I already searched everywhere for a solution for my problem, but didn't get one. So what I'm trying to do ist use recursion to find out whats a passed integer variable's base to the power of the passed exponent. So for example 3² is 9. My solution really looks like what I found in these forums, but it constantly gives me a stack overflow error. Here is what I have so far.(To make it easier, I tried it with the ints directly not using scanner to test my recursion) Any idea?
public class Power {
public static int exp(int x,int n) {
n = 3;
x = 2;
if (x == 0) {
return 1;
}
else {
return n * exp(n,x-1);
}
}
public static void main(String[] args) {
System.out.println(exp(2,3));
}
}
Well, you've got three problems.
First, inside of the method, you're reassigning x and n. So, regardless of what you pass in, x is always 2, and n is always 3. This is the main cause of your infinite recursion - as far as the method is concerned, those values never update. Remove those assignments from your code.
Next, your base case is incorrect - you want to stop when n == 0. Change your if statement to reflect that.
Third, your recursive step is wrong. You want to call your next method with a reduction to n, not to x. It should read return x * exp(x, n-1); instead.
Related
I've ran the below code and I think it's correct. However, it just keeps returning stack overflow. When I run it in debug mode, I noticed somehow within the function x%y returns y instead of the remainder which is suppose to be 0. Can someone please help and see why this is?
public class test
{
public static void main (String [] args)
{
System.out.println(gcd(50,10));
}
static double gcd(double x, double y)
{
if (x > y)
{
return gcd(y, x);
}
else if (y <= x && x%y == 0)
{
return y;
}
else
{
return gcd(y, x%y);
}
}
}
Technically speaking, the implementation causes a stack overflow because for the arguments 50 and 10 the recursive calls reach the first and the last case alternatively, causing an infinite recursion. Apparently the algorithm for determining the greatest common divisor is implemented incorrectly; an elaborate presentation of it can be found here. That being said, it might not be a good idea to perform the calculations using the type double; I doubt that the division remainder operator % will behave as expected due to rounding.
In this code, I've used a global variable to increase the value of p whenever control touches the base case. But I want to do it without using a global variable. Is that possible?
public class stairCase {
static int p=0;
public static void main(String[] args) {
// TODO Auto-generated method stub
int n = func(14,0);
System.out.println(n);
}
public static int func(int n, int c){
if(n==c){
p++;
return 1;
}
if(n-c>=1){
func(n,c+1);
}
if(n-c>=2){
func(n,c+2);
}
if(n-c>=3){
func(n,c+3);
}
return p;
}}
Your problem is that you're throwing away a major communication resource: the return value. You recur in three places, but ignore the value. Harness that, and you'll solve your problem.
Consider something like this:
if (n < c) return 0 // Jumping too far gives no solution
else if (n == c) return 1 // Jumping to the top step is 1 solution
else
return func(n, c+1) + // Other jumps: sum the solutions from
func(n, c+2) + // each of the reachable steps.
func(n, c+3)
For future programming, please learn about useful variable names and documentation. I would not have followed this decently, had I not solved this problem yesterday in another posting.
You can do a little better with this problem if you reverse your counting. Note that you never change n as you recur -- in that case, why pass it at all? Start c at 14 and count to step 0 (the top).
Converting the code is left as an exercise for the student. :-)
I'm new to java programming, and our teacher taught us the concept of recursion and I found it to be a bit complicated. All I understood that it works like a loop(like the factorial of 4) but I still don't quite get it why it works like that. Can I get a detailed explanation on this topic? Here is the piece of code and a picture my teacher used to explain.
package javaapplication1;
public class JavaApplication1 {
static int factorial(int n){
int t;
if(n == 0){
return 1;
} else {
t = factorial(n - 1);
return n * t;
}
}
public static void main(String[] args) {
System.out.println(factorial(5));
}
}
In the following image, the blue color represents stack winding, and the green is stack unwinding, and again I don't know what stack winding and unwinding is.
http://i.stack.imgur.com/pjqJy.png
A recursive function is a function that calls itself until it reaches a return statement, that stops it from recalling itself. Take your example, the Factorial function.
Factorial is a mathematical function that returns the number multiplied by itself - 1 multiplied by itself - 2, ... multiplied by 1, example: factorial of 5 = 5! = 5x4x3x2x1 = 120.
it is also equal to itself multiplied by the factorial of itself -1, which is: 5! = 5x4!
