Move matrix elements in given direction and add elements with same value

Given a matrix m[ ][ ] of size n x n consisting of integers and given a character ‘x’ indicating the direction. Value of ‘x’ can be ‘u’, ‘d’, ‘l’, ‘r’ indicating Up, Down, Left, Right correspondingly. The task is to move the element to given direction such that the consecutive elements having same value are added into single value and shift the rest element. Also, shift the element if the next element in given direction is 0.
For example :
Consider x = ‘l’ and matrix m[][],
32 3 3
0 0 1
10 10 8

After adding 3 in first row, 10 in third row and moving 1 in second row,
Matrix will become
32 6 0
1 0 0
20 8 0

Examples :

Input : x = 'l'
m[][] = { { 32, 3, 3, 3, 3 },
          { 0, 0, 1, 0, 0 },
          { 10, 10, 8, 1, 2},
          { 0, 0, 0, 0, 1},
          { 4, 5, 6, 7, 8 } }
Output :
32 6 6 0 0
1 0 0 0 0
20 8 1 2 0
1 0 0 0 0 0
4 5 6 7 8

Input : x = 'u'
m[][] = { { 10, 3, 32 },
        { 10, 0, 96 },
        { 5, 32, 96 } }
Output :
20 3 32
5 32 192
0 0 0

Approach : The idea is to traverse each row or column (depending on given direction) from side x of row or column towards x’ (opposite of x). For example, if given value of x is ‘l’ (left) then start scanning each row from left side to right. While traversing, store row or column element in temporary 1-D array (say temp[]) by skipping elements having value 0 and sum of consecutive element if they have equal value. After that, start copying the temporary array temp[0..k] to the current row or column from the x side (of row or column) to x’ (opposite of x) and fill reset of the element by 0.

Let, x = ‘l’ i.e move towards left. So, start coping each row from left most index to right most index of the row and store in temporary array with processing of ignoring 0s and adding two consecutive element into one if they have same value. Below is the illustration for row 1,

Now, for each, copy temporary array to current row from left most index to right most index. Below is illustration for row 1,

Below is the implementation of this approach :

C++

// CPP code to move matrix elements 
// in given direction with add 
// element with same value 
#include <bits/stdc++.h> 
using namespace std; 
  
#define MAX 50 
  
// Function to shift the matrix 
// in the given direction 
void moveMatrix(char d[], int n, 
                int a[MAX][MAX]) 
{ 
  
    // For right shift move. 
    if (d[0] == 'r') { 
  
        // for each row from 
        // top to bottom 
        for (int i = 0; i < n; i++) { 
            vector<int> v, w; 
            int j; 
  
            // for each element of 
            // row from right to left 
            for (j = n - 1; j >= 0; j--) { 
                // if not 0 
                if (a[i][j]) 
                    v.push_back(a[i][j]); 
            } 
  
            // for each temporary array 
            for (j = 0; j < v.size(); j++) { 
                // if two element have same 
                // value at consecutive position. 
                if (j < v.size() - 1 && v[j] == v[j + 1]) { 
                    // insert only one element 
                    // as sum of two same element. 
                    w.push_back(2 * v[j]); 
                    j++; 
                } 
                else
                    w.push_back(v[j]); 
            } 
  
            // filling the each row element to 0. 
            for (j = 0; j < n; j++) 
                a[i][j] = 0; 
  
            j = n - 1; 
  
            // Copying the temporary 
            // array to the current row. 
            for (auto it = w.begin(); 
                 it != w.end(); it++) 
                a[i][j--] = *it; 
        } 
    } 
  
    // for left shift move 
    else if (d[0] == 'l') { 
  
        // for each row 
        for (int i = 0; i < n; i++) { 
            vector<int> v, w; 
            int j; 
  
            // for each element of the 
            // row from left to right 
            for (j = 0; j < n; j++) { 
                // if not 0 
                if (a[i][j]) 
                    v.push_back(a[i][j]); 
            } 
  
            // for each temporary array 
            for (j = 0; j < v.size(); j++) { 
                // if two element have same 
                // value at consecutive position. 
                if (j < v.size() - 1 && v[j] == v[j + 1]) { 
                    // insert only one element 
                    // as sum of two same element. 
                    w.push_back(2 * v[j]); 
                    j++; 
                } 
                else
                    w.push_back(v[j]); 
            } 
  
