I have an enormous directed graph I need to traverse in search for the shortest path to a specific node from a given starting point. The graph in question does not exist explicitly; the child nodes are determined algorithmically from the parent nodes.
(To give an illustration: imagine a graph of chess positions. Each node is a chess position and its children are all the legal moves from that position.)
So I have a queue for open nodes, and every time I process the next node in the queue I enqueue all of its children. But since the graph can have cycles I also need to maintain a hashset of all visited nodes so I can check if I have visited one before.
This works okay, but since this graph is so large, I run into memory problems. All of the nodes in the queue are also stored in the hashset, which tends to be around 50% of the total number or visited nodes in practice in my case.
Is there some magical way to get rid of this redundancy while keeping the speed of the hashset? (Obviously, I could get rid of the redundancy by NOT hashing and just doing a linear search, but that is out of the question.)
I solved it by writing a class that stores the keys in a list and stores the indices of the keys in a hashtable. The next node "in the queue" is always the the next node in the list until you find what you're looking for or you've traversed the entire graph.
class IndexMap<T>
{
private List<T> values;
private LinkedList<int>[] buckets;
public int Count { get; private set; } = 0;
public IndexMap(int capacity)
{
values = new List<T>(capacity);
buckets = new LinkedList<int>[NextPowerOfTwo(capacity)];
for (int i = 0; i < buckets.Length; ++i)
buckets[i] = new LinkedList<int>();
}
public void Add(T item) //assumes item is not yet in map
{
if (Count == buckets.Length)
ReHash();
int bucketIndex = item.GetHashCode() & (buckets.Length - 1);
buckets[bucketIndex].AddFirst(Count++);
values.Add(item);
}
public bool Contains(T item)
{
int bucketIndex = item.GetHashCode() & (buckets.Length - 1);
foreach(int i in buckets[bucketIndex])
{
if (values[i].Equals(item))
return true;
}
return false;
}
public T this[int index]
{
get => values[index];
}
private void ReHash()
{
LinkedList<int>[] newBuckets = new LinkedList<int>[2 * buckets.Length];
for (int i = 0; i < newBuckets.Length; ++i)
newBuckets[i] = new LinkedList<int>();
for (int i = 0; i < buckets.Length; ++i)
{
foreach (int index in buckets[i])
{
int bucketIndex = values[index].GetHashCode() & (newBuckets.Length - 1);
newBuckets[bucketIndex].AddFirst(index);
}
buckets[i] = null;
}
buckets = newBuckets;
}
private int NextPowerOfTwo(int n)
{
if ((n & n-1) == 0)
return n;
int output = 0;
while (n > output)
{
output <<= 1;
}
return output;
}
}
The old method of maintaining both an array of the open nodes and a hashtable of the visited nodes needed n*(1+a)*size(T) space, where a is the ratio of nodes_in_the_queue over total_nodes_found and size(T) is the size of a node.
This method needs n*(size(T) + size(int)). If your nodes are significantly larger than an int, this can save a lot.
I am trying to find the K-th largest element in a Binary Search Tree using reverse inorder approach by using a counter. Here is what I have implemented:
int klargest(Node root,int k,int count)
{
if(root != null)
{
klargest(root.right,k,count);
count++;
if(count == k)
return root.data;
klargest(root.left,k,count);
}
return -1;
}
But the issue is that when count = k, the code does not return the answer to the caller function but instead to a sub-call. Due to this, the answer is lost. In other words, the recursion does not stop there and it keeps on going until all the nodes are visited. In the end, I get the answer -1. What I want is that the recursion should end when count = k and the required answer should be returned to the caller function. How can I do this?
Note: I neither want to use a global variable nor an iterative approach.
