# Flood Fill Algorithm

Given a 2D screen arr[][] where each arr[i][j] is an integer representing the colour of that pixel, also given the location of a pixel (X, Y) and a colour C, the task is to replace the colour of the given pixel and all the adjacent same-coloured pixels with the given colour.

Example:

Input: arr[][] = {
{1, 1, 1, 1, 1, 1, 1, 1},
{1, 1, 1, 1, 1, 1, 0, 0},
{1, 0, 0, 1, 1, 0, 1, 1},
{1, 2, 2, 2, 2, 0, 1, 0},
{1, 1, 1, 2, 2, 0, 1, 0},
{1, 1, 1, 2, 2, 2, 2, 0},
{1, 1, 1, 1, 1, 2, 1, 1},
{1, 1, 1, 1, 1, 2, 2, 1}}
X = 4, Y = 4, C = 3
Output:
1 1 1 1 1 1 1 1
1 1 1 1 1 1 0 0
1 0 0 1 1 0 1 1
1 3 3 3 3 0 1 0
1 1 1 3 3 0 1 0
1 1 1 3 3 3 3 0
1 1 1 1 1 3 1 1
1 1 1 1 1 3 3 1
Explanation:
The values in the given 2D screen indicate colours of the pixels. X and Y are coordinates of the brush, C is the colour that should replace the previous colour on screen[X][Y] and all surrounding pixels with the same colour. Hence all the 2 are replaced with 3.

BFS Approach: The idea is to use BFS traversal to replace the colour with the new colour.

• Create an empty queue lets say Q.
• Push the starting location of the pixel as given in the input and apply replacement colour to it.
• Iterate until Q is not empty and pop the front node (pixel position).
• Check the pixels adjacent to the current pixel and push into the queue if valid (had not been coloured with replacement colour and have the same colour as the old colour).

Below is the implementation of the above approach:

 `# Python3 implementation of the approach ` ` `  `# Function that returns true if  ` `# the given pixel is valid ` `def` `isValid(screen, m, n, x, y, prevC, newC): ` `    ``if` `x<``0` `or` `x>``=` `m\ ` `       ``or` `y<``0` `or` `y>``=` `n ``or``\ ` `       ``screen[x][y]!``=` `prevC\ ` `       ``or` `screen[x][y]``=``=` `newC: ` `        ``return` `False` `    ``return` `True` ` `  ` `  `# FloodFill function ` `def` `floodFill(screen,   ` `            ``m, n, x,   ` `            ``y, prevC, newC): ` `    ``queue ``=` `[] ` `     `  `    ``# Append the position of starting  ` `    ``# pixel of the component ` `    ``queue.append([x, y]) ` ` `  `    ``# Color the pixel with the new color ` `    ``screen[x][y] ``=` `newC ` ` `  `    ``# While the queue is not empty i.e. the  ` `    ``# whole component having prevC color  ` `    ``# is not colored with newC color ` `    ``while` `queue: ` `         `  `        ``# Dequeue the front node ` `        ``currPixel ``=` `queue.pop() ` `         `  `        ``posX ``=` `currPixel[``0``] ` `        ``posY ``=` `currPixel[``1``] ` `         `  `        ``# Check if the adjacent ` `        ``# pixels are valid ` `        ``if` `isValid(screen, m, n,   ` `                ``posX ``+` `1``, posY,   ` `                        ``prevC, newC): ` `             `  `            ``# Color with newC ` `            ``# if valid and enqueue ` `            ``screen[posX ``+` `1``][posY] ``=` `newC ` `            ``queue.append([posX ``+` `1``, posY]) ` `         `  `        ``if` `isValid(screen, m, n,   ` `                    ``posX``-``1``, posY,   ` `                        ``prevC, newC): ` `            ``screen[posX``-``1``][posY]``=` `newC ` `            ``queue.append([posX``-``1``, posY]) ` `         `  `        ``if` `isValid(screen, m, n,   ` `                ``posX, posY ``+` `1``,   ` `                        ``prevC, newC): ` `            ``screen[posX][posY ``+` `1``]``=` `newC ` `            ``queue.append([posX, posY ``+` `1``]) ` `         `  `        ``if` `isValid(screen, m, n,   ` `                    ``posX, posY``-``1``,   ` `                        ``prevC, newC): ` `            ``screen[posX][posY``-``1``]``=` `newC ` `            ``queue.append([posX, posY``-``1``]) ` ` `  ` `  ` `  `# Driver code ` `screen ``=``[ ` `[``1``, ``1``, ``1``, ``1``, ``1``, ``1``, ``1``, ``1``],  ` `[``1``, ``1``, ``1``, ``1``, ``1``, ``1``, ``0``, ``0``],  ` `[``1``, ``0``, ``0``, ``1``, ``1``, ``0``, ``1``, ``1``],  ` `[``1``, ``2``, ``2``, ``2``, ``2``, ``0``, ``1``, ``0``],  ` `[``1``, ``1``, ``1``, ``2``, ``2``, ``0``, ``1``, ``0``],  ` `[``1``, ``1``, ``1``, ``2``, ``2``, ``2``, ``2``, ``0``],  ` `[``1``, ``1``, ``1``, ``1``, ``1``, ``2``, ``1``, ``1``],  ` `[``1``, ``1``, ``1``, ``1``, ``1``, ``2``, ``2``, ``1``],  ` `    ``] ` `     `  `# Row of the display ` `m ``=` `len``(screen) ` ` `  `# Column of the display ` `n ``=` `len``(screen[``0``]) ` ` `  `# Co-ordinate provided by the user ` `x ``=` `4` `y ``=` `4` ` `  `# Current colour at that co-ordinate ` `prevC ``=` `screen[x][y] ` ` `  `# New colour that has to be filled ` `newC ``=` `3` ` `  `floodFill(screen, m, n, x, y, prevC, newC) ` ` `  ` `  `# Priting the updated screen ` `for` `i ``in` `range``(m): ` `    ``for` `j ``in` `range``(n): ` `        ``print``(screen[i][j], end ``=``' '``) ` `    ``print``() `

Output:

```1 1 1 1 1 1 1 1
1 1 1 1 1 1 0 0
1 0 0 1 1 0 1 1
1 3 3 3 3 0 1 0
1 1 1 3 3 0 1 0
1 1 1 3 3 3 3 0
1 1 1 1 1 3 1 1
1 1 1 1 1 3 3 1
```

DFS Approach: Similarly DFS approach can be used to implement the Flood Fill algorithm as well.

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