Take into consideration that 0! = 1.
to represent this in a Java code, you need a loop that multiplies the numbers starting from 1, and going till the number you are calculating its factorial.
Further more, explaining your code, let us calculate Factorial(5):
Factorial() returns an integer.
Initial Call from main(): 5 != 0, then skip the condition (n == 0); t
= Factorial(5-1) = Factorial(4);
Second call from Factorial(4): 4 != 0, then skip the condition (n ==
0); t = Factorial(4-1) = Factorial(3);
Third call from Factorial(3): 3 != 0, then skip the condition (n ==
0); t = Factorial(3-1) = Factorial(2);
Fourth call from Factorial(2): 2 != 0, then skip the condition (n ==
0); t = Factorial(2-1) = Factorial(1);
Fifth call from Factorial(1): 1 != 0, then skip the condition (n ==
0); t = Factorial(1-1) = Factorial(0);
Sixth call from Factorial(0): 0 == 0, then return value 1;
First return, 1, to Fifth call (Factorial(1)): return n*t = return 1*1
= return value 1;
Second return, 1, to Fourth call (Factorial(2)): return n*t = return
2*1 = return value 2;
Third return, 2, to third call (Factorial(3)): return n*t = return 3*2
= return value 6;
Second return, 6, to second call (Factorial(4)): return n*t = return
4*6 = return value 24;
Second return, 24, to First call (Factorial(5)): return n*t = return
5*24 = return value 120;
Second return, 120, to Initial call (from main()): print(120);
Hope this helps you understand recursion.
When a call is made to another method, a stack frame is created to hold the state of the current method and it is pushed onto the stack. This is regardless of a method calling itself or another method.
When the call returns, the stack frame is popped of the stack, the state of the method is restored and execution continues in the calling method.
Recursion is when a method (directly or indirectly) calls itself. The general form of a recursive method is:
If a parameter meets a terminating condition, return (usually a result)
Else adjust parameters for the next iteration and call self
The code your teacher wrote has some style issues. It would be clearer if written like this:
static int factorial(int n) {
if (n == 0) {
return 1;
}
return n * factorial(n - 1);
}
Eradicating the unnecessary variable t and redundant else (there is no "else" when the "if" returns - there is merely continuation of execution)
I would write it like this, eliminating the if altogether:
static int factorial(int n) {
return n == 0 ? 1 : n * factorial(n - 1);
}
When one knows that a task can be broken into similar smaller tasks ,then we use recursion or calling the same method(until we met a certain condition).Recursion not only helps in execution of a problem without having to define or invoke another method,it also helps in visualizing a pattern by which the task is getting executed
Personally, I do not like the factorial problem. I find it hard to understand and I do not think it explains recursion in a clear way. So lets look at a different example. Lets say that we want to print numbers from 1-100. This is a very simple task with a for loop and a counter, but it can also be done with recursion. For example:
public static void main(String[] args) {
numbersAscending(1);
numbersDescending(1);
}
//Prints 1 2 3 ... 100
public void numbersAscending(int x){
System.out.println(x);
if(x < 100){
numbersAscending(x+1);
}
}
//Prints 100 99 98 ... 1
public void numbersDescending(int x){
if(x < 100){
numbersDescending(x+1);
}
System.out.println(x);
}
When a function is called, that call goes on top of the stack. Think of this like a stack of cards. Each one has a number on it (1-100). When a function calls itself, a new card gets added to the stack. When the function finishes, it is taken off of the stack.
So for the example above, every time numbersAscending is called, it prints out the current value for x before calling that function again. This results in the numbers being printed in order from 1-100. As soon as 100 is reached, it stops calling itself and pops each function off of the stack.
On the other hand, every time numbersDescending is called, it calls itself again before printing out the number. In this way, x doesn't start printing until it reaches 100. It then moves back down the stack, printing each number as it goes back to the main method.