            // filling the each row element to 0. 
            for (j = 0; j < n; j++) 
                a[i][j] = 0; 
  
            j = 0; 
  
            for (auto it = w.begin(); 
                 it != w.end(); it++) 
                a[i][j++] = *it; 
        } 
    } 
  
    // for down shift move. 
    else if (d[0] == 'd') { 
        // for each column 
        for (int i = 0; i < n; i++) { 
            vector<int> v, w; 
            int j; 
  
            // for each element of 
            // column from bottom to top 
            for (j = n - 1; j >= 0; j--) { 
                // if not 0 
                if (a[j][i]) 
                    v.push_back(a[j][i]); 
            } 
  
            // for each temporary array 
            for (j = 0; j < v.size(); j++) { 
  
                // if two element have same 
                // value at consecutive position. 
                if (j < v.size() - 1 && v[j] == v[j + 1]) { 
                    // insert only one element 
                    // as sum of two same element. 
                    w.push_back(2 * v[j]); 
                    j++; 
                } 
                else
                    w.push_back(v[j]); 
            } 
  
            // filling the each column element to 0. 
            for (j = 0; j < n; j++) 
                a[j][i] = 0; 
  
            j = n - 1; 
  
            // Copying the temporary array 
            // to the current column 
            for (auto it = w.begin(); 
                 it != w.end(); it++) 
                a[j--][i] = *it; 
        } 
    } 
  
    // for up shift move 
    else if (d[0] == 'u') { 
        // for each column 
        for (int i = 0; i < n; i++) { 
            vector<int> v, w; 
            int j; 
  
            // for each element of column 
            // from top to bottom 
            for (j = 0; j < n; j++) { 
                // if not 0 
                if (a[j][i]) 
                    v.push_back(a[j][i]); 
            } 
  
            // for each temporary array 
            for (j = 0; j < v.size(); j++) { 
                // if two element have same 
                // value at consecutive position. 
                if (j < v.size() - 1 && v[j] == v[j + 1]) { 
                    // insert only one element 
                    // as sum of two same element. 
                    w.push_back(2 * v[j]); 
                    j++; 
                } 
                else
                    w.push_back(v[j]); 
            } 
  
            // filling the each column element to 0. 
            for (j = 0; j < n; j++) 
                a[j][i] = 0; 
  
            j = 0; 
  
            // Copying the temporary array 
            // to the current column 
            for (auto it = w.begin(); 
                 it != w.end(); it++) 
                a[j++][i] = *it; 
        } 
    } 
} 
  
// Driven Program 
int main() 
{ 
    char d[2] = "l"; 
    int n = 5; 
    int a[MAX][MAX] = { { 32, 3, 3, 3, 3 }, 
                        { 0, 0, 1, 0, 0 }, 
                        { 10, 10, 8, 1, 2 }, 
                        { 0, 0, 0, 0, 1 }, 
                        { 4, 5, 6, 7, 8 } }; 
  
    moveMatrix(d, n, a); 
  
    // Printing the final array 
    for (int i = 0; i < n; i++) { 
        for (int j = 0; j < n; j++) 
            cout << a[i][j] << " "; 
  
        cout << endl; 
    } 
  
    return 0; 
} 

Java

// Java code to move matrix 
// elements in given direction 
// with add element with same value 
import java.io.*; 
import java.util.*; 
  
class GFG { 
    // Function to shift the matrix 
    // in the given direction 
    static void moveMatrix(char d, 
                           int n, 
                           int a[][]) 
    { 
  
        // For right shift move. 
        if (d == 'r') { 
  
            // for each row from 
            // top to bottom 
            for (int i = 0; i < n; i++) { 
                ArrayList<Integer> v = new ArrayList<Integer>(); 
                ArrayList<Integer> w = new ArrayList<Integer>(); 
                int j; 
  
                // for each element of 
                // row from right to left 
                for (j = n - 1; j >= 0; j--) { 
                    // if not 0 
                    if (a[i][j] != 0) 
                        v.add(a[i][j]); 
                } 
  
