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<!DOCTYPE html>
<html lang="en-US">
<head>
<title>Coding Challenges in a Technical Interview</title>
<meta charset="utf-8">
<meta charset="utf-8">
<meta name='keywords' content='test, quiz, interview, interview questions, technical interview, technical questions'>
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</head>
<body ng-app="technical" style='margin: 20px;' ng-controller='tabCtrl'>
<header ng-controller="navCtrl">
<div nav></div>
</header>
<section style='text-align: center'>
<h2 style='color: steelblue'>Coding Challenges</h2>
<h4 style='color: darkgray'>All the coding challenges are hand coded and tested by me. They are not copied from other sources.</h4>
<h5><a href="technical-interview-coding-challenges.pdf">Download as PDF</a></h5>
</section>
<p>
The coding challenges in this section are basic algorithms. A coding portion of a technical interview will likely start with one of these types
of algorithms. Typically, after asking you to code the basic algorithm, you will be ask to make improvements or other variations. If you are
unable to pass this part of the coding portion, you will probably not continue to the next round of an interview.
</p>
<ol class='w3-ul'>
<li><a class='index' href='#prime'>Prime Numbers</a><span class='expand' ng-click='prime=!prime'> +</span>
<ul ng-show='prime'>
<li><a class='list' href="#prime1">Standard</a></li>
<li><a class='list' href="#prime2">Skip Even Numbers</a></li>
<li><a class='list' href="#prime3">Skip Even Numbers, and divide only by numbers one-third or less than the number.</a></li>
</ul>
</li>
<li><a class='index' href='#fibonacci'>Fibonacci Sequence</a><span class='expand' ng-click='fibonacci=!fibonacci'> +</span>
<ul ng-show='fibonacci'>
<li><a class='list' href="#fibonacci1">Recursive</a></li>
<li><a class='list' href="#fibonacci2">Iterative</a></li>
</ul>
</li>
<li><a class='index' href='#dynamic'>Dynamic Arrays</a><span class='expand' ng-click='dynamic=!dynamic'> +</span>
<ul ng-show='dynamic'>
<li><a class='list' href="#dynamic1">Add/Get</a></li>
<li><a class='list' href="#dynamic2">Delete</a></li>
</ul>
</li>
<li><a class='index' href='#queue'>Linked Lists - Queue</a><span class='expand' ng-click='queue=!queue'> +</span>
<ul ng-show='queue'>
<li><a class='list' href="#queue1">Queue</a></li>
<li><a class='list' href="#queue2">Queue with Task Priority</a></li>
<li><a class='list' href="#queue3">Queue with Dynamic Priority Update</a></li>
</ul>
</li>
<li><a class='index' href='#stack'>Linked Lists - Stack</a><span class='expand' ng-click='stack=!stack'> +</span>
<ul ng-show='stack'>
<li><a class='list' href="#stack1">Stack</a></li>
<li><a class='list' href="#stack2">Chain of Stacks</a></li>
<li><a class='list' href="#stack3">Towers of Hanoi</a></li>
</ul>
</li>
<li><a class='index' href='#btree'>Binary Trees</a><span class='expand' ng-click='btree=!btree'> +</span>
<ul ng-show='btree'>
<li><a class='list' href="#btree1">Standard</a></li>
<li><a class='list' href="#btree2">Generalize from K-ary Tree</a></li>
</ul>
</li>
<li><a class='index' href='#bts'>Binary Tree Traversals</a><span class='expand' ng-click='bts=!bts'> +</span>
<ul ng-show='bts'>
<li><a class='list' href="#bts1">Inorder</a></li>
<li><a class='list' href="#bts2">Preorder</a></li>
