Given a grid of numbers, find maximum length Snake sequence and print it. If multiple snake sequences exists with the maximum length, print any one of them.
A snake sequence is made up of adjacent numbers in the grid such that for each number, the number on the right or the number below it is +1 or -1 its value. For example, if you are at location (x, y) in the grid, you can either move right i.e. (x, y+1) if that number is ± 1 or move down i.e. (x+1, y) if that number is ± 1.
9, 6, 5, 2
8, 7, 6, 5
7, 3, 1, 6
1, 1, 1, 7
In above grid, the longest snake sequence is: (9, 8, 7, 6, 5, 6, 7)
Below figure shows all possible paths –
We strongly recommend you to minimize your browser and try this yourself first.
The idea is to use Dynamic Programming. For each cell of the matrix, we keep maximum length of a snake which ends in current cell. The maximum length snake sequence will have maximum value. The maximum value cell will correspond to tail of the snake. In order to print the snake, we need to backtrack from tail all the way back to snake’s head.
Let T[i][i] represent maximum length of a snake which ends at cell (i, j), then for given matrix M, the DP relation is defined as –
T = 0
T[i][j] = max(T[i][j], T[i][j – 1] + 1) if M[i][j] = M[i][j – 1] ± 1
T[i][j] = max(T[i][j], T[i – 1][j] + 1) if M[i][j] = M[i – 1][j] ± 1
Below is C++ implementation of the idea –
Maximum length of Snake sequence is: 6 Snake sequence is: 9 (0, 0) 8 (1, 0) 7 (1, 1) 6 (1, 2) 5 (1, 3) 6 (2, 3) 7 (3, 3)
Time complexity of above solution is O(M*N). Auxiliary space used by above solution is O(M*N). If we are not required to print the snake, space can be further reduced to O(N) as we only uses the result from last row.
Reference: Stack Overflow
This article is contributed by Aditya Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
- Find minimum length sub-array which has given sub-sequence in it
- Find maximum sum array of length less than or equal to m
- Find maximum path length in a binary matrix
- Find Maximum side length of square in a Matrix
- Minimum sum possible of any bracket sequence of length N
- Total number of odd length palindrome sub-sequence around each centre
- Maximum sum Bi-tonic Sub-sequence
- Maximum sum possible for a sub-sequence such that no two elements appear at a distance < K in the array
- Maximum sub-sequence sum such that indices of any two adjacent elements differs at least by 3
- Maximum length of segments of 0's and 1's
- Maximum Sum Subsequence of length k
- Maximum Length Chain of Pairs | DP-20
- Maximum sum of non-overlapping subarrays of length atmost K
- Print Maximum Length Chain of Pairs
- Print matrix in snake pattern