BOND - Editorial

easy
implementation
kjcs2018
modulo
observations

#1

PROBLEM LINK:

Practice
Contest

Author: Nishchith Shetty

Tester: Neel Shah

Editorialist: Rushang Gajjal

DIFFICULTY:

EASY

PREREQUISITES:

implemenatation, observation

PROBLEM:

Given a number X , take each digit in turn from left to right . For each digit follow that many black arrows in a row and then follow one white arrow , initial position being point A . We have to find the node on which BOND will land after performing the given operations on X.

EXPLANATION:

We can Solve this problem in two ways : 1. straight off Implementation and 2. Observation.

Method 1: Implementation

Each element is the list [A,B,C,D,E,F,G] is denoted by its index i ranging from 0 to 6. So A -> 0, B -> 1 and so on.
For each node let’s store the next node it will reach if we follow the black arrow or the white arrow respectively.

l = [[1, 0], [3, 2], [4, 3], [2, 5], [6, 6], [0, 4], [5, 1]]

i.e. A -> l[0] = [1,0] -> [ B , A ]. From A if we move along black arrow we reach B or if we move along white arrow we reach A.

Starting from A i.e 0 (start = 0), Now for each digit n in the integer X we perform n moves along black arrow and then move along a white arrow. We can do this by

for i in range(n):
    start = l[start][0]   #move along black arrow
start = l[start][1]     #move along white arrow

Value of start is initially 0.
After the above operations we just print the element denoted by the start variable.

  • Time Complexity: O(|X|)

Method 2: Observation

Similarly if we perform X moves along black arrows and then a move along white arrow we can notice that each node can be represented by the value obtained by X mod 7.

A -> (X mod 7 = 0)

C -> (X mod 7 = 1)

F -> (X mod 7 = 2)

D -> (X mod 7 = 3)

G -> (X mod 7 = 4)

B -> (X mod 7 = 5)

E -> (X mod 7 = 6)

  • Time Complexity: O(1)

AUTHOR’S AND TESTER’S SOLUTIONS:

Author’s solution can be found here

Tester’s solution can be found here


#2

James bond 007 . It was really clever hint for this problem.

@inishchith Really nice ! I liked idea !

It was really hilarious !