<li><a class='list' href="#bts3">Postorder</a></li>
<li><a class='list' href="#bts4">Level Order</a></li>
<li><a class='list' href="#bts5">Maximum and Minimum Depth of Binary Tree</a></li>
<li><a class='list' href="#bts6">Maximum and Minimum Value</a></li>
</ul>
</li>
<li><a class='index' href='#kary'>K-ary Trees</a><span class='expand' ng-click='kary=!kary'> +</span>
<ul ng-show='kary'>
<li><a class='list' href="#kary1">Standard</a></li>
</ul>
</li>
<li><a class='index' href='#bst'>Binary Search Trees</a><span class='expand' ng-click='bst=!bst'> +</span>
<ul ng-show='bst'>
<li><a class='list' href="#bst1">Insert</a></li>
<li><a class='list' href="#bst2">Find</a></li>
<li><a class='list' href="#bst3">Delete</a></li>
</ul>
</li>
<li><a class='index' href='#arith'>Arithmetic Operations</a><span class='expand' ng-click='arith=!arith'> +</span>
<ul ng-show='arith'>
<li><a class='list' href="#arith1">Multiply</a></li>
<li><a class='list' href="#arith2">Exponent</a></li>
<li><a class='list' href="#arith3">Exponent with Fewer Multiplication Steps</a></li>
<li><a class='list' href="#arith4">GCD Iterative Solution</a></li>
<li><a class='list' href="#arith5">GCD Recursive Solution</a></li>
<li><a class='list' href="#arith6">LCM</a></li>
</ul>
</li>
<li><a class='index' href='#encoding'>Variable Length Byte Encoding</a><span class='expand' ng-click='encoding=!encoding'> +</span>
<ul ng-show='encoding'>
<li><a class='list' href="#encoding1">Byte Encoding</a></li>
</ul>
</li>
<li><a class='index' href='#sort'>Sorting</a><span class='expand' ng-click='sort=!sort'> +</span>
<ul ng-show='sort'>
<li><a class='list' href="#sort1">Bubble Sort</a></li>
<li><a class='list' href="#sort2">Insertion Sort</a></li>
<li><a class='list' href="#sort3">Quick Sort</a></li>
<li><a class='list' href="#sort4">Merge Sort</a></li>
</ul>
</li>
<li><a class='index' href='#hash'>Hashing</a><span class='expand' ng-click='hash=!hash'> +</span>
<ul ng-show='hash'>
<li><a class='list' href="#hash1">Integer Hash</a></li>
<li><a class='list' href="#hash2">String (Object) Hash</a></li>
<li><a class='list' href="#hash3">Hash Table with Linear Probing</a></li>
</ul>
</li>
<li><a class='index' href='#string'>String Manipulations</a><span class='expand' ng-click='string=!string'> +</span>
<ul ng-show='string'>
<li><a class='list' href="#string1">Reverse String (Iterative)</a></li>
<li><a class='list' href="#string2">Reverse String (Recursive)</a></li>
<li><a class='list' href="#string3">Palindrome</a></li>
<li><a class='list' href="#string4">Palindrome (Phrases)</a></li>
<li><a class='list' href="#string5">Character Count</a></li>
<li><a class='list' href="#string6">Duplicate Characters</a></li>
</ul>
</li>
<li><a class='index' href='#graph'>Graphs</a><span class='expand' ng-click='graph=!graph'> +</span>
<ul ng-show='graph'>
<li><a class='list' href="#graph1">BFS Graph Traversal</a></li>
<li><a class='list' href="#graph2">DFS Graph Traversal (Iterative)</a></li>
<li><a class='list' href="#graph3">DFS Graph Traversal (Recursive)</a></li>
</ul>
</li>
</ol>
<a name="prime"></a>
<h3>1. Prime Numbers</h3>
<p>
The most basic coding example you might get asked is to write an algorithm to output a series of prime numbers.
Prime numbers are numbers that are only divisible by one and itself. The algorithm is a
straight forward iterative algorithm.
