Longest Path In Matrix.cpp

#include <bits/stdc++.h>
#define n 3
using namespace std;

int findLongestFromACell(int i, int j, int mat[n][n],
                         int dp[n][n])
{
    if (i < 0 || i >= n || j < 0 || j >= n)
        return 0;

    if (dp[i][j] != -1)
        return dp[i][j];

    int x = INT_MIN, y = INT_MIN, z = INT_MIN, w = INT_MIN;

    if (j < n - 1 && ((mat[i][j] + 1) == mat[i][j + 1]))
        x = 1 + findLongestFromACell(i, j + 1, mat, dp);

    if (j > 0 && (mat[i][j] + 1 == mat[i][j - 1]))
        y = 1 + findLongestFromACell(i, j - 1, mat, dp);

    if (i > 0 && (mat[i][j] + 1 == mat[i - 1][j]))
        z = 1 + findLongestFromACell(i - 1, j, mat, dp);

    if (i < n - 1 && (mat[i][j] + 1 == mat[i + 1][j]))
        w = 1 + findLongestFromACell(i + 1, j, mat, dp);

    return dp[i][j] = max({x, y, z, w, 1});
}

int finLongestOverAll(int mat[n][n])
{
    int result = 1;
    int dp[n][n];
    memset(dp, -1, sizeof dp);
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < n; j++)
        {
            if (dp[i][j] == -1)
                findLongestFromACell(i, j, mat, dp);
            result = max(result, dp[i][j]);
        }
    }

    return result;
}

int main()
{
    int mat[n][n] = {{1, 2, 9}, {5, 3, 8}, {4, 6, 7}};
    cout << "Length of the longest path is "
         << finLongestOverAll(mat);
    return 0;
}