Actually, you do not return your node - the recursive call results are ignored. Rewrite it so it returns a Node:
Node klargest(Node root,int k,int count)
{
Node result = null;
if(root != null)
{
result = klargest(root.right,k,count);
if (result != null)
return result;
count++;
if(count == k)
return root;
result = klargest(root.left,k,count);
}
return result;
}
You can use this approach:
int kthLargest(Node node, int k) {
int rightCount = count(node.right);
if (k <= rightCount) {
return kthLargest(node.right, k);
} else if (k == rightCount+1) {
return node.data;
} else {
return kthLargest(node.left, k - rightCount + 1);
}
}
int count(Node node) {
if (node != null) {
return count(node.left) + count(node.right) + 1;
}
return 0;
}
Given a Binary Tree of size N, find size of the Largest Independent Set(LIS) in it. A subset of all tree nodes is an independent set if there is no edge between any two nodes of the subset. Your task is to complete the function LISS(), which finds the size of the Largest Independent Set.
I came up with this recursive solution.
int rec(struct Node *root,bool t)
{
if(root==NULL)
return 0;
if(t==true)
{
return max(1+rec(root->left,!t)+rec(root->right,!t),rec(root->left,t)+rec(root->right,t));
}
else
{
return max(rec(root->left,!t)+rec(root->right,!t),rec(root->left,t)+rec(root->right,t));
}
}
int LISS(struct Node *root)
{
int x,y;
y=rec(root,true);
return y;
}
To solve this problem via DP, I modified the code as follows, but then it gives wrong answer.
It doesn't even work with Binary tree with distinct elements.
map<int,int> mm;
int rec(struct Node *root,bool t)
{
if(root==NULL)
return 0;
if(mm.find(root->data)!=mm.end())
return mm[root->data];
if(t==true)
{
mm[root->data]=max(1+rec(root->left,!t)+rec(root->right,!t),rec(root->left,t)+rec(root->right,t));
return mm[root->data];
}else
{
mm[root->data]=max(rec(root->left,!t)+rec(root->right,!t),rec(root->left,t)+rec(root->right,t));
return mm[root-s>data];
}
}
int LISS(struct Node *root)
{
//Code here
mm={};
int y=0;
y=rec(root,true);
return max(x,y);
}
What's the mistake?
You have two states in your function but you are memoizing only one state. Let's say for root x,
rec(x,true) = 5 and
rec(x,false) = 10 .
You calculated the rec(x, true) first and saved it in your map "mm" as mm[x] = 5.
So when you are trying to get the value of rec(x, false) it is getting the value of rec(x, true) which is 5.
Hi. I am having trouble writing this method (in the photo) in a recursuve format. The method gets the amount of occurences of a given element in the binary search tree.
To solve this recursively, I was trying to implement it with a private helper method of the same name, like this:
public int count(){
count = 0;
if (root == null)
return count;
return count (root.getInfo());
private int count(T element){
(Basically the same code you see in the photo)
}
but I ended up with overflow errors. Would you mind taking a look and telling me how I can structure this method recursively?
Cheers, and thanks.
A tentative implementation may looks like this.
public int count(T element, T root){
if(element == null) {
return 0;
}
int count = 0;
int compare = element.compareTo(root.getInfo());
if(compare == 0){
count++;
}
count += count(element, root.getLeft());
count += count(element, root.getRight());
return count;
}
count(item, root);
I have just been studying the concept of recursion and I thought that I would try a simple example. In the following code, I am attempting to take the numbers: 1, 2, 3, 4, 5, and add them together using recursion. I expected the result to be 15, but my code is returning 16.
What am I doing wrong?
Code:
static void Main(string[] args)
{
Console.WriteLine(Sum(5));
Console.Read();
}
static int Sum(int value)
{
if (value > 0)
{
return value + Sum(value - 1);
}
else
{
return 1;
}
}
You're returning 1 in the else clause. You should be returning 0:
else
{
return 0;
}
If the value is not greater than zero, why would you return one in the first place?
Your code executes as follows:
Sum --> 5
Sum --> 4
Sum --> 3
Sum --> 2
Sum --> 1
Sum --> 0
1 <---
2 <---
4 <---
7 <---
11 <---
16 <---
Check your base case.
Others already noted the error, and I will elaborate on recursion.
Although C# does not currently perform tail call optimization (although IL has special tail instruction), it's worth mentioning that tail recursion is generally a good thing.