</p>
<a name="prime1"></a>
<h4>Standard</h4>
<ul class="w3-navbar w3-light-grey" ng-init="pri1[0] = true; pri1cls[0] = 'w3-black'">
<li><a href="javascript:void(0)" ng-click="pri1=[true,false,false,false]; pri1cls=['w3-black','w3-lightgray','w3-lightgray','w3-lightgray']; Algo('pri1')" ng-class='pri1cls[0]'>Algorithm</a></li>
<li><a href="javascript:void(0)" ng-click="pri1=[false,true,false,false]; pri1cls=['w3-lightgray','w3-black','w3-lightgray','w3-lightgray']; Python('pri1')" ng-class='pri1cls[1]'>Python</a></li>
<li><a href="javascript:void(0)" ng-click="pri1=[false,false,true,false]; pri1cls=['w3-lightgray','w3-lightgray','w3-black','w3-lightgray']; Java('pri1')" ng-class='pri1cls[2]'>Java</a></li>
<li><a href="javascript:void(0)" ng-click="pri1=[false,false,false,true]; pri1cls=['w3-lightgray','w3-lightgray','w3-lightgray','w3-black']; Javascript('pri1')" ng-class='pri1cls[3]'>Javascript</a></li>
</ul>
<div ng-show='pri1[0]'>
<p>
The number one is a prime number, since it can only be divisible by itself. The
number two is also a prime number, since there are no numbers between one and two
to divide by. Therefore, I generally like to start the iterative process at three, though
you may choose to start it at two.
</p>
<ol class='w3-ul'>
<li>For each number, we attempt to divide it by every number less than it, except for one.</li>
<li>The integer modulo operator is used to test if there is a remainder from the integer division.</li>
<li>If there is no remainder, it is divisible by the number and therefore not a prime.</li>
<li>If each of the numbers it is divided by has a remainder, it is a prime.</li>
</ol>
</div>
<pre class='w3-container' ng-show='pri1[1]'>
print( "Prime Numbers between 1 and 100")
# Prime Numbers are numbers only divisible by 1 and itself.
print( "1" )
print( "2" )
# Primes for numbers above 2
for number in range( 3, 101 ):
# Attempt to divide this number by every number between 2 and one less than itself
for div in range(2,number):
# use the mod function to see if their is a remainder in the division
if ( number % div ) == 0:
break
else:
print(number)
</pre>
<pre class='w3-container' ng-show='pri1[2]'>
public class prime {
public static void main( String args[] ) {
System.out.println( "Prime Numbers between 1 and 100");
// Prime Numbers are numbers only divisible by 1 and itself.
System.out.println( "1" );
System.out.println( "2" );
// Primes for numbers above 2
for ( int number = 3; number <=100; number++ ) {
// Attempt to divide this number by every number between 2 and one less than itself
int div = 2;
for ( /**/; div < number; div++ ) {
// use the mod function to see if their is a remainder in the division
if ( ( number % div ) == 0 )
break;
}
if ( div == number )
System.out.println(number);
}
}
}
</pre>
<pre class='w3-container' ng-show='pri1[3]'>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script>
$(function() {
var output = $("#output");
function println( text ) {
output.html( output.html() + "<br/>" + text );
}
println( "Prime Numbers between 1 and 100" );
// Prime Numbers are numbers only divisible by 1 and itself.
println( "1" );
println( "2" );
// Primes for numbers above 2
for ( var number = 3; number <=100; number++ ) {
// Attempt to divide this number by every number between 2 and one less than itself
var div = 2;
for ( /**/; div < number; div++ ) {
// use the mod function to see if their is a remainder in the division
if ( ( number % div ) == 0 )
break;
}
if ( div == number )
println(number);
}
});
</script>
<body>
<div id='output'></div>
</body>
</pre>
<a name="prime2"></a>
<h4>Skip Even Numbers</h4>
<ul class="w3-navbar w3-light-grey" ng-init="pri2[0] = true; pri2cls[0] = 'w3-black'">
<li><a href="javascript:void(0)" ng-click="pri2=[true,false,false,false]; pri2cls=['w3-black','w3-lightgray','w3-lightgray','w3-lightgray']; Algo('pri2')" ng-class='pri2cls[0]'>Algorithm</a></li>
<li><a href="javascript:void(0)" ng-click="pri2=[false,true,false,false]; pri2cls=['w3-lightgray','w3-black','w3-lightgray','w3-lightgray']; Python('pri2')" ng-class='pri2cls[1]'>Python</a></li>
<li><a href="javascript:void(0)" ng-click="pri2=[false,false,true,false]; pri2cls=['w3-lightgray','w3-lightgray','w3-black','w3-lightgray']; Java('pri2')" ng-class='pri2cls[2]'>Java</a></li>
<li><a href="javascript:void(0)" ng-click="pri2=[false,false,false,true]; pri2cls=['w3-lightgray','w3-lightgray','w3-lightgray','w3-black']; Javascript('pri2')" ng-class='pri2cls[3]'>Javascript</a></li>
</ul>
<div ng-show='pri2[0]'>
<p>
Can we make an improvement? Yes. Since we know all even numbers are divisible by two, we
can skip checking even numbers and only check odd numbers. Likewise, since we know odd numbers are not divisible by even numbers,
we can skip dividing by even numbers and only divide by odd numbers.
