 # Algorithms

This section is about solving simple algorithms, coding challenges, puzzles, katas and dojos in Java and Groovy.

## Palindrome

A Palindrome is a word phrase, or number that reads the same backward or forward.

Boolean isPalindrome(String string){
string.reverse().equals(string)
}

assert isPalindrome('anitalavalatina')


## Biggest Number

From a string list with character, number pair elements, extract number and get the biggest

example: “a1”, “b2”, “c3” biggest: 3

import java.util.OptionalInt;
import java.util.Arrays;
import java.util.List;

public class BiggestNumber {

private OptionalInt find(List<String> strings){
return strings.stream().map(s -> s.substring(1))
.mapToInt(Integer::parseInt)
.max();
}

public static void main(String[] args){
List<String> strings = Arrays.asList("a1","b2","c3");
OptionalInt result = new BiggestNumber().find(strings);
assert result.getAsInt() == 3;
}

}


## Sum a Collection

Given an array of integers, find the sum of its elements.

Groovy Version

def array = [1, 2, 3, 4, 10, 11]
println array.sum{it}


Java Version

import java.util.List;
import java.util.Arrays;
import java.util.stream.IntStream;

public class CollectionSum {

private Integer sum(List<Integer> array){
return array.stream().mapToInt(it -> it).sum();
}

public static void main(String[] args){
List<Integer> array = Arrays.asList(1,2,3,4,10,11);
Integer result = new CollectionSum().sum(array);
System.out.println(result);
}

}


## Staircase

Consider a staircase of size 4:

#
##
###
####


Observe that its base and height are both equal. Write a program that prints a staircase of size n.

public class Staircase {

private void printStair(Integer size){
for(int j=1; j<=size; j++){
for(int i=1; i<=j; i++){
System.out.print("#");
}
System.out.print("\n");
}
}

public static void main(String[] args){
Integer size = 4;
new Staircase().printStair(size);
}

}


Assume I have an array that looks like the following:

def array = [34,31,34,56,12,35,24,34,69,18]


Write a function that can determine what is the most popular in the array, in this case “34” because it is the number that appears the most often.

Groovy Version

Integer mostPopular(def array){
Integer occurrences = 0
Integer mostPopular = 0
array.each{
if(array.count { it } > occurrences){
occurrences = array.count { it }
mostPopular = it
}
}
mostPopular
}


Java Version

import java.util.Map;
import java.util.List;
import java.util.Arrays;
import java.util.Comparator;
import java.util.stream.Collectors;

public class PopularDetector {

private Integer find(List<Integer> numbers){
Integer value = numbers.stream()
.collect(Collectors.groupingBy(it -> it, Collectors.counting()))
.entrySet()                                     // 1
.stream()
.max(Comparator.comparing(Map.Entry::getValue))
.get()                                          // 2
.getKey();
return value;
}

public static void main(String[] args){
List<Integer> numbers = Arrays.asList(34,31,34,56,12,35,24,34,69,18);
Integer result = new PopularDetector().find(numbers);
assert result == 34;
}

}

1. Gets Map.Entry interface
2. Gets entry resultant from max comparator

## Center Point in 2d Array

Compute average all the x, y coordinates and find the location in the dead center of them.

class Point{
Integer x
Integer y
}

def computeAverage(List<Point> points){
Float totalX = 0;
Float totalY = 0;

points.each{
totalX += it.x
totalY += it.y
}
[totalX/points.size(),totalY/points.size()]
}

computeAverage([new Point(x:3,y:4), new Point(x:2,y:1)])


Output:

[2.5, 2.5]


## Power Set

Problem

Solve power set algorithm. Power set is the set of all subsets of a set. For example, the power set of the set {a, b, c} consists of the sets:

{}
{a}
{b}
{c}
{a,b}
{a,c}
{b,c}
{a,b,c}


Note that:

• The empty set {} is in the power set
• The set itself is in the power set

Solution

A subset can be represented as an array of boolean values of the same size as the set, called a characteristic vector. Each boolean value indicates whether the corresponding element in the set is present or absent in the subset.

