I am supposed to show that two algorithms execute identical statements in identical order. One is a tail recursive version of the other. They are written in Eiffel.

```
tail_rec(x:instance_type):result_type is
local
y:instance_type;
do
if b(x) then
Result :=c(x)
else
y:=d(x);
Result:=tail_rec(y)
end
end
```

Then the non-tail recursive version.

```
non_rec(x:instance_type):result_type is
do
from until b(x) loop
x:= d(x)
end;
Result:= c(x)
end
```

where b(x), c(x), and d(x) are any functions of type BOOLEAN, result_type, and instance_type respectively.

How are these two algorithms similar and how do they execute identical statements in identical order?

Answer:

By substituting all flow-of-control constructs with `goto`

s, (essentially turning the code from `Eiffel`

into pseudocode,) and allowing `if`

statements to execute only `goto`

s, it can be shown that both functions end up consisting of the exact same set of instructions.

Let me begin by copying the original `tail_rec`

here for convenience:

```
tail_rec(x:instance_type):result_type is
local
y:instance_type;
do
if b(x) then
Result := c(x)
else
y := d(x);
Result := tail_rec(y)
end
end
```

First, get rid of Eiffel's silly `Result :=`

construct and replace it with `return`

for convenience. (Otherwise, we are going to have to add more `goto`

s, and frankly, the fewer the better.)

```
tail_rec(x:instance_type):result_type is
local
y:instance_type;
do
if b(x) then
return c(x)
end
y := d(x);
return tail_rec(y)
end
```

Substitute the `if`

-`then`

-`end`

with `if`

-`then goto`

:

```
tail_rec(x:instance_type):result_type is
local
y:instance_type;
do
if not b(x) then goto label1
return c(x)
label1:
y := d(x);
return tail_rec(y)
end
```

Replace tail recursion with another `goto`

:

```
tail_rec(x:instance_type):result_type is
do
label0:
if not b(x) then goto label1
return c(x)
label1:
x := d(x);
goto label0
end
```

Replace `if not b(x)`

with `if b(x)`

:

```
tail_rec(x:instance_type):result_type is
do
label0:
if b(x) then goto label1
x := d(x);
goto label0
label1:
return c(x)
end
```

Similar transformations to `tail_rec`

should turn it into the exact same thing.

c++,algorithm,parallel-processing,c++14

Proposal N3554 (A Parallel Algorithms Library) for C++14, proposes (among other things), what seem to be parallel versions of the current std::partial_sum, e.g.: template< class ExecutionPolicy, class InputIterator, class OutputIterator, class BinaryOperation> OutputIterator inclusive_scan( ExecutionPolicy &&exec, InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op); With the explanation Effects: For each...

python,algorithm

I am trying to calculate least completion time of a project schedule, which has n number of tasks and each task can have a dependency task. example Task ID Duration Days Dependent ID 1 10 0 2 3 0 3 6 1 4 5 2 5 10 1 Task with...

algorithm,data-structures

In an exam I see a question: Which one of the following is true? For a binary search, the best-case occurs when the target item is in the beginning of the search list. For a binary search, the best-case occurs when the target is at the end of the search...

c++,algorithm,inheritance,time-complexity

Here I have 800 derived classes of Base and a list of 8000000 objects of these types, which can be of any order. The goal is to separate the list into the 800 types as efficiently as possible. Here I have written two functions to do that. The first is...

c++,algorithm,math,recursion

I'm trying to find all possible solutions to the 3X3 magic square. There should be exactly 8 solutions. My code gets them all but there are a lot of repeats. I'm having a hard time tracking the recursive steps to see why I'm getting all the repeats. // This program...

algorithm

You are managing a software project that involves building a computer-assisted instrument for medical surgery. The exact placement of the surgical knife is dependent on a number of different parameters, usually at least 25, sometimes more. Your programmer has developed two algorithms for positioning the cutting tool, and is seeking...