</p>
<ol class='w3-ul'>
<li>For each odd number, we attempt to divide it by every odd number less than it, except for one.</li>
<li>The integer modulo operator is used to test if there is a remainder from the integer division.</li>
<li>If there is no remainder, it is divisible by the number and therefore not a prime.</li>
<li>If each of the numbers it is divided by has a remainder, it is a prime.</li>
</ol>
</div>
<pre class='w3-container' ng-show='pri2[1]'>
print( "Prime Numbers between 1 and 100")
# Prime Numbers are numbers only divisible by 1 and itself.
print( "1" )
print( "2" )
print( "3" )
# Primes for numbers above 5
for number in range( 5, 101, 2 ):
# Attempt to divide this number by every odd number between 2 and one less than itself
for div in range(3,number,2):
# use the mod function to see if their is a remainder in the division
if ( number % div ) == 0:
break
else:
print(number)
</pre>
<pre class='w3-container' ng-show='pri2[2]'>
public class prime {
public static void main( String args[] ) {
System.out.println( "Prime Numbers between 1 and 100");
// Prime Numbers are numbers only divisible by 1 and itself.
System.out.println( "1" );
System.out.println( "2" );
System.out.println( "3" );
// Primes for numbers above 5
for ( int number = 5; number <=100; number += 2 ) {
int div = 3;
// Attempt to divide this number by every odd number between 3 and one less than itself
for ( /**/; div < number; div += 2 ) {
// use the mod function to see if their is a remainder in the division
if ( ( number % div ) == 0 )
break;
}
if ( div == number )
System.out.println(number);
}
}
}
</pre>
<pre class='w3-container' ng-show='pri2[3]'>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script>
$(function() {
var output = $("#output");
function println( text ) {
output.html( output.html() + "<br/>" + text );
}
println( "Prime Numbers between 1 and 100" );
// Prime Numbers are numbers only divisible by 1 and itself.
println( "1" );
println( "2" );
println( "3" );
// Primes for numbers above 5
for ( var number = 5; number <=100; number += 2 ) {
var div = 3;
// Attempt to divide this number by every odd number between 3 and one less than itself
for ( /**/; div < number; div += 2 ) {
// use the mod function to see if their is a remainder in the division
if ( ( number % div ) == 0 )
break;
}
if ( div == number )
println(number);
}
});
</script>
<body>
<div id='output'></div>
</body>
</pre>
<a name="prime3"></a>
<h4>Skip Even Numbers, and divide only by numbers one-third or less than the number</h4>
<ul class="w3-navbar w3-light-grey" ng-init="pri3[0] = true; pri3cls[0] = 'w3-black'">
<li><a href="javascript:void(0)" ng-click="pri3=[true,false,false,false]; pri3cls=['w3-black','w3-lightgray','w3-lightgray','w3-lightgray']; Algo('pri3')" ng-class='pri3cls[0]'>Algorithm</a></li>
<li><a href="javascript:void(0)" ng-click="pri3=[false,true,false,false]; pri3cls=['w3-lightgray','w3-black','w3-lightgray','w3-lightgray']; Python('pri3')" ng-class='pri3cls[1]'>Python</a></li>
<li><a href="javascript:void(0)" ng-click="pri3=[false,false,true,false]; pri3cls=['w3-lightgray','w3-lightgray','w3-black','w3-lightgray']; Java('pri3')" ng-class='pri3cls[2]'>Java</a></li>
<li><a href="javascript:void(0)" ng-click="pri3=[false,false,false,true]; pri3cls=['w3-lightgray','w3-lightgray','w3-lightgray','w3-black']; Java('pri3')" ng-class='pri3cls[3]'>Javascript</a></li>
</ul>
<div ng-show='pri3[0]'>
<p>
Can we make another improvement? Yes. Since we are skipping even numbers, we know that each number to be prime must be divisible by at least the number three.
