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Alogrithm recursion codingbat

Recursion-2 > groupSum6
http://codingbat.com/prob/p199368
I modified the solution from the first one example where the condition of using 6 is not present.
Below working solution:
public boolean groupSum6(int start, int[] nums, int target) {
// Base case: if there are no numbers left, then there is a
// solution only if target is 0.
if (start >= nums.length) return (target == 0);
// Key idea: nums[start] is chosen or it is not.
// Deal with nums[start], letting recursion
// deal with all the rest of the array.
// Recursive call trying the case that nums[start] is chosen --
// subtract it from target in the call.
if (nums[start] == 6)
return groupSum6(start + 1, nums, target - nums[start]);
if (groupSum6(start + 1, nums, target - nums[start]))
return true;
// Recursive call trying the case that nums[start] is not chosen.
if (groupSum6(start + 1, nums, target)) return true;
// If neither of the above worked, it's not possible.
return false;
}
HOWEVER it is not working when I'd replace
if (nums[start] == 6)
return groupSum6(start + 1, nums, target - nums[start]);
with :
if (nums[start] == 6)
groupSum6(start + 1, nums, target - nums[start]);
//NOTE: missing return statement.
Then algo fails for arrays where the target is possible to get but without using 6. eg groupSum6(0, [5, 6, 2], 7) expected value false but returns true. takes 5+2, skipps 6, but as in description every 6 must be used.
My question is: how does the 'return' statement changes the flow of recursion

Because java is pass by reference you aren't passing the actual object when you pass parameters to a method. You are passing a reference to the objects. So when you pass a reference to your objects, but take out the return call, the reference never gets resolved back to the variables, and you essentially throw away the results of your recursive call
Try this simple program to see what I mean:
public static int foo(int x) {
x++;
if(x < 10) {
foo(x);
}
return x;
}
If we call System.out.println(foo(1)); this will print out 2, since the first x++ gets resolved, but you essentially throw away the results from all your recursive calls.
However if we change
if(x < 10) {
foo(x);
}
To:
if(x < 10) {
return foo(x);
}
The result will be 10 because we return the results from the recursive calls

Finding the largest element in an array using recursion in Java

This is what I have so far, but I'm confused on how to keep track of the index. I would change the parameters of the method, but I'm not allowed.
I can only use a loop to make another array. Those are the restrictions.
public class RecursiveFinder {
static int checkedIndex = 0;
static int largest = 0;
public static int largestElement(int[] start){
int length = start.length;
if(start[length-1] > largest){
largest = start[length-1];
int[] newArray = Arrays.copyOf(start, length-1);
largestElement(newArray);
}
else{
return largest;
}
}
/**
* #param args
*/
public static void main(String[] args) {
int[] array1 = {0,3,3643,25,252,25232,3534,25,25235,2523,2426548,765836,7475,35,547,636,367,364,355,2,5,5,5,535};
System.out.println(largestElement(array1));
int[] array2 = {1,2,3,4,5,6,7,8,9};
System.out.println(largestElement(array2));
}
}

Recursive method doesn't need to keep the largest value inside.
2 parameters method
Start to call with:
largestElement(array, array.length-1)
Here is the method:
public static int largestElement(int[] start, int index) {
if (index>0) {
return Math.max(start[index], largestElement(start, index-1))
} else {
return start[0];
}
}
The 3rd line of method is the hardest one to understand. It returns one of two elements, larges of the one of current index and of remaining elements to be checked recursively.
The condition if (index>0) is similar to while-loop. The function is called as long as the index remains positive (reaches elements in the array).
1 parameter method
This one is a bit tricky, because you have to pass the smaller array than in the previous iteration.
public static int largestElement(int[] start) {
if (start.length == 1) {
return start[0];
}
int max = largestElement(Arrays.copyOfRange(start, 1, start.length));
return start[0] > max ? start[0] : max;
}
I hope you do this for the study purposes, actually noone has a need do this in Java.