c++,arrays,algorithm,sum

I tried to find all pairs in the array with sum equal to k, the solution to that takes O(n*log(n)) time. Here is the code snippet - map<int,int> mymap; map<int,int>::iterator it; cin>>n>>k; for( int i = 0 ; i < n ; i++ ){ cin>>a; if( mymap.find(a) != mymap.end() )...

design-patterns,logic,structure

The following method filters a data collection based on order statuses. Im wondering what would be the best way to extract the business logic held within about the order statuses. For example, say the order statuses were to change down the line i.e. ('in_transit', 'at_courier') then this method, and associated...

algorithm,go

I am trying to solve the following problem from project euler (please take a look at description and the example in the link, but here is the short explanation). in the matrix, find the minimal path sum from the top left to the bottom right, by moving left, right, up,...

c++,algorithm

I'm trying to make a program to check whether the word "nadia" is present with this sequence in a string. if you can delete zero or more characters to get this word then you should print "YES" else print "NO". Can anyone help me find what are the test cases...

javascript,algorithm,recursion

While working through some Coderbyte challenges, I was able to solve the following problem recursively, but was hoping to get some feedback on how I can improve it. Have the function AdditivePersistence(num) take the num parameter being passed which will always be a positive integer and return its additive persistence...

algorithm,graph,tree,runtime,big-o

I have a possible solution for the following question, but not sure if correct: Assume we have already found a minimum spanning tree T for a weighted, undirected graph G = (V,E). We would like to be able to efficiently update T should G be altered slightly. An edge is...

c#,regex,algorithm

I'm making a script to try and hack into an account whose login password is at least 8 characters long and includes at least 1 number, 1 special character and 1 capital letter. I will use brute force. Is there a compact, elegant and efficient way to iterate through every...

java,c++,algorithm,recursion,dfs

For example, given a set like below - S=[1,3] we want to get the list of list with following values: [[],[1],[3],[1,3]] I used C++ with the following code and it worked perfect for me. However, after I changed it to Java, the code didn't give me right results. Any help?...

c++,algorithm,matrix

I am trying to print the right hemisphere of a matrix. If we draw the main and the secondary diagonals in a matrix we see that we got 4 equal parts, the right part is called (in my algorithms textbook) the right hemisphere of a square matrix. For example, in...

c,algorithm,security,math,encryption

I'm trying to reverse the following code in order to provide a function which takes the buffer and decrypts it. void crypt_buffer(unsigned char *buffer, size_t size, char *key) { size_t i; int j; j = 0; for(i = 0; i < size; i++) { if(j >= KEY_SIZE) j = 0;...

string,algorithm,palindrome

Given length L find the shortest string >= L formed only of as & bs such that adding some character (Either a or b) doesn't produce a new palindrome substring (never seen before palindrome) For example for L = 1 there is the string aabbaba, adding "a" to it to...

r,if-statement,double,logic

This question already has an answer here: Why are these numbers not equal? 3 answers I am running the code below. The function Ax returtns the value 1. But the ifelse statement does not recognize that Ax==1. I've tried making the output of the function double-precision and all numeric...

algorithm,discrete-mathematics

I'm doing an online course and i'm stuck on this question. I know there are similar questions but they don't help me. What is the order of growth of the worst case running time of the following code fragment as a function of N? int sum = 0; for (int...

algorithm,graph,cycle,dfs

I came around one of those questions in my exams: Topologocial sorting using Kahn's Algorithm requires the graph to be DAG (Directed Acyclic Graph). How can we determine if a graph contains no cycles without using DFS/BFS first? I am trying to answer that for too long now and I...

c,if-statement,macros,logic

#define MACRO(num, str) {\ printf("%d", num);\ printf(" is");\ printf(" %s number", str);\ printf("\n");\ } int main(void) { int num; printf("Enter a number: "); scanf("%d", &num); if (num & 1) { MACRO(num, "Odd"); } else { MACRO(num, "Even"); } return 0; } Please explain the above code (if/else condition and how...

algorithm,coordinates,coordinate-systems,coordinate

I'm writing a program for visualizing crystals. As a part of the program, I have to generate all different basic points in a lattice structure. For those that aren't familiar with crystallography, you can find the most general cases of these structures here: https://en.wikipedia.org/wiki/Hermann%E2%80%93Mauguin_notation#Lattice_types The problem was that I wanted...

