# Suggested problems

## Binary

March 28, 2022, 12:28 p.m. by talkroom

## Biological Motivation

[TTR][1]

Binary search is the ultimate divide-and-conquer algorithm. To find a key k in a large file containing keys A[1..n] in sorted order, we first compare k with A[n/2], and depending on the result we recurse either on the first half of the file, A[1..n/2], or on the second half, A[n/2+1..n]. The recurrence now is T(n)=T(n/2)+O(1). Plugging into the master theorem (with a=1,b=2,d=0) we get the familiar solution: a running time of just O(logn).

Source: Algorithms by Dasgupta, Papadimitriou, Vazirani. McGraw-Hill. 2006.

Problem The problem is to find a given set of keys in a given array.

Given: Two positive integers n≤105 and m≤105, a sorted array A[1..n] of integers from −105 to 105 and a list of m integers −105≤k1,k2,…,km≤105.

Return: For each ki, output an index 1≤j≤n s.t. A[j]=ki or "-1" if there is no such index. ...

## Problem

A string is simply an ordered collection of symbols selected from some alphabet and formed into a word; the length of a string is the number of symbols that it contains.

An example of an DNA string (whose alphabet contains the symbols A, C, G, and T) is ATGCTTCAGAAAGGTCTTACG.

Given: A DNA string $s$ of length at most 1000 nucleotides.

Return: Four integers corresponding to the number of times that the symbols A, C, G, and T occur in $s$.

## Sample Dataset

AGCTTTTCATTCTGACTGCAACGGGCAATATGTCTCTGTGTGGATTAAAAAAAGAGTGTCTGATAGCAGC

20 12 17 21