                // for each temporary array 
                for (j = 0; j < v.size(); j++) { 
                    // if two element have 
                    // same value at 
                    // consecutive position. 
                    if (j < v.size() - 1 && v.get(j) == v.get(j + 1)) { 
                        // insert only one element 
                        // as sum of two same element. 
                        w.add(2 * v.get(j)); 
                        j++; 
                    } 
                    else
                        w.add(v.get(j)); 
                } 
  
                // filling the each 
                // row element to 0. 
                for (j = 0; j < n; j++) 
                    a[i][j] = 0; 
  
                j = n - 1; 
  
                // Copying the temporary 
                // array to the current row. 
                for (int it = 0; it < w.size(); it++) 
                    a[i][j--] = w.get(it); 
            } 
        } 
  
        // for left shift move 
        else if (d == 'l') { 
  
            // for each row 
            for (int i = 0; i < n; i++) { 
                ArrayList<Integer> v = new ArrayList<Integer>(); 
                ArrayList<Integer> w = new ArrayList<Integer>(); 
                int j; 
  
                // for each element of the 
                // row from left to right 
                for (j = 0; j < n; j++) { 
                    // if not 0 
                    if (a[i][j] != 0) 
                        v.add(a[i][j]); 
                } 
  
                // for each temporary array 
                for (j = 0; j < v.size(); j++) { 
                    // if two element have 
                    // same value at 
                    // consecutive position. 
                    if (j < v.size() - 1 && v.get(j) == v.get(j + 1)) { 
                        // insert only one 
                        // element as sum 
                        // of two same element. 
                        w.add(2 * v.get(j)); 
                        j++; 
                    } 
                    else
                        w.add(v.get(j)); 
                } 
  
                // filling the each 
                // row element to 0. 
                for (j = 0; j < n; j++) 
                    a[i][j] = 0; 
  
                j = 0; 
  
                for (int it = 0; it < w.size(); it++) 
                    a[i][j++] = w.get(it); 
            } 
        } 
  
        // for down shift move. 
        else if (d == 'd') { 
            // for each column 
            for (int i = 0; i < n; i++) { 
                ArrayList<Integer> v = new ArrayList<Integer>(); 
                ArrayList<Integer> w = new ArrayList<Integer>(); 
                int j; 
  
                // for each element of 
                // column from bottom to top 
                for (j = n - 1; j >= 0; j--) { 
                    // if not 0 
                    if (a[j][i] != 0) 
                        v.add(a[j][i]); 
                } 
  
                // for each temporary array 
                for (j = 0; j < v.size(); j++) { 
  
                    // if two element have 
                    // same value at consecutive 
                    // position. 
                    if (j < v.size() - 1 && v.get(j) == v.get(j + 1)) { 
                        // insert only one element 
                        // as sum of two same element. 
                        w.add(2 * v.get(j)); 
                        j++; 
                    } 
                    else
                        w.add(v.get(j)); 
                } 
  
                // filling the each 
                // column element to 0. 
                for (j = 0; j < n; j++) 
                    a[j][i] = 0; 
  
                j = n - 1; 
  
                // Copying the temporary array 
                // to the current column 
                for (int it = 0; it < w.size(); it++) 
                    a[j--][i] = w.get(it); 
            } 
        } 
  
        // for up shift move 
        else if (d == 'u') { 
            // for each column 
            for (int i = 0; i < n; i++) { 
                ArrayList<Integer> v = new ArrayList<Integer>(); 
                ArrayList<Integer> w = new ArrayList<Integer>(); 
                int j; 
  
                // for each element of column 
                // from top to bottom 
                for (j = 0; j < n; j++) { 
                    // if not 0 
                    if (a[j][i] != 0) 
                        v.add(a[j][i]); 
                } 
  
                // for each temporary array 
                for (j = 0; j < v.size(); j++) { 
                    // if two element have 
                    // same value at 
                    // consecutive position. 
                    if (j < v.size() - 1 && v.get(j) == v.get(j + 1)) { 
                        // insert only one element 
                        // as sum of two same element. 
                        w.add(2 * v.get(j)); 
                        j++; 
                    } 
                    else
                        w.add(v.get(j)); 
                } 
  
                // filling the each 
                // column element to 0. 
                for (j = 0; j < n; j++) 
                    a[j][i] = 0; 
  
                j = 0; 
  
