Direction Arrays in Grid Problems

Direction arrays are used in grid-based problems to move in the four or eight possible directions without writing separate code for each move.

Why Use Direction Arrays?

Without direction arrays:

row - 1, col     // Up
row + 1, col     // Down
row, col - 1     // Left
row, col + 1     // Right

This becomes repetitive and error-prone.

With direction arrays:

int[] dr = {-1, 0, 1, 0};
int[] dc = {0, 1, 0, -1};

Now all directions can be traversed using a loop.

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4-Directional Movement

int[] dr = {-1, 0, 1, 0};
int[] dc = {0, 1, 0, -1};

Index	Direction	Row Change	Col Change
0	Up	-1	0
1	Right	0	+1
2	Down	+1	0
3	Left	0	-1

Traversal:

for(int i = 0; i < 4; i++) {
    int nr = row + dr[i];
    int nc = col + dc[i];
}

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Example

Current Cell:

row = 2;
col = 3;

Generated Neighbors:

(1,3)  // Up
(2,4)  // Right
(3,3)  // Down
(2,2)  // Left

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Boundary Check

Always check whether the new cell is inside the grid.

if(nr >= 0 && nr < n &&
   nc >= 0 && nc < m) {

}

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8-Directional Movement

Used in problems where diagonal movement is allowed.

int[] dr = {-1,-1,-1,0,0,1,1,1};
int[] dc = {-1,0,1,-1,1,-1,0,1};

Directions:

↖ ↑ ↗
← X →
↙ ↓ ↘

Traversal:

for(int i = 0; i < 8; i++) {
    int nr = row + dr[i];
    int nc = col + dc[i];
}

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Where It Is Used?

• Number of Islands

• Rotten Oranges

• Flood Fill

• Shortest Path in Binary Matrix

• Path With Minimum Effort

• BFS on Grid

• DFS on Grid

• Multi-source BFS

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Complete Template

int[] dr = {-1, 0, 1, 0};
int[] dc = {0, 1, 0, -1};

for(int i = 0; i < 4; i++) {

    int nr = row + dr[i];
    int nc = col + dc[i];

    if(nr >= 0 && nr < n &&
       nc >= 0 && nc < m) {

        // process neighbour
    }
}

Key Insight

Think of dr and dc as instructions for movement.

newRow = currentRow + dr[i];
newCol = currentCol + dc[i];

Instead of manually writing all directions, we store movement patterns in arrays and iterate through them. This makes BFS, DFS, and Dijkstra grid solutions much cleaner and easier to maintain.