Building a segment tree in c++ - c++

I am trying to build a segment tree in c++. Following the recursive function for the same:
int buildTree(int node,int start,int end,int tree[])
{
// printf("Node is: %d\n",node);
printf("start: %d\tend:%d\tnode:%d\t\n",start,end,node);
if ( start == end )
{
// printf("start: %d,node: %d,array[start] : %d\n",start,node,array[start] );
tree[node] = array[start];
return array[start];
}
else
{
int mid = ( start + end ) / 2;
buildTree(2 * node ,mid + 1,end,tree);
buildTree(2 * node + 1,start,mid,tree);
tree[node] = tree[ 2 * node ] + tree[ 2 * node + 1 ];
return tree[node];
}
}
The array is globally defined:
int array[] = {1,2,3,4,5};
The tree after following call:
int main(int argc, char const *argv[])
{
int tree[100];
buildTree(0,0,4,tree);
for (int i = 0; i < 9; ++i)
{
printf("%d : %d\n",i, tree[i]);
}
return 0;
}
gives the output:
start: 0 end:4 node:0
start: 3 end:4 node:0
start: 4 end:4 node:0
start: 3 end:3 node:1
start: 0 end:2 node:1
start: 2 end:2 node:2
start: 0 end:1 node:3
start: 1 end:1 node:6
start: 0 end:0 node:7
0 : 15
1 : 6
2 : 3
3 : 3
4 : 474810352
5 : 32766
6 : 2
7 : 1
8 : 0
So, the nodes 4 and 5 are never processed. Where am I doing wrong? I think I am having hard time with recursion.

I build a segment tree using somehow the same implementation.
You should call the function buildTree with initial node = 1.
buildTree(1,0,4,tree);
This should fix the error.
Also most of the segment tree implementation codes use the node (2*node) for the range (start -> mid) and the node (2*node+1) for the range(mid+1 -> end).
I think it's a matter of convention. However sticking to the convention makes it easier for you to debug your code, and easier for other programmers to understand it.
So you can rewrite the recursive calls as:
buildTree(2 * node ,start,mid,tree);
buildTree(2 * node + 1,mid+1,end,tree);
Instead of:
buildTree(2 * node ,mid + 1,end,tree);
buildTree(2 * node + 1,start,mid,tree);

Related

Construct Binary Tree from Parent Array test case failing

Link of the question-[Link][1]
Basically we are given an array of integers and it's size. Question is to construct a binary tree from it. Each index corresponds to data stored in a node, and the value of that index is the data of the parent. Value of the root node index would always be -1 as there is no parent for root. The Output will be the sorted level order traversal of the tree.
Now my approach is that I parse the array from 1 to n(not the 0th element/root node), and for each element, I get it's parent using the first function, and insert the child accordingly. But one particular test case is failing. Maybe the website's own output is not correct. I will post everything below:-
Example test case-
Size of array-7
Elements- -1 0 0 1 1 3 5
Output- 0 1 2 3 4 5 6
Particular test case(which is my doubt)-
Size of array- 42
Elements-
3 19 1 41 35 29 27 11 17 23 9 15 33 13 39 23 19 25 21 1 33 15 31 21 5 7 37 29 7 11 31 39 -1 27 3 9 25 17 13 41 37 35
Website's output- 32
My output - 0
Functions
void getParent(Node* root, int val, Node* &main)
{
if(root==NULL) return;
if(root->data==val){
main=root;
return;
}
getParent(root->left,val,main);
getParent(root->right,val,main);
}
Node *createTree(int parent[], int n)
{
if(n==0) return NULL;
Node * root=new Node(0);
for(int i=1;i<n;i++)
{
Node* main=NULL;
getParent(root,parent[i],main);
//main has the parent
Node* child=new Node(i);
if(main==NULL) break;
if(main->left==NULL)
{
main->left=child;
}
else if(main->right==NULL)
{
main->right=child;
}
}
return root;
}
[1]: https://www.geeksforgeeks.org/construct-a-binary-tree-from-parent-array-representation/
[2]: https://i.stack.imgur.com/0fRmn.png
Not sure what you are doing with your getParent method. Also you are initiating a root node with value 0 and not doing anywith it in the loop and then finally you return the root. I suspect your root will always have a value 0.
The solution is very simple actually. You initialize an array of nodes with each node's value as the index of the array. For example for an array of size 5, you create an array of 5 nodes with each node having a value of the index at which it is located.
Then next step is go through the parent array and see if the node located at parent[i] has either left or right "available", if yes assign the node accordingly.
the code is :
Node* createTree(int parent[], int n) {
Node** nodes = new Node*[n];
for ( int i = 0; i < n; i++ )
nodes[i] = new Node(i);
int rootIndex = 0;
for ( int i = 0; i < n; i++ ) {
if ( parent[i] == -1 ) {
rootIndex = i;
} else {
if ( nodes[parent[i]] -> left == NULL ) {
nodes[parent[i]] -> left = nodes[i];
} else if ( nodes[parent[i]] -> right == NULL ) {
nodes[parent[i]] -> right = nodes[i];
}
}
}
return nodes[rootIndex];
}