                // Copying the temporary 
                // array to the current 
                // column 
                for (int it = 0; it < w.size(); it++) 
                    a[j++][i] = w.get(it); 
            } 
        } 
    } 
  
    // Driver Code 
    public static void main(String args[]) 
    { 
        char d = 'l'; 
        int n = 5; 
        int a[][] = { { 32, 3, 3, 3, 3 }, 
                      { 0, 0, 1, 0, 0 }, 
                      { 10, 10, 8, 1, 2 }, 
                      { 0, 0, 0, 0, 1 }, 
                      { 4, 5, 6, 7, 8 } }; 
  
        moveMatrix(d, n, a); 
  
        // Printing the 
        // final array 
        for (int i = 0; i < n; i++) { 
            for (int j = 0; j < n; j++) 
                System.out.print(a[i][j] + " "); 
  
            System.out.println(); 
        } 
    } 
} 
  
// This code is contributed by 
// Manish Shaw(manishshaw1) 

C#

// C# code to move matrix elements 
// in given direction with add 
// element with same value 
using System; 
using System.Collections.Generic; 
  
class GFG { 
    // Function to shift the matrix 
    // in the given direction 
    static void moveMatrix(char d, int n, 
                           int[, ] a) 
    { 
  
        // For right shift move. 
        if (d == 'r') { 
  
            // for each row from 
            // top to bottom 
            for (int i = 0; i < n; i++) { 
                List<int> v = new List<int>(); 
                List<int> w = new List<int>(); 
                int j; 
  
                // for each element of 
                // row from right to left 
                for (j = n - 1; j >= 0; j--) { 
                    // if not 0 
                    if (a[i, j] != 0) 
                        v.Add(a[i, j]); 
                } 
  
                // for each temporary array 
                for (j = 0; j < v.Count; j++) { 
                    // if two element have 
                    // same value at 
                    // consecutive position. 
                    if (j < v.Count - 1 && v[j] == v[j + 1]) { 
                        // insert only one element 
                        // as sum of two same element. 
                        w.Add(2 * v[j]); 
                        j++; 
                    } 
                    else
                        w.Add(v[j]); 
                } 
  
                // filling the each 
                // row element to 0. 
                for (j = 0; j < n; j++) 
                    a[i, j] = 0; 
  
                j = n - 1; 
  
                // Copying the temporary 
                // array to the current row. 
                for (int it = 0; it < w.Count; it++) 
                    a[i, j--] = w[it]; 
            } 
        } 
  
        // for left shift move 
        else if (d == 'l') { 
  
            // for each row 
            for (int i = 0; i < n; i++) { 
                List<int> v = new List<int>(); 
                List<int> w = new List<int>(); 
                int j; 
  
                // for each element of the 
                // row from left to right 
                for (j = 0; j < n; j++) { 
                    // if not 0 
                    if (a[i, j] != 0) 
                        v.Add(a[i, j]); 
                } 
  
                // for each temporary array 
                for (j = 0; j < v.Count; j++) { 
                    // if two element have 
                    // same value at 
                    // consecutive position. 
                    if (j < v.Count - 1 && v[j] == v[j + 1]) { 
                        // insert only one element 
                        // as sum of two same element. 
                        w.Add(2 * v[j]); 
                        j++; 
                    } 
                    else
                        w.Add(v[j]); 
                } 
  
                // filling the each 
                // row element to 0. 
                for (j = 0; j < n; j++) 
                    a[i, j] = 0; 
  
                j = 0; 
  
                for (int it = 0; it < w.Count; it++) 
                    a[i, j++] = w[it]; 
            } 
        } 
  
        // for down shift move. 
        else if (d == 'd') { 
            // for each column 
            for (int i = 0; i < n; i++) { 
                List<int> v = new List<int>(); 
                List<int> w = new List<int>(); 
                int j; 
  
                // for each element of 
                // column from bottom to top 
                for (j = n - 1; j >= 0; j--) { 
                    // if not 0 
                    if (a[j, i] != 0) 
                        v.Add(a[j, i]); 
                } 
  
                // for each temporary array 
                for (j = 0; j < v.Count; j++) { 
  
                    // if two element have same 
                    // value at consecutive position. 
                    if (j < v.Count - 1 && v[j] == v[j + 1]) { 
                        // insert only one element 
                        // as sum of two same element. 
                        w.Add(2 * v[j]); 
                        j++; 
                    } 
                    else
                        w.Add(v[j]); 
                } 
  
