Problem 79: Passcode derivation

(see projecteuler.net/problem=79)

A common security method used for online banking is to ask the user for three random characters from a passcode.
For example, if the passcode was 531278, they may ask for the 2nd, 3rd, and 5th characters; the expected reply would be: 317.

The text file, keylog.txt, contains fifty successful login attempts.

Given that the three characters are always asked for in order, analyse the file so as to determine the shortest possible secret passcode of unknown length.

Algorithm

A very important facts is missing in the problem description: each character is unique in the passcode.

My input routine works as follows:
- for each logged character: keep track of all characters that were entered immediately before it (in the same login attempt)
- store this information in previous, e.g. for 317 it contains { 1 => {3}, 3 => {}, 7 => {1} }

Assuming we tracked more logins: 518, 538 and 327:
previous = { 1 => {3,5}, 2 => {3}, 3 => {5}, 5 => {}, 7 => {1,2}, 8 => {1,3} }

When all logins are processed, I look for the lexicographically smallest (due to Hackerrank's problem modifications) without any successor.
In the example above, 5 points to an empty set and would be printed first.

Then my algorithm removes 5 from previous: remove it whereever it appears as a key and as a value.
previous = { 1 => {3}, 2 => {3}, 3 => {}, 7 => {1,2}, 8 => {1,3} }

The next character without successor is 3 ... print 3 and remove it from previous:
previous = { 1 => {}, 2 => {}, 7 => {1,2}, 8 => {1} }

Now there are several possible keyphrases. We don't know for sure whether the next character is 1 or 2.
1 is lexicographically smaller and is chosen by my program.
previous = { 2 => {}, 7 => {2}, 8 => {} }

Then 2 (again: ambiguous !):
previous = { 7 => {}, 8 => {} }

After that the program picks 7 and finally 8.

My program accepts numbers as well as letters. The "lexicographical order" is based on the ASCII code.

The input can be scrambled in a way that no solution is possible (Hackerrank only, an example would be 123 321).
Then "SMTH WRONG" is printed.

My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, as well as the input data, too.

The code contains #ifdefs to switch between the original problem and the Hackerrank version.
Enable #ifdef ORIGINAL to produce the result for the original problem (default setting for most problems).

#include <set>
#include <map>
#include <string>
#include <iostream>
 
int main()
{
unsigned int logins = 50; // p079_keylog.txt contains 50 logins
 
//#define ORIGINAL
#ifndef ORIGINAL
std::cin >> logins;
#endif
 
// read all logged inputs
// for each digit/letter, store its predecessor
std::map<char, std::set<char>> previous;
while (logins--)
{
std::string line;
std::cin >> line;
// create an empty set for the initial letter (if it doesn't exist yet)
previous[line[0]];
// and for the other letters, store their predecessors
for (unsigned int i = 1; i < line.size(); i++)
previous[line[i]].insert(line[i - 1]);
}
 
// until we have no characters left ...
std::string result;
while (!previous.empty())
{
// find lexicographically smallest letter with no predecessor
auto emptySet = previous.begin();
while (emptySet != previous.end() && !emptySet->second.empty())
emptySet++;
 
// invalid ?
if (emptySet == previous.end())
{
result = "SMTH WRONG"; // Hackerrank's message if code cannot be decrypted
break;
}
 
// print letter
auto current = emptySet->first;
result += current;
 
// that letter won't appear in the keyphrase anymore
previous.erase(current);
 
// remove from the predecessor list of all other letters
for (auto& p : previous)
p.second.erase(current);
}
 
// print keyphrase
std::cout << result << std::endl;
return 0;
}

This solution contains 10 empty lines, 12 comments and 6 preprocessor commands.

Interactive test

You can submit your own input to my program and it will be instantly processed at my server:

This live test is based on the Hackerrank problem.

Input data (separated by spaces or newlines):
Note: The first line contains the number of logins, then each line has a login attempts

This is equivalent to
echo "" | ./79

Output:

(please click 'Go !')

(this interactive test is still under development, computations will be aborted after one second)

Benchmark

The correct solution to the original Project Euler problem was found in less than 0.01 seconds on a Intel® Core™ i7-2600K CPU @ 3.40GHz.
(compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=c++11 -DORIGINAL)

See here for a comparison of all solutions.

Note: interactive tests run on a weaker (=slower) computer. Some interactive tests are compiled without -DORIGINAL.

Changelog

March 13, 2017 submitted solution
May 3, 2017 added comments

Hackerrank

see https://www.hackerrank.com/contests/projecteuler/challenges/euler079

My code solves 22 out of 22 test cases (score: 100%)

Difficulty

Project Euler ranks this problem at 5% (out of 100%).

Hackerrank describes this problem as easy.

Note:
Hackerrank has strict execution time limits (typically 2 seconds for C++ code) and often a much wider input range than the original problem.
In my opinion, Hackerrank's modified problems are usually a lot harder to solve. As a rule thumb: brute-force is never an option.

Links

projecteuler.net/thread=79 - the best forum on the subject (note: you have to submit the correct solution first)

Code in various languages:

Python: www.mathblog.dk/project-euler-79-secret-numeric-passcode/ (written by Kristian Edlund)
Java: github.com/nayuki/Project-Euler-solutions/blob/master/java/p079.java (written by Nayuki)
Go: github.com/frrad/project-euler/blob/master/golang/Problem079.go (written by Frederick Robinson)
Scala: github.com/samskivert/euler-scala/blob/master/Euler079.scala (written by Michael Bayne)

Heatmap

green problems solve the original Project Euler problem and have a perfect score of 100% at Hackerrank, too.
yellow problems score less than 100% at Hackerrank (but still solve the original problem).
gray problems are already solved but I haven't published my solution yet.
blue problems are solved and there wasn't a Hackerrank version of it at the time I solved it or I didn't care about it because it differed too much.

Please click on a problem's number to open my solution to that problem:

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The 160 solved problems had an average difficulty of 21.8% at Project Euler and I scored 11,807 points (out of 13100) at Hackerrank's Project Euler+.
My username at Project Euler is stephanbrumme while it's stbrumme at Hackerrank.
more about me can be found on my homepage.
some names mentioned on this site may be trademarks of their respective owners.
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