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Count All Paths from Top left to bottom right in Two Dimensional Array including Diagonal Paths

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

Input: Two Dimen­sional array

Out­put: No of paths.

Approach :

1. Recur­sive

Recur­sive solu­tion to this prob­lem is sim­i­lar to Print All Paths from Top left to bot­tom right in Two Dimen­sional Array

But the Time com­plex­ity will be expo­nen­tial because there will be many sub prob­lems which will be solved again and again to get the final solu­tion. read this : “Dynamic pro­gram­ming vs Recursion

2. Dynamic Pro­gram­ming (Bet­ter Solu­tion)

Cre­ate two dimen­sional result­Count array to store the num­ber of paths from top left corner.

Base Case: To reach to any cell in either first row or col­umn from first cell(top left at 0,0) will be 1.

You can reach to any cell from 3 dif­fer­ent ways, from left, from top, from diag­o­nal. So total no of paths to reach to that cell will be sum of all the paths to reach to left, top and diag­o­nal cell. see picture

Count Paths

Count Paths


Count All Paths Example

Count All Paths Example

Com­plete Code:


No of Paths By Recursion: 13
No of paths By Dynamic Programming: 13

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  • Steffi Keran Rani J

    what is arrA.length? and what is arrA[0].length?