[Python] 5x5 matrix traversal problem by traversing maximum of 4-neighbours [closed]

Write a python code for the bellow defined problem:

First a create a 5x5 matrix. The conditions or properties for the matrix is as,

1. Dimension of the matrix is 5x5
2. The matrix consist of any random values from 1 to 99
3. The value of the matrix must be unique, that means repetition of the values are not allowed
4. The value 1 and 99 must be present in the matrix, also
5. The value 1 must be present in the middle of the matrix, that is at cell (2,2) and
6. The value 99 must be present in the matrix somewhere

There is a sample matrix:

[ [35, 67, 93, 25, 48],
[50, 32, 69, 70, 95],
[ 2, 3, 1, 41, 73],
[10, 15, 20, 81, 35],
[99, 27, 5, 6, 7] ]


Now starting from 1 we have to reach 99. We can only traverse the maximum of 4-neighbours of the current cell. For instance, initially we are in 1. In the above sample matrix the 4-neighbours of 1 are 3, 41, 69, 20. Then in this case we are only allowed to traverse 69 as it is the maximum 4-neighbours. So from 1 we move to 69. Now we have to again find the largest 4-neighboours of 69 and move to this value. Following this process we have to reach 99. But starting from 1 we must be reach 99 in 24 moves. We can't reach 99 from 1 in less than or greater than 24 moves. And most importantly back traverse is not allowed, i.e., we can not traverse a cell that has been already traversed, a cell can be traverse only once.

I tried to solve the problem. But following above constraints I found that I reach 99 in less than 24 steps. So, I decided to ignore the 99 (if it is found to be largest 4-neighbours in any moves) until I reach at 24 steps as shown the image. But I can't reach 99, the path has been blocked after a certain moves as shown in the image. There is no valid path exist after 18 moves. Now is it possible to solve this problem. If it is possible then provide the Python code to solve the problem

I write an algorithm of the above steps as,

Step 1: Declare a dictionary called "neighbours" to store the 4-neighbours of a cell
Step 2: Declarea a list called "visited" to store the visited cell coordinate so that the visited cell be avoid in next moves
Step 3: Initialize a tupple (r,c) to (2,2) to start from center
Step 4: Initialize step_count = 0
Step 5: Calculate the 4 neighbours of (r,c) using formula (r-1, c), (r+1, c), (r, c-1), and (r, c+1)
Step 6: Check that these 4 neighbours remain within the matrix boundaries to avoid out-of-bounds errors
Step 7: Store the value of the 4 neighbours in dictionary "neighbours" where key is the cell coordinate and value is corresponding coordinate value
Step 8: Arrange value of the dictionary "neighbours" in descending order
Step 9: While loop: repeat until step_count = 24:
a) Calculate the 4 neighbours of (r,c) using formula (r-1, c), (r+1, c), (r, c-1), and (r, c+1)
b) Exclude neighbors already in visited.
c) Ignore the cell containing 99 until the 24 step.
d) Clear "neighbours" dictionary
e) Store the values of remaining neighbours in the "neighbours" dictionary (key = coordinate, value = cell value)
f) Sort "neighbours" in descending order by value.
g) Pick the first coordinate from the sorted dictionary.
h) Update (r,c) to this coordinate.
i) Append (r,c) to visited.
j) Increment step_count by 1.

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