Find Max. Paths to last Index in a 2D Matrix in Javascript
Dhilip kumar Updated on γ»3 min read
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PROBLEM STATEMENT:
 Given the length of Row and Column of a 2D matrix.
 Starting from origin (0,0), find the maximum number of Paths one can take to reach the last index.
 Allowed ways to move => Right and Bottom.
Example:
 Let, row's length and column length be (2, 2)
 Starting from (0,0) one should reach (1,1)
 So the number of paths for that are: 2
Path 1: (0,0) > (0,1) > (1,1)
Path 2: (0,0) > (1,0) > (1,1)
Thought Process:
Checking for a Pattern:
 We are allowed to traverse in two ways Down and Right for every Index. So this is a pattern.
Edge Cases:
 While we iterate we need to be careful about the ending index's count and so we should handle those cases.
 Path is 0 when the input is less than 1 for either row or column.(i.e.) Input cant be less than 1 for row length and column length
We found a pattern to go through for every index we can choose to solve with iteration / recursion.
Here we will solve it through RECURSION!
const num_of_paths = findMaxPathSrcToDes(3, 3);
console.log('Number of Paths', num_of_paths);
We call findMaxPathSrcToDes
and pass row length and column length and log it.
The intermediate Function:
function findMaxPathSrcToDes(rows, cols) {
// Initial rows and columns to begin with.0,0 is the first row and col index we are choosing
return findMaxPath(0, 0, rows  1, cols  1);
}

findMaxPathSrcToDes
function accepts the row length and column length from the user.  It then returns the output from
findMaxPath
function to which we pass the origin which is (0,0) and destination index(rows 1, cols  1).  We can modify this origin and destination index to user defined positions by accepting those, so that we can identify the number of paths any index from any index.
Finding the Paths:
findMaxPath
function takes in 4 params and outputs the number of path.

currentRow
 Which indicates the current index's Row that is being processed. 
currentColumn
 Which indicates the current index's Column that is being processed. 
destRow
 Destination row index 
destCol
 Destination column index
In any Recursive solution, start with writing the base conditions or Exit conditions.
So, what is a Base condition or Exit condition?
It is basically the case on satisfying which our algorithm should terminate. So, let's formulate one.
 When
currentRow > destRow
(In this case it indicates that thecurrentRow
count has gone out of bound).  When
currentColumn > destCol
(In this case it indicates that thecurrentColumn
count has gone out of bound). So we return '0' in both the cases.
function findMaxPath(currentRow, currentColumn, destRow, destCol) {
// Base condition
if (currentRow > destRow  currentColumn > destCol) {
return 0;
}
}
Success Case:
 if
currentRow === destRow
orcurrentColumn === destCol
this indicates that we have reached the destination index so we return1
to indicate a successful path.
if (currentRow === destRow && currentColumn === destCol) {
return 1;
}
Recursion Case:
 For each index there are two ways 1.Right and 2.Down
 So, we have to recurse in both ways and add the path formed from each ways.
 We call
findMaxPath
by incrementingcurrentRow
by 1.  Then again by incrementing
currentColumn
by 1 and adding the outputs of these two and return them.
const pathsInRows = findMaxPath(currentRow + 1, currentColumn, destRow, destCol);
const pathsInColums = findMaxPath(currentRow, currentColumn + 1, destRow, destCol);
return (pathsInRows + pathsInColums);
CodePen link here
Next Step:
 You could try printing all possible paths along with count.
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