Try that for the upper class, leave the main method it's is correct.
public class dammm {
public static int largestElement(int[] start){
int largest = start[0];
for(int i = 0; i<start.length; i++) {
if(start[i] > largest){
largest = start[i];
}
}return largest;
}

If your goal is to achieve this by using recursion, this is the code that you need. It is not the most efficient and it is not the best way to deal with the problem but it is probably what you need.
public static int largestElement(int[] start){
int length = start.length;
if (start.lenght == 1){
return start[0];
} else {
int x = largestElement(Arrays.copyOf(start, length-1))
if (x > start[length-1]){
return x;
} else {
return start[length-1];
}
}
}
Imagine that you have a set of numbers you just have to compare one number with the rest of them.
For example, given the set {1,8,5} we just have to check if 5 is larger than the largest of {1,8}. In the same way you have to check if 8 is larger than the largest of {1}. In the next iteration, when the set one have one value, you know that that value is the bigger of the set.
So, you go back to the previous level and check if the returned value (1) is larger than 8. The result (8) is returned to the previous level and is checked against 5. The conclusion is that 8 is the larger value

One parameter, no copying. Tricky thing is, we need to pass a smaller array to the same method. So a global variable is required.
// Number of elements checked so far.
private static int current = -1;
// returns the largest element.
// current should be -1 when user calls this method.
public static int largestElement(int[] array) {
if (array.length > 0) {
boolean resetCurrent = false;
if (current == -1) {
// Initialization
current = 0;
resetCurrent = true;
} else if (current >= array.length - 1) {
// Base case
return array[array.length - 1];
}
try {
int i = current++;
return Math.max(array[i], largestElement(array));
} finally {
if (resetCurrent) {
current = -1;
}
}
}
throw new IllegalArgumentException("Input array is empty.");
}
If you can create another method, everything would be much simpler.
private static int recursiveFindLargest(int [] array, int i) {
if (i > 0) {
return Math.max(array[i], recursiveFindLargest(array, i-1));
} else {
return array[0];
}
}
public static int largestElement(int [] array) {
// For empty array, we cannot return a value to indicate this situation,
//all integer values are possible for non-empty arrays.
if (array.length == 0) throw new IllegalArgumentException();
return recursiveFindLargest(array, array.length - 1);
}

For this problem you really need to think about working with the base case. Take a look at some of the simple cases you would have to deal with:
If the array is length 1, then you return the only value
If the array is length 2, then you return the maximum of the two values
If the array is length 3, then ?
From the above we can get an idea of the structure of the problem:
if array.length == 1 then
return array[0]
else
return the maximum of the values
In the above if we have only one element, it is the maximum value in the list. If we have two values, then we have to find the maximum of those values. From this, we can then use the idea that if we have three values, we can find the maximum of two of them, then compare the maximum with the third value. Expanding this into pseudo code, we can get something like:
if array.length == 1 then
return array[0]
else
new array = array without the first element (e.g. {1, 2, 3} => {2, 3})
return maximum(array[0], largestElement(new array))
To explain the above a little better, think of execution like a chain (example for {1, 2, 3}).
Array: {1, 2, 3}, maximum(array[0] = 1, largestElement(new array = {2, 3}))
Array: {2, 3}, maximum(array[0] = 2, largestElement(new array = {3}))
Array: {3}, array[0] = 3 => length is 1 so return 3
The above then rolls back up the 'tree' structure where we get:
maximum (1, maximum(2, (return 3)))
Once you have the maximum value, you can use the sample principle as above to find the index with a separate method:
indexOf(array, maximum)
if array[0] == maximum then
return 0
else if array.length == 1 then
return -1
else
new array = array without the first element (e.g. {1, 2, 3} => {2, 3})
result = indexOf(new array, maximum)
return (result == -1) ? result : result + 1
For looking into this more, I would read this from the Racket language. In essence it shows the idea of array made purely from pairs and how you can use recursion to do iteration on it.
If you are interested, Racket is a pretty good resource for understanding recursion. You can check out University of Waterloo tutorial on Racket. It can give you a brief introduction to recursion in an easy to understand way, as well as walking you through some examples to understand it better.