                // filling the each 
                // column element to 0. 
                for (j = 0; j < n; j++) 
                    a[j, i] = 0; 
  
                j = n - 1; 
  
                // Copying the temporary array 
                // to the current column 
                for (int it = 0; it < w.Count; it++) 
                    a[j--, i] = w[it]; 
            } 
        } 
  
        // for up shift move 
        else if (d == 'u') { 
            // for each column 
            for (int i = 0; i < n; i++) { 
                List<int> v = new List<int>(); 
                List<int> w = new List<int>(); 
                int j; 
  
                // for each element of column 
                // from top to bottom 
                for (j = 0; j < n; j++) { 
                    // if not 0 
                    if (a[j, i] != 0) 
                        v.Add(a[j, i]); 
                } 
  
                // for each temporary array 
                for (j = 0; j < v.Count; j++) { 
                    // if two element have same 
                    // value at consecutive position. 
                    if (j < v.Count - 1 && v[j] == v[j + 1]) { 
                        // insert only one element 
                        // as sum of two same element. 
                        w.Add(2 * v[j]); 
                        j++; 
                    } 
                    else
                        w.Add(v[j]); 
                } 
  
                // filling the each 
                // column element to 0. 
                for (j = 0; j < n; j++) 
                    a[j, i] = 0; 
  
                j = 0; 
  
                // Copying the temporary array 
                // to the current column 
  
                for (int it = 0; it < w.Count; it++) 
                    a[j++, i] = w[it]; 
            } 
        } 
    } 
  
    // Driven Code 
    static void Main() 
    { 
        char d = 'l'; 
        int n = 5; 
        int[, ] a = new int[, ] { { 32, 3, 3, 3, 3 }, 
                                  { 0, 0, 1, 0, 0 }, 
                                  { 10, 10, 8, 1, 2 }, 
                                  { 0, 0, 0, 0, 1 }, 
                                  { 4, 5, 6, 7, 8 } }; 
  
        moveMatrix(d, n, a); 
  
        // Printing the final array 
        for (int i = 0; i < n; i++) { 
            for (int j = 0; j < n; j++) 
                Console.Write(a[i, j] + " "); 
  
            Console.WriteLine(); 
        } 
    } 
} 
// This code is contributed by 
// Manish Shaw(manishshaw1) 

PHP

<?php 
// PHP code to move matrix  
// elements in given  
// direction with add element 
// with same value 
$MAX = 50; 
  
// Function to shift the matrix 
// in the given direction 
function moveMatrix($d, $n, &$a) 
{  
    global $MAX; 
      
    // For right shift move. 
    if ($d[0] == 'r')  
    { 
          
        // for each row from  
        // top to bottom 
        for ($i = 0; $i < $n; $i++)  
        { 
            $v = array(); 
            $w = array(); 
            $j = 0; 
  
            // for each element of  
            // row from right to left 
            for ($j = $n - 1; $j >= 0; $j--)  
            { 
                // if not 0 
                if ($a[$i][$j]) 
                    array_push($v, $a[$i][$j]); 
            } 
  
            // for each temporary array 
            for ($j = 0; $j < count($v); $j++)  
            { 
                // if two element have same 
                // value at consecutive position. 
                if ($j < count($v) - 1 &&  
                    $v[$j] == $v[$j + 1])  
                { 
                    // insert only one element  
                    // as sum of two same element. 
                    array_push($w, 2 * $v[$j]); 
                    $j++; 
                } 
                else
                    array_push($w, $v[$j]); 
            } 
  
            // filling the each  
            // row element to 0. 
            for ($j = 0; $j < $n; $j++) 
                $a[$i][$j] = 0; 
  
            $j = $n - 1; 
  
            // Copying the temporary  
            // array to the current row. 
            for ($it = 0; $it != count($w); $it++) 
                    $a[$i][$j--] = $w[$it]; 
        } 
    } 
  
    // for left shift move 
    else if ($d[0] == 'l')  
    {  
        // for each row 
        for ($i = 0; $i < $n; $i++)  
        { 
            $v = array(); $w = array(); 
            $j = 0; 
  
