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Longest Increasing Path

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C program to find the length of the longest increasing path in a matrix. You can move in four directions (up, down, left, right) from each cell. You cannot move diagonally or outside the matrix boundaries. An increasing path means each cell value must be strictly greater than the previous cell value.

Example 1
    
  
  • Input: matrix = [[9,9,4],[6,6,8],[2,1,1]]
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  • Output: 4
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  • Explanation: 
     Step 1: The longest increasing path is [1, 2, 6, 9]

     Step 2: Path: (2,1) -> (2,0) -> (1,0) -> (0,0)

     Step 3: Values: 1 -> 2 -> 6 -> 9 (strictly increasing)

     Step 4: Length = 4
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Example 2
    
  
  • Input: matrix = [[3,4,5],[3,2,6],[2,2,1]]
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  • Output: 4
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  • Explanation: 
     Step 1: The longest increasing path is [3, 4, 5, 6]

     Step 2: Path: (0,0) -> (0,1) -> (0,2) -> (1,2)

     Step 3: Values: 3 -> 4 -> 5 -> 6 (strictly increasing)

     Step 4: Length = 4
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Constraints
    
  
  • 1 ≤ matrix.length, matrix[i].length ≤ 200
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  • 0 ≤ matrix[i][j] ≤ 2^31 - 1
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  • You must find the longest strictly increasing path
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  • Time Complexity: O(m * n)
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  • Space Complexity: O(m * n)
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MatrixCapgeminiPhillips
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Hint
Solution

Solution Hints

    
  
  • Use dynamic programming with memoization to avoid recalculating paths
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  • For each cell, try all four directions and find the maximum path length
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  • Use DFS (Depth-First Search) with memoization to explore all possible paths
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  • A cell's longest path is 1 + maximum of its valid neighbors' longest paths
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  • Create a memoization table to store computed results for each cell
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  • Only move to a cell if its value is strictly greater than current cell
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Steps to solve by this approach:

 Step 1: Create a memoization table to store computed results for each cell
  Step 2: For each cell in the matrix, perform DFS to find the longest increasing path
  Step 3: In DFS, check all four directions (up, down, left, right) from current cell
  Step 4: Only move to a neighbor if its value is strictly greater than current cell
  Step 5: Recursively calculate the longest path from valid neighbors
  Step 6: Store the result in memoization table to avoid recalculation
  Step 7: Return the maximum path length found among all cells

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