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I've been doing a recursive function for exercise and there's a part which really confuses me. Here's what the entire code looks like:
void RekFunkcija(int * pok, int max)
{
if (max != 0)
{
cout << pok[max - 1] << endl;
RekFunkcija(pok + 1, max - 1);
}
}
void main()
{
const int max = 5;
int niz[] = { max, 63, max, 126, 252 };
RekFunkcija(niz, max);
}
So the output here is:
What's been confusing me is this part of the recursive function: cout << pok[max - 1] << endl;
I don't understand why does it output always the last member of the array(252)? While the index number(max-1) is decrementing by 1? Shouldn't the output be: 252,126,5,63,5? Does it have anything to do with the pok+1 argument?
Thank you in advance.
The real problem is the use of pok+1 and max-1 together in the function.
That is after the first iteration when 252 is printed, the situation is:
pok on incrementing becomes [63,4,126,252] and max becomes 4.
Now pok[max-1] again gives 4.
So if you want all the array elements to be printed replace pok+1 in the function call RekFunkcija(pok + 1, max - 1); to RekFunkcija(pok, max - 1);
The recursive function shrinks the array (pointer increment on pok + 1) each turn and corrects the max argument. This is what happens in pseudo-ish code:
RekFunkcija([5, 63, 5, 126, 252], 5)
RekFunkcija([63, 5, 126, 252], 4)
RekFunkcija([5, 126, 252], 3)
RekFunkcija([126, 252], 2)
RekFunkcija([252], 1)
RekFunkcija(pok + 1, max - 1);
you have got a problem in this recursive call. each call decreases max by 1 and that makes you print the max - (number of recursive calls) element, but you are also moving pok 1 element ahead, so you are printing the 5th element from the start, and then the 4th from the 2nd place, and so on.
Replace with: RekFunkcija(pok, max - 1);
Additionally, I would recommend using int main() instead of void main, as said here
Hello I have a homework question I am stuck in..any hint or tips would be appreciated. the questions is:
Write a single recursive function in C++ that takes as argument a positive integer n then print n, n-1, n-2,...3,2,1,2,3,...n. How many recursive call does your algorithm makes? What is the worst case running time of your algorithm?
I am stuck in the first part. writing a recursive function that prints n, n-1, n-2,...3,2,1,2,3,...n
so far I have:
print(int n)
{
if (n==0)
return;
cout<<n<<" ";
print(n-1);
return;
}
but this only prints from n to 1
I am lost about how I would print from 2 to n using just one parameter and recursively single function.
I tried this: which gives the correct output but has a loop and has two parameters:
p and z has the same value.
void print(int p,int z)
{
if (p==0)
{
for(int x=2;x<=z; x++)
cout<<x<<" ";
return;
}
else
cout<<p<<" ";
print(p-1,z);
return;
}
any hint or tips is much appreciated thank you.
so it is working now, but I am having trouble understanding how (question in comment):
void print(int n)
{
if (n==1){
cout<<n;
return;
}
else
cout<< n;
print(n-1); // how does it get passed this? to the line below?
cout<<n; // print(n-1) takes it back to the top?
return;
}
The output you want is mirrored, so you can have this series of steps:
print num
recursive step on num-1
print num again
That's the recursive case. Now you need an appropriate base case upon which to stop the recursion, which shouldn't be difficult.
Given the pseudocode:
recursive_print(n):
if n == 1:
print 1
return
print n
recursive_print(n-1)
print n
(If you prefer, just look at your solution instead).
Let's trace it. A dot will mark where we're up to in terms of printing.
. recursive_print(3) // Haven't printed anything
3 . recursive_print(2) 3 // Print the 3
3 2 . recursive_print(1) 2 3 //Print 2
3 2 1 . 2 3 // Print 1
3 2 1 2 . 3 // Print 2
3 2 1 2 3 . // Print 3
Each unrolling of the function gives us 2 numbers on opposite sides and we build down to the "1", then go back and print the rest of the numbers.
The "unrolling" is shown in this picture:
If you strip away the functions and leave yourself with a sequence of commands, you'll get:
print 3
print 2
print 1
print 2
print 3
where each indentation signifies a different function.