This gives following correspondences for the set {a, b, c}:

[0,0,0] = {}
[1,0,0] = {a}
[0,1,0] = {b}
[0,0,1] = {c}
[1,1,0] = {a,b}
[1,0,1] = {a,c}
[0,1,1] = {b,c}
[1,1,1] = {a,b,c}

def array = ['a','b','c']

def computeSubsets(def array){
def matcher = [[0,0,0],[1,0,0],[0,1,0],[0,0,1],[1,1,0],[1,0,1],[0,1,1],[1,1,1]]
def all = []
matcher.each { col ->
def subset = []
col.eachWithIndex { row, i ->
if(row == 1){
subset << array[i]
}
}
if(!subset.isEmpty())
all << subset
}
all.add(0,[])
all
}

computeSubsets(array)



Output

[[], [a], [b], [c], [a, b], [a, c], [b, c], [a, b, c]]


## Collection Adder

Problem

You have two arrays, sum each element from right to left following same rules we know about sum.

Solution

1. If first collection and second collection size is zero then return empty list
2. Iterate every collection from right to left sum each element and storing carrier as local variable
3. Store the resultant value in the specific index in the resultant array list

Example

[1,0] => 10
[  5] =>  5
------------
[1,5]

import java.util.List;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.stream.Collectors;

public class CollectionAdder {

List<Integer> integerAdder(int[] first, int[] second) {
int carrier = 0;
List<Integer> result = new ArrayList<Integer>();

if(first.length == 0 && second.length == 0){
return new ArrayList<Integer>();
}

int j = second.length-1;
for(int i=first.length-1; i>=0; i--){
int valueA = first[i];
int valueB = 0;

if(j>=0){
valueB = second[j];
}

int parcialValue = valueA + valueB + carrier;
int mod = parcialValue % 10;
result.add(0,mod);

carrier = parcialValue / 10;
j--;
}

if(carrier > 0){
result.add(0,carrier);
}

return result;
}

public static void main(String[] args){
int[] first = {1,0};
int[] second = {5};
List<Integer> result = new CollectionAdder().integerAdder(first, second);
assert new ArrayList<Integer>(Arrays.asList(1,5)).equals(result);
}

}


## Common Elements in two Collections

I have two arrays with integers. I want to return elements in common.

Example

first = [1,2,3,4,5]
second = [1,3,5,7,9]
result = [1,3,5]


Solution

import java.util.List;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.stream.Collectors;

public class CommonElementsFinder {

private List<Integer> find(List<Integer> first, List<Integer> second){
return first.stream().filter(second::contains).collect(Collectors.toList());
}

public static void main(String[] args){
List<Integer> first = Arrays.asList(1, 2, 3, 4, 5);
List<Integer> second = Arrays.asList(1, 3, 5, 7, 9);
List<Integer> result = new CommonElementsFinder().find(first, second);
assert new ArrayList<Integer>(Arrays.asList(1,3,5)).equals(result);
}

}


## Plus Minus

Given an array of integers, calculate which fraction of its elements are positive, which fraction of its elements are negative, and which fraction of its elements are zeroes, respectively.

Output

• A decimal representing of the fraction of positive numbers in the array compared to its size.
• A decimal representing of the fraction of negative numbers in the array compared to its size.
• A decimal representing of the fraction of zeroes in the array compared to its size.

Sample Input

[-4,3,-9,0,4,1]


Sample Output

0.5
0.333333
0.166667


Explanation

There are 3 positive numbers, 2 negative numbers, and 1 zero in the array.

The respective fractions of positive numbers, negative numbers and zeroes are: $\frac{3}{6} = 0.5, \frac{2}{6} = 0.333333, \frac{1}{6} = 0.166667$ respectively.

Solution

import java.util.List;
import java.util.Arrays;
import java.util.ArrayList;

public class PlusMinusFinder {

private float[] find(List<Integer> numbers){
float[] result = new float;
result = numbers.stream().filter(it -> it > 0).count() / (float)numbers.size();
result = numbers.stream().filter(it -> it < 0).count() / (float)numbers.size();
result = numbers.stream().filter(it -> it == 0).count() / (float)numbers.size();
return result;
}

public static void main(String[] args){
List<Integer> numbers = Arrays.asList(-4,3,-9,0,4,1);
float[] result = new PlusMinusFinder().find(numbers);
assert 0.5f == result;
assert 0.33333334f == result;
assert 0.16666667f == result;
}

}


## Min-Max Sum

Given five positive integers, find the minimum and maximum values that can be calculated by summing exactly four of the five integers. Then get the respective minimum and maximum values.

Output

• A integer denoting minimum value that can be calculated by summing exactly four of the five integers.
• A integer denoting maximum value that can be calculated by summing exactly four of the five integers.