You don't need to keep a largest variable outside your method - that's generally not a good practice with recursion which should return all context of the results.
When you think about recursion try to think in terms of a simple base case where the answer is obvious and then, for all other cases how to break it down into a simpler case.
So in pseduo-code your algorithm should be something like:
func largest(int[] array)
if array has 1 element
return that element
else
return the larger of the first element and the result of calling largest(remaining elements)
You could use Math.max for the 'larger' calculation.
It's unfortunate that you can't change the arguments as it would be easier if you could pass the index to start at or use lists and sublists. But your copying method should work fine (assuming efficiency isn't a concern).
An alternative to the algorithm above is to make an empty array the base case. This has the advantage of coping with empty arrays (by return Integer.MIN_VALUE):
int largest(int[] array) {
return array.length == 0
? Integer.MIN_VALUE
: Math.max(array[0], largest(Arrays.copyOfRange(array, 1, array.length)));
}

Here is working example of code with one method param
public int max(int[] list) {
if (list.length == 2) return Math.max(list[0], list[1]);
int max = max(Arrays.copyOfRange(list, 1, list.length));
return list[0] < max ? max : list[0];
}

private static int maxNumber(int[] arr,int n,int max){
if(n<0){
return max;
}
max = Math.max(arr[n],max);
return maxNumber(arr,n-1,max);
}

Recursion confusion

I am writing a function according to the following guidelines:
Given an array of ints, is it possible to choose a group of some of the ints, beginning at the start index, such that the group sums to the given target? However, with the additional constraint that all 6's must be chosen. (No loops needed.)
groupSum6(0, {5, 6, 2}, 8) → true
groupSum6(0, {5, 6, 2}, 9) → false
groupSum6(0, {5, 6, 2}, 7) → false
This is the solution:
public boolean groupSum6(int start, int[] nums, int target) {
if (start == nums.length) {
if (target == 0) {
return true;
}
return false;
}
if (nums[start] == 6) {
return groupSum6(start + 1, nums, target - nums[start]);
}
if (groupSum6(start + 1, nums, target - nums[start])) {
return true;
}
return groupSum6(start + 1, nums, target);
}
I am a little confused about why this works. I understand how it adds 6s, but where are the other numbers tested to see if they will add up to the target after the 6s have been added? Where are other non-6 numbers added?

The reason this works is that the recursive call always checks to see if the number at the current index is a 6 and subtracts that from the target. So the order of evaluation is:
1)
if (start == nums.length) {
if (target == 0) {
return true;
}
return false;
}
Check to see if the passed index is the length of the array (so this would mean the index is BEYOND the bounds of the array - the last index of the array would be nums[nums.length - 1] ). If yes, AND if the target is 0, return true. Otherwise return false, because there are no more values to check
2)
if (nums[start] == 6) {
return groupSum6(start + 1, nums, target - nums[start]);
}
Check if the number at the index is 6. If it is, subtract 6 from the target, add one to the index, and check the remaining values.
3) Otherwise...
if (groupSum6(start + 1, nums, target - nums[start])) {
return true;
}
Evaluate if the rest of the array works to add up to the target. If it does return true. The key is to notice that this step will always happen AFTER we check if the value is a 6. Essentially here you are looking for a solution that COUNTS the number in the start index. If a solution is found we can end. If no solution is found using the number at num[start], then we go on to:
4)
return groupSum6(start + 1, nums, target);
Checking for a solution that exists when we DON'T use the number at num[start].
The key is that each time the recursive call is made the check for a 6 is done first ( assuming you aren't beyond the bounds of the array).