algorithm,graph

I am looking for an algorithm that finds minimal subset of vertices such that by removing this subset (and edges connecting these vertices) from graph all other vertices become unconnected (i.e. the graph won't have any edges). Is there such algorithm? If not: Could you recommend some kind of heuristics...

c++,algorithm

The project Euler problem 5 is stated as : "2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?" Here's...

python,algorithm,sorting,math

I am looking for a basic algorithm that gives more weigh to the recent reviews. So, the output value of the algorithm is mutable. For example, two reviews with exactly the same score, will have a different ranking based on the timestamp of the creation. Review_1 Score 10 creation 10/5/2014...

c,string,algorithm,data-structures

int myStrCmp (const char *s1, const char *s2) { const unsigned char *p1 = (const unsigned char *)s1; const unsigned char *p2 = (const unsigned char *)s2; while (*p1 != '\0') { if (*p2 == '\0') return 1; if (*p2 > *p1) return -1; if (*p1 > *p2) return 1;...

javascript,algorithm

I accidentally got undefined == true and undefined == false that both of them returns false. But !undefined returns true. And this is the question: What's the algorithmic difference(s) between !someVariable and someVariable == false? If i want to explain it more, type undefined == false ? 't' : 'f'...

c++,algorithm,sorting,c++11

I have implemented three different sorting algorithms and now I want to confirm that my approach of counting the total number of comparisons is correct. In my mind, the number of comparisons shouldn't be tied to the conditional branches because if the condition isn't met, the comparison was still made...

algorithm,optimization,dynamic-programming,frequency

I have the following problem and I only have a slight idea about it: Consider a tape storage problem. Given n files of length l1,...,ln and frequencies with which they are accessed f1,...,fn, where sum of all frequencies is 1 and 0<fi<1. "Optimal" means to minimize the average retrieval time...

php,algorithm,assign,subgraph,pairing-heap

In the following we are facing the problem of multiple assignments of the hungarian algorithm. Scenario: We have 100 students and 5 courses, which the students can vote with priority. So every student will get assigned for one specific cours. Priority from 1 to 5. 1 lowest 5 highest The...

algorithm,recursion,permutation

Assuming I have a list of elements [1,2,3,4,] and a number of bins (let's assume 2 bins), I want to come up with a list of all combinations of splitting up items 1-4 into the 2 bins. Solution should look something like this [{{1}, {2,3,4}}, {{2}, {1,3,4}}, {{3}, {1,2,4}}, {{4},...

algorithm,math,statistics,variance,standard-deviation

I'm successfully using Welford's method to compute running variance and standard deviation as described many times on Stack Overflow and John D Cook's excellent blog post. However in the stream of samples, sometimes I encounter a "rollback", or "remove sample" order, meaning that a previous sample is no longer valid...

algorithm

I attended a programming competition(it has ended now). I don't know why my solution is giving WA, I read the editorial, saw other people solution but unable to find a flaw in my solution. Obviously I am missing somewhere. Please help! Question Link My Solution My approach If the pattern...

php,mysql,json,parsing,logic

Objective: To parse following json string and get mentioned values separately, later those separated values are going to be inserted to mysql database. I have checked my json string on JsonLint user_name, selected_date, selected_project, tasks , 4.1.task_name, 4.2 work_hours { "user_name": "USER", "selected_date": "2015-06-08", "selected_project": "Project1", "tasks": [ { "task_name":...

algorithm,numerical-methods,numerical,numerical-integration

Consider the following differential equation f(x) = g'(x) I have a build a code that spits out values of the function f(x) for the variable x, where x goes from 0 to very large. Now, I'm looking for a scheme that will analyse these values of f(x) in order to...

c++,arrays,algorithm,recursion

I'm trying to write a recursive algorithm that returns true if at least one array[i] == i. And false if there is no array[i] = i. Also, the parameters needed are (int * arr, int start, int end). So i'll be traversing the array with a pointer. For example: int...

