SDE - 2

You have been given a matrix of ‘N’ rows and ‘M’ columns filled up with integers. Find the minimum sum that can be obtained from a path which from cell (x,y) and ends at the top left corner (1,1).

From any cell in a row, we can move to the right, down or the down right diagonal cell. So from a particular cell (row, col), we can move to the following three cells:

Down: (row+1,col)
Right: (row, col+1)
Down right diagonal: (row+1, col+1)

You are given a real number, 'NUM'. You have to represent this number as an irreducible fraction of the form A/B, where 'A' and 'B' are the numerator and denominator respectively.

A fraction is called irreducible when the greatest common divisor (GCD/HCF) of the numerator and denominator is one.

Example :

Given 'NUM' : 1.75
Irreducible fraction  can be represented as 7/4.

Note that 14/8 = 1.75 as well, but 14/8 is not an irreducible fraction.

Note :

In order to preserve precision, the real number will be given to you in the form of two strings : the integer part, and the fractional part. 

The integer part will contain not more than 8 digits, whereas the fractional part will always contain 8 digits.

You have been given an integer 'N'. Your task is to print the Magical Pattern(see examples) for the given 'N'.

Example :

For 'N' : 4
Pattern :
4 3 2 1 2 3 4                                                                   
3 3 2 1 2 3 3                                                                   
2 2 2 1 2 2 2                                                                   
1 1 1 1 1 1 1                                                                   
2 2 2 1 2 2 2                                                                   
3 3 2 1 2 3 3                                                                   
4 3 2 1 2 3 4

Given an undirected and disconnected graph G(V, E), containing 'V' vertices and 'E' edges, the information about edges is given using 'GRAPH' matrix, where i-th edge is between GRAPH[i][0] and GRAPH[i][1]. print its DFS traversal.

V is the number of vertices present in graph G and vertices are numbered from 0 to V-1. 

E is the number of edges present in graph G.

Note :

The Graph may not be connected i.e there may exist multiple components in a graph.

You have been given an integer array/list 'ARR' of size 'N'. Your task is to return the total number of those subsequences of the array in which all the elements are equal.

A subsequence of a given array is an array generated by deleting some elements of the given array with the order of elements in the subsequence remaining the same as the order of elements in the array.

Note :

As this value might be large, print it modulo 10^9 + 7

You are given two strings 'S' and 'T' of lengths 'N' and 'M' respectively. Find the "Edit Distance" between the strings.

Edit Distance of two strings is the minimum number of steps required to make one string equal to the other. In order to do so, you can perform the following three operations:

1. Delete a character
2. Replace a character with another one
3. Insert a character

Note:

Strings don't contain spaces in between.