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ISI2016PCBCS8
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Consider all possible trees with $n$ nodes. Let $k$ be the number of nodes with degree greater than 1 in a given tree. What is the maximum possible value of $k$? Justify your answer.
Consider $2n$ committees, each having at least $2n$ persons, formed from a group of $4n$ persons. Prove that there exists at least one person who belongs to at least $n$ committees.
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ISI2016PCBCS1
Consider the array $A=[20,13,19,8,3,5,4]$ that represents a heap. Draw the heap after removing the element $20.$ List all the distinct integer keys $k$ such that, when $k$ is inserted in the Binary Search Tree of Figure $1,$ its height increases. Note that you are not allowed to insert an already existing key again. Justify your answer.
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ISI2016PCBCS2
Consider sending a large file of $360,000$ bits from Host $A$ to Host $B,$ connected through a router, as shown in the below figure $2.$ Assume that there is no queuing and propagation delay, and the router has sufficient buffer space. Host ... transferring one byte involves $4$ operations: instatus, checkstatus, branch and read/write in memory, each requiring one machine cycle.
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ISI2016PCBCS3
Consider the following extract from a program, written in a Clike language, that computes the transpose of a matrix. for (i=0; i<N; i++) for (j=0; j<N; j++) B[i,j]=A[i,j]; $A$ and $B$ are $N \times N$ matrices with floating point entries ... Each of $A$ and $B$ is stored starting from the beginning of a page None of the pages allocated to $A$ and $B$ are initially in memory.
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Commodity items have some positive or negative changes in their prices each week. Each trading company picks a portfolio of commodity items, that is, they have one or more items and they own some nonzero quantity of each one. The database table for this problem ... and there exists at least one company selling that item only. (i.e., not selling any other item) in that week.
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