The idea is to test all the possible subarray options, something like "what happen if i get next element?" and... "what happen if i don't?".
So, for any element in the array your are making two recursive calls (two options, take it or not) and... if one of them is OK the solution is reached (so return true).
In the next recursive call you pick the number, so you call with the next index element (start+1) and substract the picked number from the target (imagine your target is 8 and the current element is 2... the recursive call is to check the next numbers with target 8-2= 6).
if (groupSum6(start + 1, nums, target - nums[start])) {
return true;
}
The next recursive call is the same but you don't pick the current number so... target will be the same (in the previous example you will check the next number with target 8);
return groupSum6(start + 1, nums, target);
And... here it comes the 6 restriction... if you find a 6 then you have no more options than to pick the number so... you put that condition first (and in this scenario there is only one call because you have no options):
if (nums[start] == 6) {
return groupSum6(start + 1, nums, target - nums[start]);
}

Just do this check if the number is 6 and then decide to skip it
public boolean groupSum6(int start, int[] nums, int target) {
//exit condition and if target becomes 0
if(start >= nums.length) return (target ==0);
// subtracting the number at start from target and make a recursive //call to groupSum6
if(groupSum6(start+1 , nums , target - nums[start])) return true;
//check if the number at start is 6 or not then decide to skip it
if(nums[start] != 6 && groupSum6(start+1 , nums , target)) return true;
//if target does not becomes 0
return false;
}

Java Recursion compilation error

I am a fresh student in computer science and currently we study Java recursion. Unfortunately, the academy only explains the following regarding this topic:
What recursion means.
There are 2 types of cases when using a recursive algorithm: base cases and recursive cases and their purpose.
An example of factorial and Fibonacci implementation using recursion.
Now I got the following exercise:
Two integer numbers will be called "strangers" if their greatest common divisor (aka GTC) is ONLY 1". For example, the numbers 8 and 9 are "strangers" because their GTC is 1. However, 8 and 9 are not "strangers" because their GTC is 2.
Please implement a recursive method which receives an array of integers, and returns "true" if every pair numbers in this array are strangers, and "false" otherwise.
Method signature must be as follows:
public boolean checkGCD(int[] values)
For example:
{3, 5, 7, 11} -> method will returns true.
{4, 7, 8, 9} -> method will returns false because 4 and 8 are not strangers.
For assistance, you can use the following method for finding GTC (Euclidean algorithm):
private static int gcd(int n, int m){
if (m==0)
return n;
return gcd(m,n % m);
}
In addition, the method checkGCD(int[] values) should be overloaded...
Loops cannot be used!
The above can be done very easily with a nested loop, but I must use recursion!
I understand that I need to use an overloaded method which gets the array, lo index and hi index.
So this is what I came up in mind:
######
Base case: if there is at least one pair of numbers in the array which are not strangers, method returns false (no need to continue the comparison...).
######
Comparison will be done in the following way: lo index points to the 1st cell -> hi index points to the 2nd cell -> comparing -> hi index is incremented by 1 until it reaches the last cell of the array.
Then, lo index is incremented by 1, and then repeating the above.
So bottom line, I should compare the first cell to all consecutive cells, compare the 2nd to all consecutive cells, the 3rd etc...
########
If all pairs of numbers are strangers, I need something else to stop recursion. Therefore, if all pairs are strangers, it means that lo index and hi index will eventually point to the last cell (cause both lo and hi index has incremented gradually, and they reach the last array cell after all comparisons turned out to be OK i.e strangers).
The following is the overloaded function:
private static boolean checkGCD(int[] values, int lo, int hi)
{
if ( (gcd(values[lo], values[hi]) )!= 1 )
return false;
else if (lo < values.length-1 && hi < values.length-1)
return checkGCD(values, lo, hi+1);
else if (lo < values.length-2 && hi == values.length-1)
return checkGCD (values, lo+1, lo+2);
if (lo == values.length-1 && hi == values.length-1)
return true;
} -> Compiler says "missing return statement"**
The following is the method the exercise requires to have, and it basically just calls the overloaded method which does everything recursively.
public static boolean checkGCD(int[] values)
{
return checkGCD(values, 0, 1);
}
When I try to compile, I get "missing return statement" which points to the close bracket in the overloaded function
But I do use "return" in the overloaded function.
Please clarify how to fix. I am sure after compilation error, the above overloaded function is still not OK.