Decreasing Loop Interval by 1 in C/C++

Let's say I have 15 elements. I want to group them such a way that:
group1 = 1 - 5
group2 = 6 - 9
group3 = 10 - 12
group4 = 13 - 14
group5 = 15
This way I'll get elements in each group as below:
group1 = 5
group2 = 4
group3 = 3
group4 = 2
group5 = 1
As you can see loop interval is decreasing.
I took 15 just for an example. In actual programme it's user driven parameter which can be anything (hopefully few thousand).
Now what I'm looking for is:
Whatever is in group1 should have variable "loop" value 0, group2 should have 1, group3 should have 2 and so on... "loop" is an int variable which is being used to calculate some other stuff.
Let's put in other words too
I have an int variable called "loop". I want to assign value to it such a way that:
First n frames loop value 0 next (n -1) frames loop value 1 then next (n - 2) frames loop value 2 all the way to loop value (n - 1)
Let's say I have 15 frames on my timeline.
So n will be 5 ====>>>>> (5 + 4 + 3 + 2 + 1 = 15; as interval is decreasing by 1)
then
first 5 frames(1 - 5) loop is 0 then next 4 frames(6 - 9) loop is 1 then next 3 frames(10 - 12) loop is 2 then next 2 frames(13 - 14) loop is 3 and for last frame(15) loop is 4.
frames "loop" value
1 - 5 => 0
6 - 9 => 1
10 - 12 => 2
13 - 14 => 3
15 => 4
I've tried with modulo(%). But the issue is on frame 12 loop is 2 so (12 % (5 - 2)) remainder is 0 so it increments loop value.
The following lines are sample code which is running inside a solver. #loop is by default 0 and #Frame is current processing frame number.
int loopint = 5 - #loop;
if (#Frame % loopint == 0)
#loop += 1;
If I understand this correctly, then
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int main(int argc, char *argv[]) {
int n = atoi(argv[1]);
for(int i = 1; i <= n; ++i) {
printf("%d: %f\n", i, ceil((sqrt(8 * (n - i + 1) + 1) - 1) / 2));
}
}
is an implementation in C.
The math behind this is as follows: The 1 + 2 + 3 + 4 + 5 you have there is a Gauß sum, which has a closed form S = n * (n + 1) / 2 for n terms. Solving this for n, we get
n = (sqrt(8 * S + 1) - 1) / 2
Rounding this upward would give us the solution if you wanted the short stretches at the beginning, that is to say 1, 2, 2, 3, 3, 3, ...
Since you want the stretches to become progressively shorter, we have to invert the order, so S becomes (n - S + 1). Therefore the formula up there.
EDIT: Note that unless the number of elements in your data set fits the n * (n+1) / 2 pattern precisely, you will have shorter stretches either at the beginning or in the end. This implementation places the irregular stretch at the beginning. If you want them at the end,
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int main(int argc, char *argv[]) {
int n = atoi(argv[1]);
int n2 = (int) ceil((sqrt(8 * n + 1) - 1) / 2);
int upper = n2 * (n2 + 1) / 2;
for(int i = 1; i <= n; ++i) {
printf("%d: %f\n", i, n2 - ceil((sqrt(8 * (upper - i + 1) + 1) - 1) / 2));
}
}
does it. This calculates the next such number beyond your element count, then calculates the numbers you would have if you had that many elements.

How do I convert this recursion into iterative DP?

I am trying to solve this problem :TRT.
Here is what I have done so far:
I designed a recursion for given problem and used memoization to get the solution accepted.
int recur(int l,int r,int level)
{
if(l==r)
return level*a[l];
if(dp[l][r])
return dp[l][r];
return dp[l][r]=max(level*a[l]+recur(l+1,r,level+1),level*a[r]+recur(l,r-1,level+1));
}
I am trying to solve this problem by bottom up dynamic programming but I can't think of the approach, this happens with most of the dynamic programming problems I am solving , I am able to design the recursion but fail at building the iterative dp. Can someone please help me with the approach to iterative dp solution once I have figured out the recursion ?
Edit: My bottom up DP solution based on Tempux's explanation:
int solve()
{
REP(i,n)
{
dp[i][i]=n*a[i];
}
REPP(i,1,n)
{
for(int j=0;j+i<n;j++)
{
dp[j][j+i]=max((n-i)*a[j]+dp[j+1][j+i],(n-i)*a[j+i]+dp[j][j+i-1]);
}
}
return dp[0][n-1];
}
Generally you just have to fill the values that are independent first (base cases). Then fill the values that are dependent on the values you have filled before.
In this case when l==r you have an independent value. So you just fill these first: [0][0] [1][1] [2][2] ... [n-1][n-1].
Now you can see that value of [l][r] is dependent on [l+1][r] and [l][r-1]. So now you can fill the values of [0][1] [1][2] [2][3] ... [n][n-1].
[0][1] is dependent on [0][0] and [1][1] which you have filled before
[1][2] is dependent on [1][1] and [2][2] which you have filled before
....
So now you recognize a pattern. You can fill the whole table if you proceed diagonally.
0 * * * * 0 1 * * * 0 1 2 * * 0 1 2 3 *
* 0 * * * * 0 1 * * * 0 1 2 * * 0 1 2 3
* * 0 * * * * 0 1 * * * 0 1 2 * * 0 1 2
* * * 0 * * * * 0 1 * * * 0 1 * * * 0 1
* * * * 0 * * * * 0 * * * * 0 * * * * 0
Here is one possible implementation:
for ( int d=0; d<=n-1; ++d ){
for ( int l=0; l<=n-1; ++l ){
int r = l+d;
if ( r >= n )
break;
int level = n-(r-l);
if ( l==r ){
dp[l][r] = level*v[l];
} else {
dp[l][r] = max( level*v[l] + dp[l+1][r],
level*v[r] + dp[l][r-1] );
}
}
}