Sample Input

[1,2,3,4,5]


Sample Output

10 14


Explanation

Our initial numbers are 1, 2, 3, 4 and 5. We can calculate the following sums using four of the five integers:

• If we sum everything except 1, our sum is 2 + 3 + 4 + 5 = 14.
• If we sum everything except 2, our sum is 1 + 3 + 4 + 5 = 13.
• If we sum everything except 3, our sum is 1 + 2 + 4 + 5 = 12.
• If we sum everything except 4, our sum is 1 + 2 + 3 + 5 = 11.
• If we sum everything except 5, our sum is 1 + 2 + 3 + 4 = 10.

As you can see, the minimal sum is 10 and the maximal sum is 14.

Solution

import java.util.List;
import java.util.Arrays;
import java.util.SortedSet;
import java.util.TreeSet;

public class MinMaxFinder {

private SortedSet<Integer> find(List<Integer> numbers){
SortedSet<Integer> collection = new TreeSet<Integer>();
for(int i=0; i<numbers.size(); i++){
collection.add(numbers.stream().mapToInt(it -> it).sum() - numbers.get(i));
}
return collection;
}

public static void main(String[] args){
List<Integer> numbers = Arrays.asList(1,2,3,4,5);
SortedSet<Integer> result = new MinMaxFinder().find(numbers);
assert 10 == result.first();
assert 14 == result.last();
}

}


## Birthday Cake Candles

Colleen is having a birthday! She will have a cake with one candle for each year of her age. When she blows out the candles, she’ll only be able to blow out the tallest ones.

Output

A integer denoting the number of candles the can be blown out.

Sample Input

[3,2,1,3]


Sample Output

2


Explanation

The maximum candle height is 3 and there are two candles of that height.

Solution

import java.util.List;
import java.util.Arrays;
import java.util.Optional;

public class BirthdayCakeCandlesCounter {

private Integer count(List<Integer> sizes){
Optional<Integer> max = sizes.stream().max(Integer::compare);
Long result = sizes.stream().filter(it -> it == max.get()).count();
return result.intValue();
}

public static void main(String[] args){
List<Integer> sizes = Arrays.asList(3, 2, 1, 3);
Integer result = new BirthdayCakeCandlesCounter().count(sizes);
assert 2 == result;
}

}


## Breaking The Records

Maria plays n games of college basketball in a season. Because she wants to go pro, she tracks her points scored per game sequentially in an array defined as:

score = [s0, s1, s2, ..., sn]


After each game i, she checks to see if score s breaks her record for most or least points scored so far during that season.

Given Maria’s array of scores for a season of n games, find the number of times she breaks her record for most and least points scored during the season.

Note: Assume her records for most and least points at the start of the season are the number of points scored during the first game of the season.

Sample Input

[10, 5, 20, 20, 4, 5, 2, 25, 1]


Sample Output

[2, 4]


Explanation

She broke her best record twice and her worst record four times.

Solution

import java.util.List;
import java.util.Arrays;

public class BreackingRecordsCounter {

private Pair count(List<Integer> scores){
Integer highest = scores.get(0);
Integer lowest = scores.get(0);
Integer highestCounter = 0;
Integer lowestCoutner = 0;

for(Integer score : scores){
if(score > highest) {
highestCounter++;
highest = score;
}
if(score < lowest){
lowestCoutner++;
lowest = score;
}
}

return new Pair(highestCounter, lowestCoutner);
}

public static void main(String[] args){
List<Integer> scores = Arrays.asList(10, 5, 20, 20, 4, 5, 2, 25, 1);
Pair result = new BreackingRecordsCounter().count(scores);
assert 2 == result.getHighest();
assert 4 == result.getLowest();
}

}


Pair is just a POJO for containing highest and lowest values.

This solution kind is O(N) since the algorithm performance will grow linearly and in direct proportion to the size of the input data set.

## Birthday Chocolate

Lily has a chocolate bar consisting of a row of n squares where each square has an integer written on it. She wants to share it with Ron for his birthday, which falls on month m and day d. Lily wants to give Ron a piece of chocolate only if it contains m consecutive squares whose integers sum to d.

Given m, d, and the sequence of integers written on each square of Lily’s chocolate bar, how many different ways can Lily break off a piece of chocolate to give to Ron?

For example, if m=2, d=3 and the chocolate bar contains n squares with the integers

[1, 2, 1, 3, 2]


written on them from left to right, the following diagram shows two ways to break off a piece: Input Format

• Integer array describing the respective values of s0, s1, s2, s3, ..., sn (the numbers written on each consecutive square of chocolate).
• Integer Ron’s birth day
• Integer Ron’s birth month

Constraints

• $1 \le n \le 100$
• $1 \le s1 \le 5, where(0 \le i \le n)$
• $1 \le d \le 31$
• $1 \le m \le 12$

Output Format

Print an integer denoting the total number of ways that Lily can give a piece of chocolate to Ron.

