The number of ways in which the numbers $$1, 2, 3, 4, 5, 6, 7$$ can be inserted in an empty binary search tree, such that the resulting tree has height $$6,$$ is _____________.

$$Note:\,\,\,The\,\,height\,\,of\,\,a\,tree\,\,with\,\,a\,\,\sin gle\,\,node\,\,is\,\,0$$

Suppose we have a balanced binary search tree T holding n numbers. We are given two numbers L and H and wish to sum up all the numbers in T that lie between L and H. Suppose there are m such numbers in T. If the tightest upper bound on the time to compute the sum is O( n^a log^b n + m^c log^d n ), the value of a + 10b + 100c + 1000d is _______.

Consider the C function given below. Assume that the array listA contains n (> 0) elements, sored in ascending order.

int ProcessArray(int *listA, int x, int n) 
{ 
      int i, j, k; 
      i = 0; 
      j = n-1; 
      do 
      { 
         k = (i+j)/2; 
         if (x <= listA[k]) 
           j = k-1; 
         if (listA[k] <= x) 
           i = k+1; 
      } 
      while (i <= j); 
      if (listA[k] == x) 
           return(k); 
      else 
           return -1; 
}

Which one of the following statements about the function ProcessArray is CORRECT?

Consider the pseudocode given below. The function Dosomething () takes as argument a pointer to the root of an arbitrary tree represented by the leftMostChild-rightSibling representation. Each node of the tree is of type treeNode.

typedef struct treeNode* treeptr; 
Struct treeNode 
{ 
    Treeptr leftMostchild, rightSibiling; 
}; 
Int Dosomething (treeptr tree) 
{ 
    int value =0; 
    if (tree ! = NULL) { 
      If (tree -> leftMostchild = = NULL) 
          value=1; 
    else 
        value = Dosomething (tree->leftMostchild); 
        value = value + Dosometing (tree->rightsibiling); 
    } 
    return (value); 
}

When the pointer to the root of a tree is passed as the argument to DoSomething, the value returned by the function corresponds to the