Therefore, any divisible number must be one-third or less the value of the number. We can cut down on the number of iterations by only dividing
the first 1/3 of values less than the number.
</p>
<ol class='w3-ul'>
<li>For each odd number, we attempt to divide it by every odd number that is less than one-third of the number, except for one and two.</i>
<li>The integer modulo operator is used to test if there is a remainder from the integer division.</li>
<li>If there is no remainder, it is divisible by the number and therefore not a prime.</li>
<li>If each of the numbers it is divided by has a remainder, it is a prime.</li>
</ol>
</div>
<pre class='w3-container' ng-show='pri3[1]'>
print( "1" )
print( "2" )
print( "3" )
for number in range( 5, 101, 2 ):
# Attempt to divide this number by every number between 3 and one third less than itself
third = int( (number / 3 ) ) + 1
for div in range(3,third,2):
# use the mod function to see if their is a remainder in the division
if ( number % div ) == 0:
break
else:
print(number)
</pre>
<pre class='w3-container' ng-show='pri3[2]'>
public class prime {
public static void main( String args[] ) {
System.out.println( "Prime Numbers between 1 and 100");
// Prime Numbers are numbers only divisible by 1 and itself.
System.out.println( "1" );
System.out.println( "2" );
System.out.println( "3" );
// Primes for numbers above 5
for ( int number = 5; number <=100; number += 2 ) {
int div = 3;
int third = ( number / 3 ); // calculate one-third of the number
// Attempt to divide this number by every number between 3 and one third of the number
for ( /**/; div <= third; div += 2) {
// use the mod function to see if their is a remainder in the division
if ( ( number % div ) == 0 )
break;
}
if ( div >= third )
System.out.println(number);
}
}
}
</pre>
<pre class='w3-container' ng-show='pri3[3]'>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script>
$(function() {
var output = $("#output");
function println( text ) {
output.html( output.html() + "<br/>" + text );
}
println( "Prime Numbers between 1 and 100" );
// Prime Numbers are numbers only divisible by 1 and itself.
println( "1" );
println( "2" );
println( "3" );
// Primes for numbers above 5
for ( var number = 5; number <=100; number += 2 ) {
var div = 3;
var third = ( number / 3 ); // calculate one-third of the number
// Attempt to divide this number by every number between 3 and one third of the number
for ( /**/; div <= third; div += 2) {
// use the mod function to see if their is a remainder in the division
if ( ( number % div ) == 0 )
break;
}
if ( div >= third )
println(number);
}
});
</script>
<body>
<div id='output'></div>
</body>
</pre>
<a name="fibonacci"></a>
<h3>2. Fibonacci Sequence</h3>
<p>
One of the most common and basic coding examples is to code a solution for the Fibonacci sequence. A Fibonacci sequence is a function where F(N) equals
F(n-1) + F(n-2); that is the summation of the previous two values in the sequence. Originally, the seed sequence was F(0) = 1 and F(1) = 1, but modern
solutions use F(0) = 0 and F(1) = 1. This sequence can be written in a very short recursive algorithm.