Simple solution for this:
Def fxn(n):
if n <= n:
if n > 0:
print(n)
fxn(n - 1)
print(n)
Def main():
Number = 6
fxn(Number)
Main()
If you struggle understanding how this works:
Basically, each time you call a function in a recursive problem, it isn't a loop. It's as if you were on the woods leaving a trail behind. Each time you call a function inside a function, it does its thing, then it goes right back to were you called it.
In other words, whenever you call a recursive function, once the newer attempt is done, it will go right back to were it used to be.
In loops, once each step is done, it is done, but in recursive functions you can do a lot with a lot less.
Printing before the recurse call in my code is the descension step, and once its descension finished, it will progresively unfold step by step, printing the ascension value and going back to the former recurse.
It seems way harder than it is, but it is really easy once you grasp it.
The answer is simpler than you think.
A recursive call is no different from a regular call. The only difference is that the function called is also the caller, so you need to make sure you don't call it forever (you already did that). Let's think about a regular call. If you have the following code snippet:
statement1
f();
statement2
The statement1 is executed, then f is called and does it's thing and then, after f finishes, statement2 is executed.
Now, let's think about your problem. I can see that your hard work on this question from the second program you've written, but forget about it, the first one is very close to the answer.
Let's think about what your function does. It prints all numbers from n to 0 and then from 0 to n. At the first step, you want to print n, then all the numbers from n-1 to 0 and from 0 to n-1, and print another n. See where it's going?
So, you have to do something like this:
print(n)
call f(n-1)
print(n)
I hope my explanation is clear enough.
This is more of hack -- using the std::stream rather than recursion...
void rec(int n) {
if (n==1) { cout << 1; return; }
cout << n;
rec(n-1);
cout << n;
}
int main() {
rec(3);
}
prints
32123
First, yes it's HW - really tried but not sure of something so ill be happy if you will help me:)
I have this code:
void func(int A[], int start, int n)
{
int p = n/2;
if ( 1 < n )
{
func(A, start, p);
func(A, start + p, n-p);
for (i=0; i<n; i++)
cout << A[start+i];
}
}
func(A, 0, n);
I need to give this code a recusive formula.
What I did was - first recursion call is T(n/2).
Second - this is the problem! really confuse with adding the 'p'...is that
T(n/2) too??
Three - for is running on theta(n)
and the outside recursion call is T(n)...
Can you help me get to the final formula??
Thanks
If I read it right, you want the recurrence for the run time complexity.
For n > 1, you recur with parameter floor(n/2) and with parameter n-floor(n/2), and after that you output n items. Thus you have
T(n) = T(cost of first recursive call) + T(second rec. call) + extra work
which you should now bring into a form suitable to apply the master theorem.
This is either a trick question or you misread the question. What you have is a recursive formula. Do you need to switch this formula from C++ to more traditional math notation? Do need to find a non-recursive algorithm? In your answer to the question, what is T? The term formula does not really apply here because nothing gets computed. This is a void function that never modifies the given array. All that happens is some things elements from the array get put on the screen in some order.
I would start by tracing an example to understand what is going on.
Lets say A = {1,2,3,4} Then 'func(A, 0,4)' is:
tracing func(A,0,4) :
p = 2
func(A,0,2)
func(A,2,2)
cout << 1 2 3 4
tracing func(A,0,2) :
p = 1 //start=0; n=2
func(A,0,1)
func(A,1,1)
cout << 1 2
tracing func(A,2,2) :
p = 1 //start=2; n=2
func(A,2,1)
func(A,3,1)
cout << 3 4
tracing func(A,2,1) :
p = 0 //start=0; n=1
func(A,0,0)
func(A,0,1)
cout << 1
tracing func(A,3,1) :
p = 0 //start=3; n=1
func(A,3,0)
func(A,3,1)
cout << 3
tracing func(A,2,1) :
p = 0 //start=0; n=1
func(A,0,0)
func(A,0,1)
cout << 1
At this point I'm going to stop because this is your homework problem. You can finish it from here.
I am new to C++ programming and I am a bit lost. Here is what I am suppose to do and my code. Any ideas on what to do?
