Print All Paths from Top left to bottom right in Two Dimensional Array

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Objective: Print all the paths from left top corner to right bottom corner in two dimensional array.

Input: Two Dimensional array

Output: Print all the paths.

Note: At the End of the article you will know what needs to be included if you want to print the diagonal paths as well.

Example:

Print All Paths - Example

Approach:

As we need to explore all the paths from top left corner to bottom right corner, we will either travel down OR travel right. so every time either we increase the row or column.

  • Recursion is the key here.
  • Take the rows count and column counts say rowCount and colCount respectively
  • Take currentRow =0 and currentColumn =0 and path =””
  • Call printAll(currentRow, currentcolumn,path)
  • Add array[0][0] to the path.
  • Call recursively printAll(currentRow+1, currentcolumn,path)
  • Call recursively printAll(currentRow, currentcolumn+1,path)
  • Base Case 1: when currentRow = rowCount-1(because array index starts with 0) , print the rest of the columns, return
  • Base Case 2: when currentcolumn = colCount-1(because array index starts with 0) , print the rest of the rows, return

Like always you need to trust Recursion to get you the correct result. 🙂

Recursion Tree -Print All Paths

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Complete Code:


public class PrintAllPathIn2DArray {
int rowCount;
int colCount;
int[][] arrA;
public PrintAllPathIn2DArray(int arrA[][]) {
this.arrA = arrA;
rowCount = arrA.length;
colCount = arrA[0].length;
}
public void printAll(int currentRow, int currentColumn, String path) {
if (currentRow == rowCount – 1) {
for (int i = currentColumn; i < colCount; i++) {
path += "–" + arrA[currentRow][i];
}
System.out.println(path);
return;
}
if (currentColumn == colCount – 1) {
for (int i = currentRow; i <= rowCount – 1; i++) {
path += "–" + arrA[i][currentColumn];
}
System.out.println(path);
return;
}
path = path + "–" + arrA[currentRow][currentColumn];
printAll(currentRow + 1, currentColumn, path);
printAll(currentRow, currentColumn + 1, path);
// printAll(currentRow + 1, currentColumn + 1, path);
}
public static void main(String args[]) {
int[][] a = { { 1, 2, 3 }, { 4, 5, 6 } };
PrintAllPathIn2DArray p = new PrintAllPathIn2DArray(a);
p.printAll(0, 0, "");
}
}

view raw

PrintAllPathIn2DArray.java

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Output:

-1-4-7-8-9
-1-4-5-8-9
-1-4-5-6-9
-1-2-5-8-9
-1-2-5-6-9
-1-2-3-6-9

Note: printAll(currentRow+1,currentColumn+1,path); Add this line when you want to print diagonal paths as well (see code)

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