/*This program in java will help you to understand all the basics of
recursion:
->how control flows in recursion
->how return is executed in the recursive functions
->how and when the statements after recursive function area executed.*/
public class Understanding_Rec{
public static int rec(int x)
{
if(x<5)
{
System.out.println("-->Smaller than 5");
rec(x+1);
System.out.println("<--After recursion inside x<5");
return x;
}
else if(x<7)
{
System.out.println("-->Smaller than 7");
rec(x+1);
System.out.println("<--After recursion inside x<7");
}
System.out.println("<--No Condition Statement");
return x;
}
public static void main(String[] args)
{
int x=1;
rec(x);
System.out.print(x+"Inside main");
}
}
I am not sure if it explains, but if you had a precalculus class then you should know that factorial can be defined in two waqys.
n!=1*2*...*n
of we define
1!=1
and
n!=n*(n-1)!
Try to see yourself that those definitions are equivalent. Pick let us say, 5!
according to second definition
5!=5*4!
but 4!=4*3! so 5!=5*4*3!
but 3!=3*2! so 5!=5*4*3*2!
and so on. Keep doing it until you hit 1!. But 1!=1 so you stop.
Recursion in programming is the same thing.
TomW
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I am preparing for an exam next week, and I decided to look for some exam questions online for better preparation.
I came across this question and the answer is c. But I really want to know how or the step by step process to answer to answer a question like this. The part where I got stuck is trying to logically understand how a int m = mystery(n); How can a number equal a method? Whenever I get to a question like this is their anything important I should breakdown first?
private int[] myStuff;
/** Precondition : myStuff contains int values in no particular order.
/*/
public int mystery(int num)
{
for (int k = myStuff.length - 1; k >= 0; k--)
{
if (myStuff[k] < num)
{
return k;
}
}
return -1;
}
Which of the following best describes the contents of myStuff after the
following statement has been executed?
int m = mystery(n);
(a) All values in positions 0 through m are less than n.
(b) All values in positions m+1 through myStuff.length-1 are
less than n.
(c) All values in positions m+1 through myStuff.length-1 are
greater than or equal to n.
(d) The smallest value is at position m.
(e) The largest value that is smaller than n is at position m.
See this page to understand a method syntax
http://www.tutorialspoint.com/java/java_methods.htm
int m = mystery(n); means this method going to return int value and you are assigning that value to a int variable m. So your final result is m. the loop will run from the array's end position to 0. loop will break down when array's current position value is less than your parameter n. on that point it will return the loop's current position. s o now m=current loop position. If all the values of the loop is greater than n it will return -1 because if condition always fails.
Place the sample code into a Java IDE such as Eclipse, Netbeans or IntelliJ and then step through the code in the debugger in one of those environments.
Given that you are starting out I will give you the remainder of the code that you need to make this compile and run
public class MysteriousAlright {
private int[] myStuff;
public int mystery(int num)
{
for (int k = myStuff.length - 1; k >= 0; k--) {
if (myStuff[k] < num) {
return k;
}
}
return -1;
}
public static void main(String[] args) {
MysteriousAlright ma = new MysteriousAlright();
ma.setMyStuff(new int[] {4,5,6,7});
int m = ma.mystery(5);
System.out.println("I called ma.mystery(5) and now m is set to " + m);
m = ma.mystery(3);
System.out.println("I called ma.mystery(3) and now m is set to " + m);
m = ma.mystery(12);
System.out.println("I called ma.mystery(12) and now m is set to " + m);
}
public void setMyStuff(int[] myStuff) {
this.myStuff = myStuff;
}
}
You then need to learn how to use the debugger and/or write simple Unit Tests.
Stepping through the code a line at a time and watching the values of the variables change will help you in this learning context.
Here are two strategies that you can use to breakdown nonsense code like that which you have sadly encountered in this "educational" context.
Black Box examination Strategy
Temporarily ignore the logic in the mystery function, we treat the function as a black box that we cannot see into.
Look at what data gets passed in, what data is returned.
So for the member function called mystery we have
What goes in? : int num
What gets returned : an int, so a whole number.
There are two places where data is returned.
Sometimes it returns k
Sometimes it returns -1
Now we move on.
White Box examination Strategy
As the code is poorly written, a black box examination is insufficient to interpret its purpose.
A white box reading takes examines the member function's internal logic (In this case, pretty much the for loop)
The for loop visits every element in the array called myStuff, starting at the end of the array
k is the number that tracks the position of the visited element of the array. (Note we count down from the end of the array to 0)
If the number stored at the visited element is less than num (which is passed in) then return the position of that element..