Sample Input

numbers = [1, 2, 1, 3, 2]
day = 3
month = 2


Sample Output

2


Solution

import java.util.Map;
import java.util.List;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class BirthdayChocolateCalculator {

private Integer compute(List<Integer> numbers, final Integer month, final Integer day) {
Integer types = 0;

List<List<Integer>> sets =
IntStream.range(1, numbers.size() - month)
.mapToObj(it -> numbers.subList(it - 1, it + month - 1))
.collect(Collectors.toList());

for(List<Integer> set : sets){
if(set.stream().mapToInt(Integer::intValue).sum() == day){
types++;
}
}

return types;
}

public static void main(String[] args){
Integer month = 2;
Integer day = 3;
List<Integer> numbers = Arrays.asList(1, 2, 1, 3, 2);
Integer result = new BirthdayChocolateCalculator().compute(numbers, month, day);
assert 2 == result;
}

}


## String Compressor

Given a String “aaabbbbcc” compress it in such a way that you get pairs: character, count as: a3b4c2.

Constraints

• $a \le character \le z$
• $1 \le string(length) \le 1000$

Sample Input

String = "aaabbbbcc"


Sample Output

a3b4c2


Solution

import java.util.Map;
import java.util.stream.Collectors;

public class StringCompressor {

private String compress(String string){
Map<Character, Long> map = string.chars()
.mapToObj(i -> (char)i)
.collect(Collectors.groupingBy(it -> it, Collectors.counting()));

StringBuffer sb = new StringBuffer();

map.forEach((k,v) -> sb.append(k.toString() + v.toString()));
return sb.toString();
}

public static void main(String[] args){
String string = "aaabbbbcc";
String result = new StringCompressor().compress(string);
System.out.println(result);
}

}


## Bon Appetit

Anna and Brian order $N$ items at a restaurant, but Anna declines to eat any of the $Kth$ item (where $0 \le K \le N$) due to an allergy. When the check comes, they decide to split the cost of all the items they shared; however, Brian may have forgotten that they didn’t split the $Kth$ item and accidentally charged Anna for it.

You are given $N, K,$ the cost of each of the items, and the total amount of money that Brian charged Anna for her portion of the bill. If the bill is fairly split, print Bon Appetit; otherwise, print the amount of money that Brian must refund to Anna. It is guaranteed that the amount will always be an integer.

Input Format

An integer denoting $K$(the $0$-based index of the item that Anna did not eat). An integer arrray where each integer $i$ denotes the cost, $c[i]$, of item $i$ (where $0 \le i \le N$).

Constraints

• $0 \le K \le N$
• $0 \le c[i] \le 10^4$

Output Format

The difference (i.e., $Bcharged - Bactual$) that Brian must refund to Anna (it is guaranteed that this will always be an integer).

Sample Input

itemAvoided = 1
prices = [3, 10, 2, 9]


Sample Output

5


Explanation

Anna didn’t eat item $c[i] = 10$, but she shared the rest of the items with Brian. The total cost of the shared items is $3 + 2 + 9 = 14$ and, split in half, the cost per person is $Bactual = 7$. Brian charged her $Bcharged = 12$ for her portion of the bill, which is more than the $7$ dollars worth of food that she actually shared with him. Thus, we get the amount Anna was overcharged, $Bcharged-Bactual = 12 - 7 = 5$.

Solution

import java.util.List;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.LinkedList;

public class BonAppetitCalculator {

private Integer compute(List<Integer> prices, int itemAvoided){
Integer charged = prices.stream().mapToInt(Integer::intValue).sum() / 2;
prices.remove(itemAvoided);
Integer fair = prices.stream().mapToInt(Integer::intValue).sum() / 2;
return charged - fair;
}

public static void main(String[] args){
List<Integer> prices = new LinkedList<Integer>(Arrays.asList(3, 10, 2, 9));
int itemAvoided = 1;
Integer result = new BonAppetitCalculator().compute(prices, itemAvoided);
assert 5 == result;
}

}


## Sock Merchant

John works at a clothing store and he’s going through a pile of socks to find the number of matching pairs. More specifically, he has a pile of $N$ loose socks where each sock $i$ is labeled with an integer, $Ci$, denoting its color. He wants to sell as many socks as possible, but his customers will only buy them in matching pairs. Two socks, $i, j$, are a single matching pair if they have the same color $(Ci == Cj)$.