You get the compiler error because, if every if fails, the method does not return anything. The solution is add the appropriate return statement when the final if fails.

Not to give the answer away, but here's a strong hint: the base case is an array with two elements. All larger arrays are recursive cases.

There's a general pattern for going through a list with a recursion (pseudocode):
Result f(List f) {
if(f is an empty list) {
return Result for an empty list;
} else {
return (Result for head of list) merged with f(tail of list)
}
}
Since you're using arrays, rather than a type with convenient head() and tail() methods, you could pass in an index to say how much of the array you want to process. When index == array.length you are processing an "empty list".
boolean allMembersPositive(int[] array, int index) {
if(index == array.length) {
return true;
} else {
return (array[index] >=0) && (allMembersPositive(index + 1));
}
}
It's a small step to adapt this to consume two array items per recursive call.

I can guarantee you that when you understand recursion clearly you are going to level up your programming skills.
I recommend reading these URLs:
http://howtoprogramwithjava.com/java-recursion/
http://danzig.jct.ac.il/java_class/recursion.html
Now, lets move back to your questions. I think that is one possible way to implement it:
public class Test {
public static void main(String[] arguments) {
int[] strangers = { 3, 5, 7, 11 };
int[] acquaintances = { 4, 7, 8, 9};
boolean verifyStrangers = checkGCD(strangers);
boolean verifyAcquaintances = checkGCD(acquaintances);
System.out.println(verifyStrangers);
System.out.println(verifyAcquaintances);
}
public static boolean checkGCD(int[] values) {
return checkGCD(values, 0, 1);
}
/*
* I'm really not sure why your professor wants this method signature: "checkGCD(int[] values, int i, int j)"
* I'm coding what I understood from the problem.
*/
private static boolean checkGCD(int[] values, int i, int j) {
boolean result = true;
if (gcd(values[i], values[j]) != 1){
result = false;
}
j++;
if (j < values.length ) {
result = result && checkGCD(values, i, j);
}
return result;
}
private static int gcd(int n, int m) {
if (m == 0)
return n;
return gcd(m, n % m);
}
}

I managed to solve the exercise.
public static int gcd(int n, int m)
{
if (m==0)
return n;
return gcd(m,n % m);
}
private static boolean checkGCD(int[] values, int lo, int hi)
{
// System.out.println("lo is " + lo + " hi is " + hi);
// System.out.println("");
// System.out.println("[lo] is " + values [lo] + " [hi] is " + values[hi]);
// System.out.println("");
if ( (gcd(values[lo], values[hi]) )!= 1 )
return false;
if (lo < values.length-1 && hi < values.length-1)
return checkGCD(values, lo, hi+1);
if (lo < values.length-2 && hi == values.length-1)
return checkGCD(values, lo+1, lo+2);
if (lo == values.length-2 && hi == values.length-1)
return true;
return true;
}
public static boolean checkGCD(int[] values)
{
return checkGCD(values, 0, 1);
}
:-)

How do I use a recursive algorithm to determine whether the array contains two elements that sum to a given integer?