If none of elements of the array are less than num then return -1
So mystery reports on the first position of the element in the array (starting from the end of the array) where num is bigger than that element.
do you understand what a method is ?
this is pretty basic, the method mystery receives an int as a parameter and returns an int when you call it.
meaning, the variable m will be assigned the value that returns from the method mystery after you call it with n which is an int of some value.
"The part where I got stuck is trying to logically understand how a int m = mystery(n); How can a number equal a method?"
A method may or may not return a value. One that doesn't return a value has a return type of void. A method can return a primitive value (like in your case int) or an object of any class. The name of the return type can be any of the eight primitive types defined in Java, the name of any class, or an interface.
If a method doesn't return a value, you can't assign the result of that method to a variable.
If a method returns a value, the calling method may or may not bother to store the returned value from a method in a variable.
I am trying to learn recursion in Java and have an array that takes in continuous input until the Scanner reads in a 0.
From there I have a method that (attempts) to calculate the number of positive integers in the array using recursion. This is the first recursive function I have ever written and I keep getting a stackoverflow error.
I have read tutorials and I still can't wrap my head around the basic understanding of recursion.
public class reuncF {
private static int start = 0;
private static int end = 98;
public static void main(String[] args) {
input = input.nextDouble();
list[i] = numInput;
computeSumPositive(numList, count);
}
}
return positives += solve(numbers, count++);
}
}
You forgot to stop your recursion!
There has to be some case where computeSumPositive returns without calling itself again. Otherwise it'll just keep going forever, never getting back to you.
If you did it with a loop, the loop would look like this:
int positives = 0;
for (int i = 0; i < numList.length; ++i) {
if (numList[i] > 0) {
positives++;
}
}
To do that recursively, you just find out what are the variables used in the loop. They are i, numList and positives.
computeSumPositive(int i, double[] numList, int positives)
Then we take a look at what the loop does. First, it checks whether we went too far,
so our recursive function should do that too. It'll have to return instead of just falling through like the loop does. And obviously, it must return the result:
{
if (! (i < numList.length))
return positives;
The loop then does the test and maybe increments positives, so the recursive function should also do that:
if (numList[i] > 0) {
positives++;
}
At the end of the loop, i is updated:
i++;
The loop just starts over, but the recursive function will have to call itself. Of course, we want it to use the new value of i and positives, but fortunately we updated those, so now we can just do:
return computeSumPositives (i, numList, positives);
}
The tricky bit is that the values i, numList, and are local to each call. Each invocation of computeSumPositives can see only the arguments it were given. If it changes them, none of the other invocation can see that change.
EDIT: So if we, for reasons we can only speculate about, wanted desperately for computeSumPositive to take only 2 parameters, we would have to "split up" positives across each invocation. Each invocation knows whether or not its number was positive or not; all we have to do is add them. Then it looks like this:
computeSumPositive(int i, double[] numList)
{
if (! (i < numList.length))
return 0; // I didn't find any at index i
if (numList[i] > 0) {
// Theres one I found + however many my later
// invocations will find.
return 1 + computeSumPositive (i+1, numList);
} else {
// I didn't find any, but my later invocations might.
return computeSumPositive (i+1, numList);
}
}
I find it helpful, when dealing with recursion, to figure out the termination case first.
It looks like you are treating 'count' as an index. So you could check if your at the last index in the array, if so and if the value is positive return a 1, if the value is non-positive return a 0 - dont recurse anymore.
If your not at the last index, and the value is positive return a 1 + the recursive function call, or if the value is non-positive just continue to recurse.
This will still cause a stack overflow for large arrays.
The value of count++ is the same as the value of count; the program uses the value and then increments it. But the result is that computeSumPositive keeps calling itself with the same value of count, which leads to infinite recursion. Note that each time computeSumPositive calls another computeSumPositive, each call has its own copy of the parameters (like count) and the local variables; so incrementing one computeSumPositive's copy of count has no effect on the value of count used by other recursive calls.
Change count++ to count + 1, and also add a way to halt the recursion. (At some point, you will be calling computeSumPositive to look at zero integers, and at that point, it should just return 0 and not call itself. You need to think about: how do you test whether you've reached that point?)