Sort a 2D vector diagonally using Map Data Structure


Given a 2D vector mat[][] of integers. The task is to sort the elements of the vectors diagonally from top-left to bottom-right in increasing order.

Examples:

Input: mat[][] = 
{{9, 4, 2}, 
 {7, 4, 6},
 {2, 3, 3}}     
Output: 
3 4 2
3 4 6
2 7 9
Explanation:
There are 5 diagonals in this matrix:
1. {2} - No need to sort
2. {7, 3} - Sort - {3, 7}
3. {9, 4, 3} - Sort - {3, 4, 9}
4. {4, 6} - Already sorted
5. {2} - No need to sort



Input: mat[][] =  
{{ 4, 3, 2, 1 }, 
 { 3, 2, 1, 0 }, 
 { 2, 1, 1, 0 }, 
 { 0, 1, 2, 3 }}
Output: 
1 0 0 1 
1 2 1 2 
1 2 3 3 
0 2 3 4 

Approach:

  1. All elements in the same diagonal have the same index difference i – j where i is the row number and j is the column number. So we can use a map to store every diagonal at index i – j.
  2. Now we can sort every index of the map using the inbuilt function.
  3. Now in the original matrix, we can insert every diagonal of a matrix stored in map.
  4. Finally, we can print the Matrix.

Below is the implementation of the above approach:

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// C++ implementation to sort the
// diagonals of the matrix
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to sort the
// diagonal of the matrix
void SortDiagonal(int mat[4][4], 
                  int m, int n)
{
    // Map to store every diagonal 
    // in different indices here 
    // elements of same diagonal 
    // will be stored in same index
    unordered_map<int, vector<int> > mp;
  
    for (int i = 0; i < m; i++)
    {
        for (int j = 0; j < n; j++)
        {
            // Storing diagonal elements 
            // in map
            mp[i - j].push_back(mat[i][j]);
        }
    }
  
    // To sort each diagonal in 
    // ascending order
    for (int k = -(n - 1); k < m; k++)
    {
        sort(mp[k].begin(),
             mp[k].end());
    }
  
    // Loop to store every diagonal 
    // in ascending order
    for (int i = m - 1; i >= 0; i--)
    {
        for (int j = n - 1; j >= 0; j--)
        {
            mat[i][j] = mp[i - j].back();
            mp[i - j].pop_back();
        }
    }
  
    // Loop to print the matrix
    for (int i = 0; i < m; i++) {
        for (int j = 0; j < n; j++)
            cout << mat[i][j] << " ";
        cout << endl;
    }
}
  
// Driven Code
int main()
{
    int arr[4][4] = { { 4, 3, 2, 1 },
                    { 3, 2, 1, 0 },
                    { 2, 1, 1, 0 },
                    { 0, 1, 2, 3 } };
  
    // Sort the Diagonals
    SortDiagonal(arr, 4, 4);
  
    return 0;
}
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Output:
1 0 0 1 
1 2 1 2 
1 2 3 3 
0 2 3 4 

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