Increasing Path In Matrix

Posted: 11 Jan, 2021
Difficulty: Moderate

PROBLEM STATEMENT

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You are given a 2-D matrix ‘mat’, consisting of ’N’ rows and ‘M’ columns. The element at the i-th row and j-th column is ‘mat[i][j]’.

From mat[i][j], you can move to mat[i+1][j] if mat[i+1][j] > mat[i][j], or to mat[i][j+1] if mat[i][j+1] > mat[i][j].

Your task is to find and output the longest path length if you start from (0,0) i.e from mat[0][0] and end at any possible cell (i, j) i.e at mat[i][j].

Note :
Consider 0 based indexing.
Input Format :
The first line of input contains an integer ‘T’ denoting the number of test cases. The description of ‘T’ test cases are as follows -: 

The first line contains two space-separated positive integers ‘N’, ‘M’ representing the number of rows and columns respectively.

Each of the next ‘N’ lines contains ‘M’ space-separated integers that give the description of the matrix ‘mat’.
Output Format :
For each test case, print the length of the longest path in the matrix.

Print the output of each test case in a separate line.
Note :
You do not need to print anything, it has already been taken care of. Just implement the given function.
Constraints :
1 <= T <= 50
1 <= N <= 100
1 <= M <= 100
-10^9 <= mat[i][j] <= 10^9

Time Limit: 1 sec
Approach 1

Algorithm

 

  • This is a recursive approach.
  • Make a recursive function ‘helper(row, col)’ and call this function with (0, 0). In each recursive step do the following-:
    • Initialize an integer variable ‘temp’: = 0.
    • If cell (row+1, c) exist and mat[row+1][col] > mat[row][col], then recursively call ‘helper(row+1, col)’ and update ‘temp’ with maximum of ‘temp’ and value return by ‘helper(row+1, col)’.
    • If cell (row, col+1) exist and mat[row][col+1] > mat[row][col], then recursively call ‘helper(row, col+1)’ and update ‘temp’ with maximum of ‘temp’ and value return by ‘helper(row, col+1)’.
    • Return ‘temp’ + 1.
  • The value returned by helper(0, 0) will be the length of the longest path start from (0, 0), we need to return this value.
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