LeetCode-in-Java

329. Longest Increasing Path in a Matrix

Hard

Given an m x n integers matrix, return the length of the longest increasing path in matrix.

From each cell, you can either move in four directions: left, right, up, or down. You may not move diagonally or move outside the boundary (i.e., wrap-around is not allowed).

Example 1:

Input: matrix = [[9,9,4],[6,6,8],[2,1,1]]

Output: 4

Explanation: The longest increasing path is [1, 2, 6, 9].

Example 2:

Input: matrix = [[3,4,5],[3,2,6],[2,2,1]]

Output: 4

Explanation: The longest increasing path is [3, 4, 5, 6]. Moving diagonally is not allowed.

Example 3:

Input: matrix = [[1]]

Output: 1

Constraints:

• m == matrix.length
• n == matrix[i].length
• 1 <= m, n <= 200
• 0 <= matrix[i][j] <= 231 - 1

Solution

public class Solution {
    public int longestIncreasingPath(int[][] matrix) {
        int maxIncreasingSequenceCount = 0;
        int n = matrix.length - 1;
        int m = matrix[0].length - 1;
        int[][] memory = new int[n + 1][m + 1];
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[i].length; j++) {
                maxIncreasingSequenceCount =
                        Math.max(maxIncreasingSequenceCount, move(i, j, n, m, matrix, memory));
            }
        }
        return maxIncreasingSequenceCount;
    }

    private int move(int row, int col, int n, int m, int[][] matrix, int[][] memory) {
        if (memory[row][col] == 0) {
            int count = 1;
            // move down
            if (row < n && matrix[row + 1][col] > matrix[row][col]) {
                count = Math.max(count, move(row + 1, col, n, m, matrix, memory) + 1);
            }
            // move right
            if (col < m && matrix[row][col + 1] > matrix[row][col]) {
                count = Math.max(count, move(row, col + 1, n, m, matrix, memory) + 1);
            }
            // move up
            if (row > 0 && matrix[row - 1][col] > matrix[row][col]) {
                count = Math.max(count, move(row - 1, col, n, m, matrix, memory) + 1);
            }
            // move left
            if (col > 0 && matrix[row][col - 1] > matrix[row][col]) {
                count = Math.max(count, move(row, col - 1, n, m, matrix, memory) + 1);
            }
            memory[row][col] = count;
        }
        return memory[row][col];
    }
}

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