<< problem 78 - Coin partitions Square root digital expansion - problem 80 >>

# Problem 79: Passcode derivation

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.

# My 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.

# 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:

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

# 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()
{

//#define ORIGINAL
#ifndef ORIGINAL
#endif

// for each digit/letter, store its predecessor
std::map<char, std::set<char>> previous;
{
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.

# Benchmark

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

# Hackerrank

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 rarely an option.

# Heatmap

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

 green solutions solve the original Project Euler problem and have a perfect score of 100% at Hackerrank, too yellow solutions score less than 100% at Hackerrank (but still solve the original problem easily) gray problems are already solved but I haven't published my solution yet blue solutions are relevant for Project Euler only: there wasn't a Hackerrank version of it (at the time I solved it) or it differed too much orange problems are solved but exceed the time limit of one minute or the memory limit of 256 MByte red problems are not solved yet but I wrote a simulation to approximate the result or verified at least the given example - usually I sketched a few ideas, too black problems are solved but access to the solution is blocked for a few days until the next problem is published [new] the flashing problem is the one I solved most recently

I stopped working on Project Euler problems around the time they released 617.
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The 310 solved problems (that's level 12) had an average difficulty of 32.6% at Project Euler and
I scored 13526 points (out of 15700 possible points, top rank was 17 out of ≈60000 in August 2017) at Hackerrank's Project Euler+.

My username at Project Euler is stephanbrumme while it's stbrumme at Hackerrank.

Look at my progress and performance pages to get more details.

 << problem 78 - Coin partitions Square root digital expansion - problem 80 >>
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