Find longest Snake sequence in a given matrix

Objective: Given two dimensional matrix, write an algorithm to find out the snake sequence which has the maximum length. There could be many snake sequence in the matrix, you need to return the one with the maximum length. Travel is allowed only in two directions, either go right OR go down.

What is snake sequence: Snake sequence can be made if number in adjacent right cell or number in the adjacent down cell is either +1 or -1 from the number in the current cell.


Snake Sequence (1)



  • This problem is the extension of the problem “Count all paths from top left to bottom right of a mXn matrix” with some extra conditions.
  • You can travel only in two directions, either go right or go down.
  • All we need to take care if one extra condition that we can travel only to the adjacent cells (right or down) only if number in those cells has difference of 1 from the current cell.
  • Have a temporary storage , two dimensional array to store the results of snake result.
  • Keep tracking of maximum length and at the end print the sequence using temporary array.
  • We will use the Bottom-up approach of Dynamic pro­gram­ming and store the results of sub prob­lems to reuse them in future.
  • See the recursive equation and code for better understanding.

Recursive Equation- Snake Sequence



Max Snake Sequence : 7
- 5 - 4 - 3 - 2 - 1 - 2 - 1

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If you find anything incorrect or you feel that there is any better approach to solve the above problem, please write comment.

  • dogbert82

    Recursive equation in that table has a typo. It never consider j-1.

  • Chandra Gopalaiah

    if I change the order of “if else” statements in print path function the printed sequence doesn’t match with the expected sequence.

    Should we always start checking the row first and then column?

    • Shilpi

      Yes, I agree, this logic alone won’t work in this case. We would have to check the original matrix as well.

  • fatih tekin

    Below function should also do that please let me know if you see any issues

    To call

    Stack longest = new Stack();
    findMaxLengthSnake(A,0,0,new Stack(),longest);

    and the function

    private static Stack findMaxLengthSnake(int[][] matrix,int row, int column, Stack currentPath,Stack longest) {
    if(currentPath.size() > longest.size()){
    if(row==matrix.length || matrix[row].length == column){
    return currentPath;
    int currentValue = matrix[row][column];
    if(!currentPath.isEmpty() && Math.abs(currentPath.peek()-currentValue) != 1){
    return currentPath;
    findMaxLengthSnake(matrix, row, column+1,currentPath,longest);
    findMaxLengthSnake(matrix, row+1, column,currentPath,longest);
    return currentPath;

  • Vida Tahmasebi

    This algorithm is not entirely right, it is missing the condition of checking for meeting the condition in the original matrix before print. If you run it for the following example you will see that it fails.
    int arrA [][] = {{1, 2, 3, 9},
    {2, 9, 2, 1},
    {3, 9, 9, 2},
    {4, 5, 6, 7}};

    Max Snake Sequence : 7
    – 7 – 2 – 1 – 2 – 3 – 2 – 1

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