Tail recursion is a special case of recursion in which the last operation of the function, the tail call, is a recursive call. Since the last call is the recursive call there is no need to preserve stack frame of the calling function and the compiler can easily use this information to generate machine instruction such that the stack doesn't grow at all. So it can basically turn recursive function into an iterative one.
Rewriting your code to support tail recursion can be done as follws:
static int Sum(int result, int value)
{
if(value == 0)
return result;
return Sum(result + 1, value - 1);
}
static int Sum(int value)
{
if (value > 0)
{
return value + Sum(value - 1);
}
else
{
return 0; //Change this.
}
}
That's because, when the value is = 0, you return 1. Then it get's added.
Sum's "else" clause should return 0.
I always prefer to put the terminating case(s) up front so they're obvious, and I have a violent near-psychopathic hatred of "if cond then return a else return b" constructs. My choice would be (making it clear that it won't work properly for negative numbers):
static unsigned int Sum(unsigned int value) {
if (value == 0)
return 0;
return value + Sum(value - 1);
}
I believe that's far more readable than a morass of braces and control flow.
The others have already answered that question, but when I work with recursion, one of the things I like to do to check that it works is to use check the base case and one additional case. I your case I would test it with 1, which would yield 2. Since this is obviously wrong you might want to check for 0 which is not going to use any recursion and so it should be obvious that the error lies in the base class.
In general recursion is easier to reason about, since you can list the limited number of things you need to check, but it does initially require a leap of faith since your intuition will be wrong. Just test the edge cases and trust the math it will never fail.
int summation(int num){
if (num==1)
return 1;
return summation(num-1)+num;
}
I'm pretty sure the problem is because you want your recursion to terminate when value == 1, and it's currently terminating when value == 0.
Your terminating expression is at issue. When value == 0 (or lower), it should return a 0 rather than 1. For sake of efficiency (which, let's admit it here, obviously isn't a concern, otherwise recursion wouldn't have been used for this task), you should terminate the recursion at value == 1 and return a literal 1 to save one unnecessary level of recursion.
using System;
using NUnit.Framework;
namespace Recursion
{
[TestFixture()]
public class Test
{
[Test()]
public void TestSum ()
{
Assert.AreEqual (Sum (new int[] { }), 0);
Assert.AreEqual (Sum (new int[] { 0 }), 0);
Assert.AreEqual (Sum (new int[] { 1 }), 1);
Assert.AreEqual (Sum (new int[] { 1, 2, 3, 4, 5 }), 15);
}
public int Sum(int[] head)
{
if (head.Length == 0) return 0;
int[] tail = new int[head.Length - 1];
for (int i = 1; i < head.Length; i++)
{
tail [i-1] = head [i];
}
return head[0] + Sum (tail);
}
}
}
It could also be written like this:
public static int sum(int n){
int total;
if(n==1){
total =1;
}else{
total = sum(n-1)+n;
}
return total;
}
Actually, I think you don't need to check case else because
public static int sum(int number){
if(number > 0){
return number + sum(--number);
}
return number; // return 0 so that's why you don't need check else condition
}
To begin at the end, a recursive Sum method looks like this:
// version 3
public static int Sum(int startRange, int endRange)
{
if (endRange > startRange)
{
return endRange + Sum(startRange, endRange - 1);
}
if (endRange < startRange)
{
return startRange + Sum(endRange, startRange - 1);
}
return endRange;
}
Hardcoding the startRange to be 0 gives us:
// version 2
public static int Sum(int range)
{
if (range > 0)
{
return range + Sum(0, range - 1);
}
if (range < 0)
{
return Sum(range, -1);
}
return range;
}
...and if you want to limit the method to positive numbers only, there's no need for a sign:
// version 1
public static unsigned int Sum(unsigned int range)
{
if (range > 0)
{
return range + Sum(0, range - 1);
}
return range;
}
I hope this helps give more of an insight into summing number ranges via recursion.
static int Sum(int[] addends)
{
if (addends.Length == 1)
{
return addends[0];
}
else
{
int tailIndex = addends.Length - 1;
var subArray = addends[0..tailIndex];
return addends[tailIndex] + Sum(subArray);
}
}
Try this code:
def sumr(n):
if n==0:
return n
return n+sumr(n-1)