Write a program that uses while loops to calculate the first n Fibonacci numbers. Recall from math the following definition of the Fibonacci sequence:
The Fibonacci numbers Fn are defined as follows. F0 is 1, F1 is 1 and Fi+2 = Fi + Fi+1 for i = 0, 1, 2, ... . In other words, each number is the sum of the previous two numbers. The first few Fibonacci numbers are 1, 1, 2, 3, 5, 8, and 13.
The program should prompt the user for n (the number of Fibonacci numbers) and print the result to the screen. If the user enters an invalid value for n (n <= 0), print an error message and ask the user to re-enter n (an input validation loop for n). This MUST be a loop, not an if statement like Lab 2.
The output should be similar to the following:
Enter the number of Fibonacci numbers to compute: 3
The first 3 Fibonacci numbers are:
1 1 2
#include <iostream>
using namespace std;
int main()
{
int f0 = 0, f1 = 1,f2= 2, i = 0, n;
cout << "Enter the number of Fibonacci numbers to compute: ";
cin >> n;
if ( n <= 0)
{
cout <<"Error: Enter a positive number: ";
return 1;
}
while ( i < n){
f2 = f0 + f1;
i++;
}
cout << "The first " << n << " Fibonacci numbers are: " << endl;
cin >> n;
return 0;
}
while ( i < n){
f2 = f0 + f1;
i++;
}
See this loop, this is where the problem is, since this is homework, i'll not tell exactly what the problem is, take a pen and paper, and start executing your statements, specially this loop, you'll find your error. Just a hint, Fibonacci number is the sum of previous two fibonacci numbers.
You got the f2=f0+f1 right. However, you should note that when you increment i, then f2 becomes f1 and f1 becomes f0.
If you name them like this, it would make more sense:
int f_i_minus_2 = 0, f_i_minus_1 = 1, f_i;
and you would have
f_i = f_i_minus_1+f_i_minus_2;
Now, imagine i is 3. You have written:
f[3] = f[2]+f[1]
When you increment i, you must have:
f[4] = f[3]+f[2]
That is f_i is put in the place of f_i_minus_1 and f_i_minus_1 is put in the place of f_i_minus_2.
(Look at this:
f[3] = f[2] + f[1]
| |
\_____ \____
\ \
f[4] = f[3] + f[2]
)
So you need two assignments after computing f_i:
f_i_minus_2 = f_i_minus_1;
f_i_minus_1 = f_i;
Note that I first changed f_i_minus_2 to f_i_minus_1 because the second assignment destroys the value of f_i_minus_1.
According to wikipedia, your definition is off. F0=0, F1=1, F2=1, F3=2, ...
http://en.wikipedia.org/wiki/Fibonacci_number
Assuming wikipedia is right your loop is basically
int i = 0, f, fprev;
while( i < n )
{
if( i == 0 )
{
f = 0;
fprev = 0;
}
else if( i == 1 )
{
f = 1;
}
else
{
int fnew = f + fprev;
fprev = f;
f = fnew;
}
i++;
}
As others have pointed out, since you never modify f0 and f1 in the
loop, f2 isn't going to depend on the number of times through the
loop. Since you have to output all of the numbers at the end anyway,
why not try keeping them in an array. I'd initialize the first two
values manually, then loop until I had enough values.
(This can be done quite nicely using the STL:
// After having read n...
std::vector<int> results( 2, 1 );
while ( results.size() < n )
results.push_back( *(results.end() - 1) + *(results.end() - 2));
I'm not sure that this is what your instructor is looking for, however.
I rather suspect that he wants you to to some indexing yourself. Just
remember that if you initialize the first two values manually, your
index must start at 2, not at 0.)
Another thing: the specification you post says that you should loop if
the user enters an illegal value. This is actually a little tricky: if
the user enters something that isn't an int (say "abc"), then 1)
std::cin will remain in error state (and all further input will fail)
until cleared (by calling std::cin.clear()), and the illegal
characters will not be extracted from the stream, so your next attempt
will fail until you remove them. (I'd suggest >>ing into an
std::string for this; that will remove everything until the next white
space.) And don't ever access the variable you >>ed into until
you've checked the stream for failure—if the input fails. If the
input fails, the variable being input is not modified. If, as here, you
haven't initialized it, then anything can happen.