</p>
<a name="fibonacci1"></a>
<h4>Recursive</h4>
<ul class="w3-navbar w3-light-grey" ng-init="fib1[0] = true; fib1cls[0] = 'w3-black'">
<li><a href="javascript:void(0)" ng-click="fib1=[true,false,false,false]; fib1cls=['w3-black','w3-lightgray','w3-lightgray','w3-lightgray']; Algo('fib1')" ng-class='fib1cls[0]'>Algorithm</a></li>
<li><a href="javascript:void(0)" ng-click="fib1=[false,true,false,false]; fib1cls=['w3-lightgray','w3-black','w3-lightgray','w3-lightgray']; Python('fib1')" ng-class='fib1cls[1]'>Python</a></li>
<li><a href="javascript:void(0)" ng-click="fib1=[false,false,true,false]; fib1cls=['w3-lightgray','w3-lightgray','w3-black','w3-lightgray']; Java('fib1')" ng-class='fib1cls[2]'>Java</a></li>
<li><a href="javascript:void(0)" ng-click="fib1=[false,false,false,true]; fib1cls=['w3-lightgray','w3-lightgray','w3-lightgray','w3-black']; Javascript('fib1')" ng-class='fib1cls[3]'>Javascript</a></li>
</ul>
<div ng-show='fib1[0]'>
<ol class='w3-ul'>
<li>If n = 0, then return 0.</li>
<li>If n = 1, then return 1.</li>
<li>If n > 1, return the sum of F(n-1) + F(n-2).</li>
</ol>
</div>
<pre class='w3-container' ng-show='fib1[1]'>
# Fibonacci Sequence
# Is a sum (addition) of the previous two numbers in the sequence, as
# F(n) = F(n-1) + F(n-2)
# Where
# F(0) = 0 and F(1) = 1
# Hence
# F(2) = 0 + 1 [F(1) + F(0)] = 1
# F(3) = 1 + 1 [F(2) + F(1)] = 2
# Recursive Solution
def Fibonacci(n):
# F(0) and F(1) case
if n==0:
return 0
if n==1:
return 1
return Fibonacci(n-1) + Fibonacci(n-2)
# Fibonacci Sequence to F(10)
for number in range( 0, 10 ):
print( Fibonacci(number) )
</pre>
<pre class='w3-container' ng-show='fib1[2]'>
public class fibonacci {
// Recursive Solution
public static int Fibonacci( int n) {
if ( n == 0 ) return 0;
if ( n == 1 ) return 1;
return Fibonacci( n - 1 ) + Fibonacci( n - 2 );
}
// Test Driver
public static void main( String args[] ) {
System.out.println( "Fibonacci Sequence to F(10)");
for ( int number = 0; number < 10; number++ )
System.out.println( Fibonacci( number ) );
}
}
</pre>
<pre class='w3-container' ng-show='fib1[3]'>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script>
$(function() {
var output = $("#output");
function println( text ) {
output.html( output.html() + "<br/>" + text );
}
// Recursive Solution
function Fibonacci( n ) {
if ( n == 0 ) return 0;
if ( n == 1 ) return 1;
return Fibonacci( n - 1 ) + Fibonacci( n - 2 );
}
// Test Driver
println( "Fibonacci Sequence to F(10)");
for ( var number = 0; number < 10; number++ )
println( Fibonacci( number ) );
});
</script>
<body>
<div id='output'></div>
</body>
</pre>
<a name="fibonacci2"></a>
<h4>Iterative</h4>
<ul class="w3-navbar w3-light-grey" ng-init="fib2[0] = true; fib2cls[0] = 'w3-black'">
<li><a href="javascript:void(0)" ng-click="fib2=[true,false,false,false]; fib2cls=['w3-black','w3-lightgray','w3-lightgray','w3-lightgray']; Algo('fib2')" ng-class='fib2cls[0]'>Algorithm</a></li>
<li><a href="javascript:void(0)" ng-click="fib2=[false,true,false,false]; fib2cls=['w3-lightgray','w3-black','w3-lightgray','w3-lightgray']; Python('fib2')" ng-class='fib2cls[1]'>Python</a></li>
<li><a href="javascript:void(0)" ng-click="fib2=[false,false,true,false]; fib2cls=['w3-lightgray','w3-lightgray','w3-black','w3-lightgray']; Java('fib2')" ng-class='fib2cls[2]'>Java</a></li>
<li><a href="javascript:void(0)" ng-click="fib2=[false,false,false,true]; fib2cls=['w3-lightgray','w3-lightgray','w3-lightgray','w3-black']; Javascript('fib2')" ng-class='fib2cls[3]'>Javascript</a></li>
</ul>
<div ng-show='fib2[0]'>
<p>
It is common to be asked if you can write the algorithm for an iterative solution (looping - no recursion).
