System Engineer

There is a country with 'N' cities and 'M' bidirectional roads of 3 types.

Type 1: Two Wheeler Road, It means only vehicles having two wheels can use this road.
Type 2: Four Wheeler Road, It means only vehicles having four wheels can use this road.
Type 3: Both two and four Wheeler Road, It means this road can be used by both type of vehicles.

The problem is to find the maximum number of roads that can be removed such that a path exists for every pair of cities for each two-wheeler and four-wheeler vehicle.

Note:

1. Roads may form a cycle.

2. The cities do not have multiple same roads i.e all the roads are unique.

3. If every city cannot be reached, then return -1.

Given a series we have to find the nth element of the series like 1 ,1,2,3,4,,9,8,2716,81,32,243,64....

You are given a 'M' x 'N' matrix of characters, 'CHARACTER_MATRIX' and a string 'WORD'. Your task is to find and print all occurrences of the string in the given character matrix. You are allowed to search the string in all eight possible directions, i.e. North, South, East, West, North-East, North-West, South-East, South-West.

Note: There should not be any cycle in the output path. The entire string must lie inside the matrix boundary. You should not jump across boundaries, i.e. from row 'N' - 1 to 0 or column 'N' - 1 to 0 or vice versa.

Example:

Consider below matrix of characters,
[ 'D', 'E', 'X', 'X', 'X' ]
[ 'X', 'O', 'E', 'X', 'E' ] 
[ 'D', 'D', 'C', 'O', 'D' ]
[ 'E', 'X', 'E', 'D', 'X' ]
[ 'C', 'X', 'X', 'E', 'X' ]

If the given string is "CODE", below are all its occurrences in the matrix:

'C'(2, 2) 'O'(1, 1) 'D'(0, 0) 'E'(0, 1)
'C'(2, 2) 'O'(1, 1) 'D'(2, 0) 'E'(3, 0)
'C'(2, 2) 'O'(1, 1) 'D'(2, 1) 'E'(1, 2)
'C'(2, 2) 'O'(1, 1) 'D'(2, 1) 'E'(3, 0)
'C'(2, 2) 'O'(1, 1) 'D'(2, 1) 'E'(3, 2)
'C'(2, 2) 'O'(2, 3) 'D'(2, 4) 'E'(1, 4)
'C'(2, 2) 'O'(2, 3) 'D'(3, 3) 'E'(3, 2)
'C'(2, 2) 'O'(2, 3) 'D'(3, 3) 'E'(4, 3)

Kevin has three children and he wants to buy chocolates for them. The shopkeeper has ‘N’ boxes of chocolates (numbered from 1 to ‘N’). Each box has some amount of chocolates. If Kevin selects the “i-th” box for buying the chocolates then he must have to buy all the chocolates present in that box. Kevin wants to distribute an equal amount of chocolates among his children.

This problem is divided into 3 subproblems. You must have to solve all three subproblems.

FIRST:

You have to find the maximum number of ways in which Kevin can buy the chocolates if he is allowed to choose boxes in random order.

SECOND:

You have to find the maximum number of ways in which Kevin can buy the chocolates if he is only allowed to choose the consecutive boxes.

THIRD:

There are ‘Q’ queries given to you and each query can be of two types:

0 I V
1 L R

The first type has 0 as a first character that represents this is an update query in which you have to update the number of chocolates in the “Ith” box to ‘V’.

The second type has 1 as a first character that represents this is a range query in which you have to find the maximum number of ways in which Kevin can buy the chocolates in the range [L, R] if he is allowed to choose boxes in any order.

Note:

1. There is no need to maximize the number of chocolates bought by Kevin. 
2. Consider 1 based indexing for queries. There must be a single query of type 1. 
3. You have to take the modulo with 10^9 + 7 as the result can be very large.

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