            // for each element of the  
            // row from left to right 
            for ($j = 0; $j < $n; $j++)  
            { 
                // if not 0 
                if ($a[$i][$j]) 
                    array_push($v,  
                               $a[$i][$j]); 
            } 
  
            // for each temporary array 
            for ($j = 0; $j < count($v); $j++)  
            { 
                // if two element have 
                // same value at consecutive  
                // position. 
                if ($j < count($v) - 1 && 
                    $v[$j] == $v[$j + 1])  
                { 
                    // insert only one element  
                    // as sum of two same element. 
                    array_push($w, 2 * $v[$j]); 
                    $j++; 
                } 
                else
                    array_push($w, $v[$j]); 
            } 
  
            // filling the each  
            // row element to 0. 
            for ($j = 0; $j < $n; $j++) 
                $a[$i][$j] = 0; 
  
            $j = 0; 
  
            for ($it = 0; $it != count($w); $it++) 
                    $a[$i][$j++] = $w[$it]; 
        } 
    } 
  
    // for down shift move. 
    else if ($d[0] == 'd')  
    { 
        // for each column 
        for ($i = 0; $i < $n; $i++)  
        { 
            $v = array(); $w = array(); 
            $j = 0; 
  
            // for each element  
            // of column from 
            // bottom to top 
            for ($j = $n - 1; $j >= 0; $j--)  
            { 
                // if not 0 
                if ($a[$j][$i]) 
                    array_push($v, $a[$j][$i]); 
            } 
  
            // for each temporary array 
            for ($j = 0; $j < count($v); $j++)  
            { 
                  
                // if two element have  
                // same value at  
                // consecutive position. 
                if ($j < count($v) - 1 &&  
                    $v[$j] == $v[$j + 1])  
                { 
                    // insert only one element 
                    // as sum of two same element. 
                    array_push($w, 2 * $v[$j]); 
                    $j++; 
                } 
                else
                    array_push($w, $v[$j]); 
            } 
  
            // filling the each  
            // column element to 0. 
            for ($j = 0; $j < $n; $j++) 
                $a[$j][$i] = 0; 
  
            $j = $n - 1; 
  
            // Copying the temporary array 
            // to the current column 
            for ($it = 0; $it != count($w); $it++) 
                    $a[$j--][$i] = $w[$it]; 
        } 
    } 
  
    // for up shift move 
    else if ($d[0] == 'u')  
    { 
        // for each column 
        for ($i = 0; $i < $n; $i++)  
        { 
            $v = array(); $w = array(); 
            $j = 0; 
  
            // for each element of column 
            // from top to bottom 
            for ($j = 0; $j < $n; $j++)  
            { 
                // if not 0 
                if ($a[$j][$i]) 
                    array_push($v,  
                               $a[$j][$i]); 
            } 
  
            // for each temporary array 
            for ($j = 0; $j < count($v); $j++)  
            { 
                // if two element have same 
                // value at consecutive position. 
                if ($j < count($v) - 1 && 
                    $v[$j] == $v[$j + 1])  
                { 
                    // insert only one element  
                    // as sum of two same element. 
                    array_push($w, 2 * $v[$j]); 
                    $j++; 
                } 
                else
                    array_push($w, $v[$j]); 
            } 
  
            // filling the each  
            // column element to 0. 
            for ($j = 0; $j < $n; $j++) 
                $a[$j][$i] = 0; 
  
            $j = 0; 
  
            // Copying the temporary array 
            // to the current column 
            for ($it = 0; $it != count($w); $it++) 
                    $a[$j++][$i] = $w[$it]; 
        } 
    } 
} 
  
// Driven Code 
$d = array("l"); 
$n = 5; 
$a = array( array(32, 3, 3, 3, 3), 
            array(0, 0, 1, 0, 0), 
            array(10, 10, 8, 1, 2), 
            array(0, 0, 0, 0, 1), 
            array(4, 5, 6, 7, 8)); 
  
moveMatrix($d, $n, $a); 
  
// Printing the final array 
for ($i = 0; $i < $n; $i++) 
{ 
    for ($j = 0; $j < $n; $j++) 
        echo ($a[$i][$j]." "); 
  
    echo ("\n"); 
} 
  
// This code is contributed 
// by Manish Shaw(manishshaw1) 
?> 

Output:

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