java,loops,if-statement,while-loop,logic

NOT ASKING FOR ANYONE TO WRITE THE PROGRAM FOR ME I am having trouble understanding how to setup the logic for a program given these following conditions: For every day late up to and including 7 days, the late fee is $0.10/day After 7 days, for every day late up...

algorithm,dynamic-programming,knapsack-problem

I am familiar with the 0-1 knapsack problem and when you are given a certain number of copies from each item but I can figure out how to solve it when you are given infinite copies of each item using dynamic programming. I am trying to solve it by hand...

algorithm,bit-manipulation

Given a 64 bit number, I need to extract every other bit from it, and convert it into a number: decimal: 357 binary: 0000 0001 0110 0101 odd bits: 0 0 0 1 1 0 1 1 decimal: 27 Any idea of a good algorithmic way to do it? And...

python,algorithm,time-complexity,longest-substring

Someone asked me a question Find the longest alphabetically increasing or equal string composed of those letters. Note that you are allowed to drop unused characters. So ghaaawxyzijbbbklccc returns aaabbbccc. Is an O(n) solution possible? and I implemented it code [in python] s = 'ghaaawxyzijbbbklccc' lst = [[] for i...

algorithm,graph,tree,runtime,big-o

I am having trouble with the following question: Assume we have already found a minimum spanning tree T for a weighted, undirected graph G = (V,E). We would like to be able to efficiently update T should G be altered slightly. An edge is removed from G to produce a...

java,algorithm,function,genetic-programming,convergence

I have a few questions about my genetic algorithm and GAs overall. I have created a GA that when given points to a curve it tries to figure out what function produced this curve. An example is the following Points {{-2, 4},{-1, 1},{0, 0},{1, 1},{2, 4}} Function x^2 Sometimes I...

c++,algorithm,graph

Someone can help me to think in the better way to adapt Dijkstra's Algorithm in these conditions? All I thought didn't was good. Example of input: GP4578 MADRID 01:00 PORTO 02:00 IK6587 PORTO 03:00 VALENCIA 05:00 05:30 TENERIFE 08:00 AB5874 VALENCIA 05:40 BERLIM 10:00 "VALENCIA 05:00 05:30" This is a...

c,algorithm

I try find out what is wrong with the program that takes n - size of serials and this same number of elements numbers. With n = 4 and numbers 1, 2, 3, 4 I get output: 1, 0, 2293428, 1990567906. Somewhere in the code something is not okey, but...

python,regex,algorithm,python-2.7,datetime

If I knew the format in which a string represents date-time information, then I can easily use datetime.datetime.strptime(s, fmt). However, without knowing the format of the string beforehand, would it be possible to determine whether a given string contains something that could be parsed as a datetime object with the...

python,algorithm,permutation

I'm trying to write a function that would input a list (of pre-determined length) and output the permutation of that list according to my choice of re-ordering. For example, suppose I have the list [1,'a',12,'b','poppy'] and I have the permutation (3,4,5,2,1) Then the function output would be a list with...

php,algorithm,digits

I'm following the programming test, and there are questions like this From this consecutive digits: 123456789101112131415161718192021.... For example The 10th digit is 1 The 11th digit is 0 and so on What is the 1,000,000th digit? What is the 1,000,000,000th digit? What is the 1,000,000,000,000th digit? Your solution should run...

ruby,algorithm,search,recursion

I'm working through a toy problem in Ruby: how to produce all possible 10-digit phone numbers where each successive number is adjacent to the last on the keypad. I've represented the adjacent relationships between numbers, and have a recursive function, but my method isn't iterating through the whole solution space....

algorithm,big-o

I was doing some reading on logarithms and the rate of growth of the running time of algorithms. I have, however, a problem understanding the Big-Ω (Big-Omega) notation. I know that we use it for 'asymptotic lower bounds', and that we can express the idea that an algorithm takes at...

java,if-statement,while-loop,int,logic

I've made this java program to find the two smallest integers as inputted by the user. I think I'm pretty much just about there except there is one issue with my logic. I'm not sure what to set values: int min, min2; to where the rest of my program would...