Check if cells numbered 1 to K in a grid can be connected after removal of atmost one blocked cell
- Count of cells in a matrix which give a Fibonacci number when the count of adjacent cells is added
- Find whether there is path between two cells in matrix
- Minimum cells to be flipped to get a 2*2 submatrix with equal elements
- Minimum cells traversed to reach corner where every cell represents jumps
- Minimum cells required to reach destination with jumps equal to cell values
- Find safe cells in a matrix
- Unique cells in a binary matrix
- Find the number of cells in the table contains X
- Number of cells in matrix which are equidistant from given two points
- Number of cells in a matrix that satisfy the given condition
- Print cells with same rectangular sums in a matrix
- Shortest distance between two cells in a matrix or grid
- Find Number of Even cells in a Zero Matrix after Q queries
- Total number of unit cells covered by all given Rectangles
- Total number of cells covered in a matrix after D days
- Number of cells in the right and left diagonals passing through (x, y) in a matrix
- Number of cells a queen can move with obstacles on the chessborad
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.
Improved By : AnkitRai01
