SDE - 1

You had a sequence of consecutive nonnegative integers. You appended all integers at the end of each other to form a string ‘S’ without any separators. While appending each integer in a string, you forgot to append exactly one integer from the sequence. Now all the integers from a string and you don’t know which integer you have missed.

For example sequence 11, 12, 13 may form a string (without any separators) “1113” if you miss 12.

Your task is to find the missing number in the string such that it is possible to obtain a sequence of consecutive non-negative integers from the given string. If more than one missing integer is present or all the integers are already present or if the string is not valid then the answer will be -1 for all such cases.

Note:

1. The string consists of only digits 0 to 9.
2. The numbers will have no more than six digits. 

You are given an 'N' * 'M' sized binary-valued matrix 'MAT, where 'N' is the number of rows and 'M' is the number of columns. You need to return the maximum size (area) of the submatrix which consists of all 1’s i.e. the maximum area of a submatrix in which each cell has only the value ‘1’.

In the above image, areas in green, red, and violet color are all submatrices of the original 4x4 matrix.

Note:

1. Binary valued matrix has only two values in each cell : 0 and 1.
2. A submatrix is a matrix formed by selecting certain rows and columns from a larger matrix.
3. The area of a matrix with 'h' rows and 'w' columns is equal to 'h' * 'w'. 

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