</p>
<ol class='w3-ul'>
<li>If n = 0, then return 0.</li>
<li>If n = 1, then return 1.</li>
<li>If n > 1, then set last F(n-2) = 0, and last F(n-1) = 0, and F(n) initialized to zero.</li>
<li>Loop from 2 to n.
<ul>
<li>Set current F(n) to current F(n-1) + F(n-2).</li>
<li>Set F(n-2) to current F(n-1).</li>
<li>Set F(n-1) to current F(n).</li>
</ul>
</li>
</ol>
</div>
<pre class='w3-container' ng-show='fib2[1]'>
def FibonacciIterative(n):
# F(0) and F(1) case
if n==0:
return 0
if n==1:
return 1
fn = 0 # current value for F(n)
f_minus_1 = 1 # current value for F(n-1)
f_minus_2 = 0 # current value for F(n-2)
for i in range( 2, n+1 ):
fn = f_minus_1 + f_minus_2 # F(n) = F(n-1) + F(n-2)
f_minus_2 = f_minus_1 # next F(n-2)
f_minus_1 = fn # next F(n-1)
return fn
# Fibonacci Sequence to F(10)
for number in range( 0, 10 ):
print( FibonacciIterative(number) )
</pre>
<pre class='w3-container' ng-show='fib2[2]'>
public class fibonacci {
// Iterative Solution
public static int Fibonacci( int n ) {
if ( n == 0 ) return 0;
if ( n == 1 ) return 1;
int fn = 0; // current value for F(n)
int f_minus_2 = 0; // current value of F(n-2)
int f_minus_1 = 1; // current value of F(n-1)
for ( int i = 2; i <= n; i++ ) {
fn = f_minus_1 + f_minus_2; // F(n) = F(n-1) + F(n-2)
f_minus_2 = f_minus_1; // next F(n-2)
f_minus_1 = fn; // next F(n-1)
}
return fn;
}
// Test Driver
public static void main( String args[] ) {
System.out.println( "Fibonacci Sequence to F(10)");
for ( int number = 0; number < 10; number++ )
System.out.println( Fibonacci( number ) );
}
}
</pre>
<pre class='w3-container' ng-show='fib2[3]'>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script>
$(function() {
var output = $("#output");
function println( text ) {
output.html( output.html() + "<br/>" + text );
}
// Iterative Solution
function FibonacciIterative( n ) {
if ( n == 0 ) return 0;
if ( n == 1 ) return 1;
var fn = 0; // current value for F(n)
var f_minus_2 = 0; // current value of F(n-2)
var f_minus_1 = 1; // current value of F(n-1)
for ( var i = 2; i <= n; i++ ) {
fn = f_minus_1 + f_minus_2; // F(n) = F(n-1) + F(n-2)
f_minus_2 = f_minus_1; // next F(n-2)
f_minus_1 = fn; // next F(n-1)
}
return fn;
}
// Test Driver
println( "Fibonacci Sequence to F(10)");
for ( var number = 0; number < 10; number++ )
println( FibonacciIterative( number ) );
});
</script>
<body>
<div id='output'></div>
</body>
</pre>
<a name="dynamic"></a>
<h3>3. Dynamic Arrays</h3>
<p>
A dynamic array is an array that can be resized, can be randomly accessed via an cardinal ordering, where there is a one-to-one relationship
between an integer index and a value. For example, if a dynamic array has the ordered elements A, B and D, they would be accessed (one-to-one relationship)
by indices 0=>A, 1=>B and 2=>D. If we insert a C between B and D, the ordering would be rearranged but there still would be a one-to-one relationship, accessed
as indices 0=>A, 1=>B, 2=>C and 3=>D. Note how index 2 now relates to C and index 3 to D.