Finally (and I'm sure this goes beyond your assignment), you really do
need to do something to check for overflow. Beyond a certain point,
your output will become more or less random; it's better to stop and
output that you're giving up in this case.
If you are interested, there are better ways to calculate it.
Just for fun I created an algorithm that computes every possible combination from a given rugby score (3, 5 or 7 points). I found two methods : The first one is brute force, 3 imbricated for loops. The other one is recursion.
Problem is some combinations appear multiple times. How can I avoid that ?
My code :
#include <iostream>
using namespace std;
void computeScore( int score, int nbTryC, int nbTryNC, int nbPenalties );
int main()
{
int score = 0;
while (true)
{
cout << "Enter score : ";
cin >> score;
cout << "---------------" << endl << "SCORE = " << score << endl
<< "---------------" << endl;
// Recursive call
computeScore(score, 0, 0, 0);
}
return 0;
}
void computeScore( int score, int nbTryC, int nbTryNC, int nbPenalties )
{
const int tryC = 7;
const int tryNC = 5;
const int penalty = 3;
if (score == 0)
{
cout << "* Tries: " << nbTryC << " | Tries NT: " << nbTryNC
<< " | Penal/Drops: " << nbPenalties << endl;
cout << "---------------" << endl;
}
else if (score < penalty)
{
// Invalid combination
}
else
{
computeScore(score - tryC, nbTryC+1, nbTryNC, nbPenalties);
computeScore(score - tryNC, nbTryC, nbTryNC+1, nbPenalties);
computeScore(score - penalty, nbTryC, nbTryNC, nbPenalties+1);
}
}
One way to think about this is to realize that any time you have a sum, you can put it into some "canonical" form by sorting all the values. For example, given
20 = 5 + 7 + 3 + 5
You could also write this as
20 = 7 + 5 + 5 + 3
This gives a few different options for how to solve your problem. First, you could always sort and record all of the sums that you make, never outputting the same sum twice. This has the problem that you're going to end up repeatedly generating the same sums multiple different times, which is extremely inefficient.
The other (and much better) way to do this is to update the recursion to work in a slightly different way. Right now, your recursion works by always adding 3, 5, and 7 at each step. This is what gets everything out of order in the first place. An alternative approach would be to think about adding in all the 7s you're going to add, then all the 5's, then all the 3's. In other words, your recursion would work something like this:
Let kValues = {7, 5, 3}
function RecursivelyMakeTarget(target, values, index) {
// Here, target is the target to make, values are the number of 7's,
// 5's, and 3's you've used, and index is the index of the number you're
// allowed to add.
// Base case: If we overshot the target, we're done.
if (target < 0) return;
// Base case: If we've used each number but didn't make it, we're done.
if (index == length(kValues)) return;
// Base case: If we made the target, we're done.
if (target == 0) print values; return;
// Otherwise, we have two options:
// 1. Add the current number into the target.
// 2. Say that we're done using the current number.
// Case one
values[index]++;
RecursivelyMakeTarget(target - kValues[index], values, index);
values[index]--;
// Case two
RecursivelyMakeTarget(target, values, index + 1);
}
function MakeTarget(target) {
RecursivelyMakeTarget(target, [0, 0, 0], 0);
}
The idea here is to add in all of the 7's you're going to use before you add in any 5's, and to add in any 5's before you add in any 3's. If you look at the shape of the recursion tree that's made this way, you will find that no two paths end up trying out the same sum, because when the path branches either a different number was added in or the recursion chose to start using the next number in the series. Consequently, each sum is generated exactly once, and no duplicates will be used.
Moreover, this above approach scales to work with any number of possible values to add, so if rugby introduces a new SUPER GOAL that's worth 15 points, you could just update the kValues array and everything would work out just fine.
Hope this helps!
Each time you find a solution you could store it in a dictionary ( a set of strings for example, with strings looking like "TC-TNT-P" )
Before printing a solution you verify it was not in the dictionary.
A nested for-loop is the natural way to do this. Using recursion is just silly (as you seem to have discovered).