Given $N$ and the color of each sock, how many pairs of socks can John sell?

Input Format

An integers collection describing the respective values of $c0, c1, c2,..., cN-1$.

Constraints

• $1 \le N \le 100$
• $1 \le Ci \le 100$

Output Format

Total number of matching pairs of socks that John can sell.

Sample Input

colors = [10, 20, 20, 10, 10, 30, 50, 10, 20]


Sample Output

3


Explanation As you can see from the figure above, we can match three pairs of socks.

Solution

import java.util.Map;
import java.util.List;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.stream.Collectors;

public class SockPairMatcher{

private Integer match(List<Integer> colors){
Map<Integer, Long> map = colors.stream()
.collect(Collectors.groupingBy(it->it, Collectors.counting()));

List<Long> values = map.entrySet().stream()
.filter(it -> it.getValue() / 2 > 0)
.map(Map.Entry::getValue)
.collect(Collectors.toList());

Long result = values.stream()
.mapToLong(it -> it / 2)
.sum();

return result.intValue();
}

public static void main(String[] args){
List<Integer> colors = Arrays.asList(10, 20, 20, 10, 10, 30, 50, 10, 20);
Integer result = new SockPairMatcher().match(colors);
assert 3 == result;
}

}


We are solving this challenge in three steps:

1. We are grouping by occurrences
2. From a map we are getting Map.Entry collection as stream, then we filtered every item value by which one is divisible by 2, finally we stored filtered values as a list.
3. We are counting how many pairs we can create by dividing every item from long collection by 2

## Electronics Shop

Monica wants to buy exactly one keyboard and one USB drive from her favorite electronics store. The store sells $N$ different brands of keyboards and $M$ different brands of USB drives. Monica has exactly $S$ dollars to spend, and she wants to spend as much of it as possible (i.e., the total cost of her purchase must be maximal).

Given the price lists for the store’s keyboards and USB drives, find and print the amount of money Monica will spend. If she doesn’t have enough money to buy one keyboard and one USB drive, print $-1$ instead.

Note: She will never buy more than one keyboard and one USB drive even if she has the leftover money to do so.

Input Format

• Amount of money Monica has to spend in electronics.
• Integer collection denoting the prices of each keyboard brand.
• Integer collection denoting the prices of each USB drive brand.

Constraints

• $1 \le N,M \le 1000$
• $1 \le S \le 10^6$
• $1 \le price \le 10^6$

Output Format

Single integer denoting the amount of money Monica will spend. If she doesn’t have enough money to buy one keyboard and one USB drive -1 instead.

Sample Input

keyboards = [3, 1]
usbs = [5, 2, 8]
amount = 10


Sample Output

9


Explanation

She can buy the $2nd$ keyboard and the $3rd$ USB drive for a total cost of $8 + 1 = 9$.

Solution

import java.util.Map;
import java.util.List;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.Optional;
import java.util.AbstractMap.SimpleEntry;

import java.util.stream.Collectors;

public class ShopCalculator {

private Integer calculate(final Integer amount, List<Integer> keyboards, List<Integer> usbs){
List<Map.Entry<Integer,Integer>> pairList = new ArrayList<Map.Entry<Integer,Integer>>();

keyboards.forEach( k ->
usbs.forEach( u ->
pairList.add(new SimpleEntry<Integer,Integer>(k,u))
)
);

List<Integer> electronicsCost = pairList.stream().map(entry -> entry.getKey() + entry.getValue()).collect(Collectors.toList());

Optional<Integer> result = electronicsCost.stream().filter(it -> it <= amount).max(Integer::compare);

return result.isPresent() ? result.get() : -1;
}

public static void main(String[] args){
List<Integer> keyboards = Arrays.asList(3, 1);
List<Integer> usbs = Arrays.asList(5, 2, 8);
Integer amount = 10;
Integer result = new ShopCalculator().calculate(amount, keyboards, usbs);
assert 9 == result;
}

}


I solved this challenge in three steps:

1. We are creating keyboard and usb price combination using a Map.Entry pair object
2. We are summarizing those price combinations and stored as a List
3. We are getting max result combination comparing with equals or less that our amount

To download the code:

git clone https://github.com/josdem/algorithms-workshop.git
cd simple-algorithms


To run Java code:

javac ${PROGRAM_NAME}.java java -ea${PROGRAM_NAME}


To run Groovy code:

groovy \${PROGRAM_NAME}.groovy


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