Sort a 2D vector diagonally

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

Examples:

Input: arr[][] = { { 10, 2, 3 }, { 4, 5, 6 }, {7, 8, 9 } }
Output:
10 2 0
4 9 0
0 0 5



Input: arr[][] = { { 10, 2, 43 }, { 40, 5, 16 }, { 71, 8, 29 }, {1, 100, 5} }
Output:
29 2 0
8 10 0
71 5 5
0 0 0

Approach:
Observations:

The above images shows the difference between the column index and row index at each cell. The cells having same difference from top-left to bottom-down cell forms a diagonal.
Below are the steps to sort diagonal in decreasing order:

  1. Store the diagonal element with positive difference in one Array of Vectors(say Pos[]) such that elements at the cell having difference(say a) is stored at index a of Pos[] array.
  2. Store the diagonal element with negative difference in another Array of Vectors(say Neg[]) such that elements at the cell having difference(say -b) is stored at index abs(-b) = b of Neg[] array.
  3. Sort both the Array of Vectors increasing order.
  4. Traverse the given 2D vector and updated the value at current cell with value stored in Pos[] and Neg[] array.
    • If difference between column and row index(say d) is positive, then updated the value from Pos[d] array and remove the last elment as:
      d = i - j
      arr[i][j] = Pos[d][Pos.size()-1]
      Pos[d].pop_back()
      
    • If difference between column and row index(say d) is negative, then updated the value from Neg[d] array and remove the last element as:
      d = j - i
      arr[i][j] = Neg[d][Neg.size()-1]
      Neg[d].pop_back()
      

Below is the implementation of the above approach:

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// C++ program to sort the 2D vector
// diagonally in decreasing order
#include "bits/stdc++.h"
using namespace std;
  
// Function that sort the elements
// of 2D vector
void diagonalSort(vector<vector<int> >& mat)
{
  
    // Calculate the rows and column
    int row = mat.size();
    int col = mat[0].size();
  
    // Array of vectors to store the
    // diagonal elements
    vector<int> Neg[row];
    vector<int> Pos[col];
  
    // Traverse the 2D vector and put
    // element in Array of vectors at
    // index difference between indexes
    for (int i = 0; i < row; i++) {
        for (int j = 0; j < col; j++) {
  
            // If diff is negative, then
            // push element to Neg[]
            if (j < i) {
                Neg[i - j].push_back(mat[i][j]);
            }
  
            // If diff is positive, then
            // push element to Pos[]
            else if (j > i) {
                Pos[j - i].push_back(mat[i][j]);
            }
  
            // If diff is 0, then push
            // element to Pos[0]
            else {
                Pos[0].push_back(mat[i][j]);
            }
        }
    }
  
    // Sort the Array of vectors
    for (int i = 0; i < row; i++) {
        sort(Neg[i].begin(), Neg[i].end());
    }
    for (int i = 0; i < col; i++) {
        sort(Pos[i].begin(), Pos[i].end());
    }
  
    // Update the value to arr[][]
    // from the sorted Array of vectors
    for (int i = 0; i < row; i++) {
        for (int j = 0; j < col; j++) {
  
            // If diff is positive
            if (j < i) {
                int d = i - j;
                int l = Neg[d].size() - 1;
                mat[i][j] = Neg[d][l - 1];
                Neg[d].pop_back();
            }
  
            // If diff is negative
            else if (j > i) {
                int d = j - i;
                int l = Pos[d].size() - 1;
                mat[i][j] = Pos[d][l - 1];
                Pos[d].pop_back();
            }
  
            // If diff is 0
            else {
                int l = Pos[0].size();
                mat[i][j] = Pos[0][l - 1];
                Pos[0].pop_back();
            }
        }
    }
}
  
// Function to print element
void printElement(vector<vector<int> >& arr)
{
  
    // Traverse the 2D vector
    for (int i = 0; i < arr.size(); i++) {
        for (int j = 0; j < arr[0].size(); j++) {
            cout << arr[i][j] << ' ';
        }
        cout << endl;
    }
}
  
// Driver Code
int main()
{
    vector<vector<int> > arr = { { 10, 2, 3 },
                                 { 4, 5, 6 },
                                 { 7, 8, 9 } };
    diagonalSort(arr);
  
    // Function call to print elements
    printElement(arr);
}

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Output:

10 2 0 
4 9 0 
0 0 5

Time Complexity: O(N2)

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