Okay guys thanks for all the help! Special thanks to #pjs for giving me an idea of how to do it. Here is my new code, but for some reason it won't reach one of the base cases. Sorry if I deleted the old code, this is the first time I posted here and I am not sure if I should answer my own question with the new code.
//initialized int start = 0
//initialized int end = length of the array
//here goes the constructor
public boolean kPairSum(Integer k) {
if (sortedIntegerArray.length < 2) { //if array is less than two return false
return false;
}
else if (start == end) { //once the start and the end meets. This is the base case that doesn't seem to work for me.
return false;
}
else {
int currentStart = sortedIntegerArray[start]; //get first int in the array
int currentEnd = sortedIntegerArray[end-1]; //get the very last int in the array
int sum = currentStart + currentEnd; //get the sum
if (k.equals(sum)) { //compare sum and k if equal
return true;
}
else if (sum <k) { //if sum is less than k then increment value of start
start++;
return kPairSum(k);
}
else if (sum > k) { //if sum is greater than k then it decrements value of end
end--;
return kPairSum(k);
}
else { //not sure if this is right, should I just get rid of the else if statement for sum > k and change it to just an else? I wrote this down cause it has to return a type of boolean.
return kPairSum(k);
}
}

Your array is called sortedIntegerArray, but you don't seem to be leveraging that fact.
Start by summing the two ends of the array. If the sum is smaller than k, one of the two elements of the sum has to be larger. You can only get a larger value by incrementing the lower index because the elements are ordered. Similarly, if the sum is larger than k, one of the two elements has to be smaller, so you need to decrement the upper index. In either case, the structure of the problem is the same but you're now operating on a subset of the array specified by which of the indices you incremented/decremented. Base cases are that you found two values which sum to k, or that the indices have met somewhere. The recursion should leap out at you. Since each recursive call either increments or decrements a boundary index until they meet in the middle, it's O(n).

Your recursive call is never invokes:
if (sum == k) { //compare to given k
return true;
} else if (xx == sortedIntegerArray.length-1 || sum != k) {
return false;
}
Note that you basically have two choices: sum==k, and then - return true, or sum!=k - and then return false. The recursive invokation is not reachable.
An O(n) (average case) solution can be achieved using a hash table. The idea is to add each element to the hash table while iterating, and check if there is an existing element that completes to k.
for each element e in arr:
if e is in table:
return true
table.add(k-e)
return false //no pair was found that sums to k
A recursive solution that checks all pairs, is basically brute force that is similar to a nested for loop.
//i is the index we are now checking, b is a boolean indicating we have already reduced one element
kSum(k,i,b):
if i == arr.length
return false
if b == true && k == 0:
return true
if b == false:
return kSum(k-arr[i],i+1,true) || kSum(k,i+1,false)
else:
return kSum(k,i+1,b)

I have two implementations here:
One I initially got to work and with Amit answer, I improved it further. It also prints/return the indices that make up the sum. works with both sorted and unsorted array in O(n). ofcourse, this is not recursive.
public static void sumArray2(int[] arr, int sum){
Map <Integer, Integer> map = new HashMap<>();
for (int i=0; i < arr.length;i++){
map.put(arr[i], i);
}
for (int i =0; i < arr.length;i++){
int diff = sum-arr[i];
if (map.containsKey(diff) && i!=map.get(diff)) {
System.out.printf("The two indices are %s and %s%n ",i,map.get(diff));
return ;
}
}
System.out.printf("The sum:%s cannot be formed with given array:%s",sum,Arrays.toString(arr));
return ;
}
//returns a boolean if sum could be formed.
public static boolean sumArray3(int[] arr, int sum){
Map <Integer, Integer> map = new HashMap<>();
for (int i =0; i < arr.length;i++){
int diff = sum-arr[i];
if (map.containsKey(arr[i])) {
System.out.printf("The two indices are %s and %s%n ",i,map.get(arr[i]));
return true;
}
map.put(diff,i);
}
System.out.printf("The sum:%s cannot be formed with given array:%s",sum,Arrays.toString(arr));
return false;
}

don't know how to add formatted comment, so here is enhanced version, than Amit provided, works with O(n) :)
def check(source, need):
target = [need-i for i in source]
target.reverse()
i = 0
j = 0
# walk thru lists same "merge" to find a match
for i in xrange(0, len(source)):
while j < len(target) and source[i] > target[j]:
j=j+1
if i != len(source)-j-1 and j < len(target) and source[i] == target[j]:
return True
return False