# Longest Increasing Path in a Matrix in Python

Suppose we have one matrix; we have to find the length of the longest increasing path. From each cell, we can either move to four directions − left, right, up or down. We cannot move diagonally or move outside of the boundary.

So, if the input is like

 9 9 4 6 6 8 2 1 1

then the output will be 4 as the longest increasing path is [3, 4, 5, 6].

To solve this, we will follow these steps −

• Define a function solve(). This will take i,j,matrix

• if dp[i,j] is non-zero, then

• return dp[i, j]

• dp[i, j] := 1

• temp := 0

• for r in range i-1 to i+2, do

• for c in range j-1 to j+2, do

• if r is same as i and c is same as j or(|r-i| is same as 1 and |c-j| is same as 1) , then

• go for the next iteration

• if c>=0 and r>=0 and r< row count of matrix and c < col size of matrix[0] and matrix[r, c]>matrix[i, j], then

• temp := maximum of temp, solve(r, c, matrix)

• dp[i, j] := dp[i, j] + temp

• return dp[i, j]

• From the main method do the following −

• if not matrix is non-zero, then

• return 0

• dp := a matrix of size same as given matrix and fill with 0

• ans := 0

• for i in range 0 to size of matrix, do

• for j in range 0 to size of matrix[0], do

• if dp[i, j] is same as 0, then

• solve(i, j, matrix)

• return ans

## Example

Let us see the following implementation to get better understanding −

class Solution(object):
def solve(self,i,j,matrix):
if self.dp[i][j]:
return self.dp[i][j]
self.dp[i][j] = 1
temp = 0
for r in range(i-1,i+2):
for c in range(j-1,j+2):
if r==i and c==j or (abs(r-i)==1 and abs(c-j)==1):
continue
if c>=0 and r>=0 and r<len(matrix) and c<len(matrix[0]) and matrix[r][c]>matrix[i][j]:
temp = max(temp,self.solve(r,c,matrix))
self.dp[i][j]+=temp
return self.dp[i][j]
def longestIncreasingPath(self, matrix):
if not matrix:
return 0
self.dp = [ [0 for i in range(len(matrix[0]))] for j in range(len(matrix))]
self.ans = 0
for i in range(len(matrix)):
for j in range(len(matrix[0])):
if self.dp[i][j]==0:
self.solve(i,j,matrix)
self.ans = max(self.ans,self.dp[i][j])
return self.ans

ob = Solution()
print(ob.longestIncreasingPath([[9,9,4],[6,6,8],[2,1,1]]))

## Input

[[9,9,4],[6,6,8],[2,1,1]]

## Output

4

Updated on: 23-Jul-2020

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