Increasing Path In Matrix
Posted: 11 Jan, 2021
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 and end at any possible cell (i, j) i.e at mat[i][j].
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.
You do not need to print anything, it has already been taken care of. Just implement the given function.
1 <= T <= 50 1 <= N <= 100 1 <= M <= 100 -10^9 <= mat[i][j] <= 10^9 Time Limit: 1 sec
- 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.