Error in Implementation of Dijkstra's Algorithm

I am trying to attempt Dijkstra's with an Adjacency list, I can't figure out why I'm failing the test cases.
Node * n = list[source].head;
while(n)
{
q.push(n);
v[n->b] = n->w;
n = n->next;
}
while(!q.empty())
{
n = q.front();
i = n->b;
o = list[i].head;
q.pop();
while(o)
{
if(!v[o->b])
{
q.push(o);
v[o->b] = v[i] + o->w;
}
else if(v[o->b] > v[i] + o->w)
{
v[o->b] = v[i] + o->w;
}
o = o->next;
}
}
i = 0;
while(i < vertices)
{
if(i != node)
printf("%d ", v[i] ? v[i] : -1);
i++;
}
cout<<"\n";
I am passing trivial test cases.
Example Input: (x y w),
1 2 3,
1 3 4,
1 4 5,
3 5 101,
Source is 1.
Output:
3 4 5 5
Example 2:
1 2 24
1 4 20
3 1 3
4 3 12
Source is 1.
Output: 24 3 15
However, I am failing the more sophisticated test cases.
It seems you are confusing the two arrays - one for which vertex is already visited, and one for the optimal special distances(i.e. optimal distance to the vertices found so far). Let's denote the visited array with v and the optimal distance array with dist.
In this statement:
if(v[o->b] > v[i] + o->w)
You need to be using dist instead of v.
After you pop a node you need to check if it is visited. If it is visited, continue on to the next node. Otherwise mark it as visited and execute the remaining logic.

Partitioning arrays by index

I am fairly new to C++, and am struggling through a problem that seems to have a solid solution but I just can't seem to find it. I have a contiguous array of ints starting at zero:
int i[6] = { 0, 1, 2, 3, 4, 5 }; // this is actually from an iterator
I would like to partition the array into groups of three. The design is to have two methods, j and k, such that given an i they will return the other two elements from the same group of three. For example:
i j(i) k(i)
0 1 2
1 0 2
2 0 1
3 4 5
4 3 5
5 3 4
The solution seems to involve summing the i with its value mod three and either plus or minus one, but I can't quite seem to work out the logic.
This should work:
int d = i % 3;
int j = i - d + ( d == 0 );
int k = i - d + 2 - ( d == 2 );
or following statement for k could be more readable:
int k = i - d + ( d == 2 ? 1 : 2 );
This should do it:
int j(int i)
{
int div = i / 3;
if (i%3 != 0)
return 3*div;
else
return 3*div+1;
}
int k(int i)
{
int div = i / 3;
if (i%3 != 2)
return 3*div+2;
else
return 3*div+1;
}
Test.
If you want shorter functions:
int j(int i)
{
return i/3*3 + (i%3 ? 0 : 1);
}
int k(int i)
{
return i/3*3 + (i%3-2 ? 2 : 1);
}
Well, first, notice that
j(i) == j(3+i) == j(6+i) == j(9+i) == ...
k(i) == k(3+i) == k(6+i) == k(9+i) == ...
In other words, you only need to find a formula for
j(i), i = 0, 1, 2
k(i), i = 0, 1, 2
and then for the rest of the cases simply plug in i mod 3.
From there, you'll have trouble finding a simple formula because your "rotation" isn't standard. Instead of
i j(i) k(i)
0 1 2
1 2 0
2 0 1
for which the formula would have been
j(i) = (i + 1) % 3
k(i) = (i + 2) % 3
you have
i j(i) k(i)
0 1 2
1 0 1
2 0 2
for which the only formula I can think of at the moment is
j(i) = (i == 0 ? 1 : 0)
k(i) = (i == 1 ? 1 : 2)
If the values of your array (let's call it arr, not i in order to avoid confusion with the index i) do not coincide with their respective index, you have to perform a reverse lookup to figure out their index first. I propose using an std::map<int,size_t> or an std::unordered_map<int,size_t>.
That structure reflects the inverse of arr and you can extra the index for a particular value with its subscript operator or the at member function. From then, you can operate purely on the indices, and use modulo (%) to access the previous and the next element as suggested in the other answers.