# Most answered questions in Programming and DS

1
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 single node is $0$.
2
Consider the following function implemented in C: void printxy(int x, int y) { int *ptr; x=0; ptr=&x; y=*ptr; *ptr=1; printf(“%d, %d”, x, y); } The output of invoking $printxy(1,1)$ is: $0, 0$ $0, 1$ $1, 0$ $1, 1$
3
Consider the following two functions. void fun1(int n) { if(n == 0) return; printf("%d", n); fun2(n - 2); printf("%d", n); } void fun2(int n) { if(n == 0) return; printf("%d", n); fun1(++n); printf("%d", n); } The output printed when $\text{fun1}(5)$ is called is $53423122233445$ $53423120112233$ $53423122132435$ $53423120213243$
4
A binary tree T has $20$ leaves. The number of nodes in T having two children is ______.
5
What will be the output of the following $C$ program? void count (int n) { static int d=1; printf ("%d",n); printf ("%d",d); d++; if (n>1) count (n-1); printf ("%d",d); } void main(){ count (3); } $3 \ 1 \ 2 \ 2 \ 1 \ 3 \ 4 \ 4 \ 4$ $3 \ 1 \ 2 \ 1 \ 1 \ 1 \ 2 \ 2 \ 2$ $3 \ 1 \ 2 \ 2 \ 1 \ 3 \ 4$ $3 \ 1 \ 2 \ 1 \ 1 \ 1 \ 2$
6
Let $Q$ denote a queue containing sixteen numbers and $S$ be an empty stack. $Head(Q)$ returns the element at the head of the queue $Q$ without removing it from $Q$. Similarly $Top(S)$ returns the element at the top of $S$ without removing it from $S$. Consider ... ); else x:= Pop(S); Enqueue (Q, x); end end The maximum possible number of iterations of the while loop in the algorithm is _______.
7
When searching for the key value $60$ in a binary search tree, nodes containing the key values $10, 20, 40, 50, 70, 80, 90$ are traversed, not necessarily in the order given. How many different orders are possible in which these key values can occur on the search path from the root to the node containing the value $60$? $35$ $64$ $128$ $5040$
8
Consider a hash function that distributes keys uniformly. The hash table size is $20$. After hashing of how many keys will the probability that any new key hashed collides with an existing one exceed $0.5$. $5$ $6$ $7$ $10$
9
In a compact single dimensional array representation for lower triangular matrices (i.e all the elements above the diagonal are zero) of size $n \times n$ ... this new representation is: $i+j$ $i+j-1$ $(j-1)+\frac{i(i-1)}{2}$ $i+\frac{j(j-1)}{2}$
10
In a binary tree with $n$ nodes, every node has an odd number of descendants. Every node is considered to be its own descendant. What is the number of nodes in the tree that have exactly one child? $0$ $1$ $\frac{(n-1)}{2}$ $n-1$
11
Consider a rooted n node binary tree represented using pointers. The best upper bound on the time required to determine the number of subtrees having exactly $4$ nodes is $O(n^a\log^bn)$. Then the value of $a+10b$ is __________.
12
What is the worst case time complexity of inserting $n$ elements into an empty linked list, if the linked list needs to be maintained in sorted order? $\Theta(n)$ $\Theta(n \log n)$ $\Theta ( n)^{2}$ $\Theta(1)$
13
Consider the following C program: #include <stdio.h> int r() { static int num=7; return num--; } int main() { for (r();r();r()) printf(“%d”,r()); return 0; } Which one of the following values will be displayed on execution of the programs? $41$ $52$ $63$ $630$
14
Let $T$ be a full binary tree with $8$ leaves. (A full binary tree has every level full.) Suppose two leaves $a$ and $b$ of $T$ are chosen uniformly and independently at random. The expected value of the distance between $a$ and $b$ in $T$ (ie., the number of edges in the unique path between $a$ and $b$) is (rounded off to $2$ decimal places) _________.
15
A hash table of length $10$ uses open addressing with hash function $h(k) = k \: mod \: 10$, and linear probing. After inserting $6$ ... insertion sequences of the key values using the same hash function and linear probing will result in the hash table shown above? $10$ $20$ $30$ $40$
16
Consider a binary tree T that has $200$ leaf nodes. Then the number of nodes in T that have exactly two children are ______.
17
Consider the following $\text{C}$ program: #include<stdio.h> int counter=0; int calc (int a, int b) { int c; counter++; if(b==3) return (a*a*a); else { c = calc(a, b/3); return (c*c*c); } } int main() { calc(4, 81); printf("%d", counter); } The output of this program is ______.
Consider the following C program. #include<stdio.h> #include<string.h> void printlength(char *s, char *t) { unsigned int c=0; int len = ((strlen(s) - strlen(t)) > c) ? strlen(s) : strlen(t); printf("%d\n", len); } void main() { char *x = "abc"; ... that $strlen$ is defined in $string.h$ as returning a value of type $size\_t$, which is an unsigned int. The output of the program is __________ .