</p>
<a name="dynamic1"></a>
<h4>Add/Get</h4>
<ul class="w3-navbar w3-light-grey" ng-init="dyn1[0] = true; dyn1cls[0] = 'w3-black'">
<li><a href="javascript:void(0)" ng-click="dyn1=[true,false,false,false]; dyn1cls=['w3-black','w3-lightgray','w3-lightgray','w3-lightgray']; Algo('dyn1')" ng-class='dyn1cls[0]'>Algorithm</a></li>
<li><a href="javascript:void(0)" ng-click="dyn1=[false,true,false,false]; dyn1cls=['w3-lightgray','w3-black','w3-lightgray','w3-lightgray']; Python('dyn1')" ng-class='dyn1cls[1]'>Python</a></li>
<li><a href="javascript:void(0)" ng-click="dyn1=[false,false,true,false]; dyn1cls=['w3-lightgray','w3-lightgray','w3-black','w3-lightgray']; Java('dyn1')" ng-class='dyn1cls[2]'>Java</a></li>
<li><a href="javascript:void(0)" ng-click="dyn1=[false,false,false,true]; dyn1cls=['w3-lightgray','w3-lightgray','w3-lightgray','w3-black']; Javascript('dyn1')" ng-class='dyn1cls[3]'>Javascript</a></li>
</ul>
<div ng-show='dyn1[0]'>
<p>
You maybe asked to implement a dynamic array using a class. You would be expected to implement at least an Add() and Get() methods.
</p>
<ol class='w3-ul'>
<li>Define a class for an element.
<ul>
<li>Has a member to hold the value.</li>
<li>Has a next pointer for the next element in the array.</li>
</ul>
</li>
<li>Define a class for an array.
<ul>
<li>Has a member to hold the head and a member to hold the tail of the array.</li>
<li>A member to hold the size of the array.</li>
<li>Define an Add method.
<ul>
<li>Instantiate a new element.</li>
<li>Add the element to the end of tail (the tail's next pointer) and update the tail to the new element.</li>
<li>If it is the first element in the array, set the head to the new element.</li>
<li>Increment the size of the array by one.</li>
</ul>
</li>
<li>Define a Get method.</li>
<ul>
<li>Check for array out of bounds condition.</li>
<li>Starting with the head, advance consecutively index number of times following the next pointer.</li>
<li>Return the value of the current element.</li>
</ul>
</li>
</ul>
</li>
</ol>
</div>
<pre class='w3-container' ng-show='dyn1[1]'>
# Definition for an element in the dynamic array
class Element:
next = None # next element in array
# Constructor: set the node data
def __init__(self, value):
self.value = value # node data
# Definition for a Dynamic Array
class DynamicArray:
head = None # head of the array
tail = None # tail of the array
size = 0 # size of the array
# The size (number of elements) of the array
def Size( self ):
return self.size;
# Add an element to the end of the dynamic array
def Add( self, value ):
e = Element(value)
# Set the next element of the previous tail to the new element
if self.tail != None:
self.tail.next = e
# set the current tail to the new element
self.tail = e
# If there is no head (first element), set the head to the new element.
if self.head == None:
self.head = e
# Increment the size of the array
self.size += 1
# Get the value at the corresponding index
def Get( self, index ):
# Check for out of bounds condition
if index > self.size - 1 or index < 0:
return None
# Step (linear) to the index position
curr = self.head;
for i in range( 0, index ):
curr = curr.next
return curr.value
# Test Driver
array = DynamicArray()
for i in range( 0, 7 ):
array.Add(i)
print("Expect 0,1,2,3,4,5,6")
for i in range( 0, array.Size() ):
print( array.Get(i) )
</pre>
<pre class='w3-container' ng-show='dyn1[2]'>
// Definition for an element in the dynamic array
class Element {
Object value = null; // Element value
Element next = null; // Next element in the array
// Constructor
public Element( Object value ) {
this.value = value;
}
}
// Definition for a Dynamic Array
class DynamicArray {
private Element head = null; // Head of the Array
private Element tail = null; // Tail of the Array
private int size = 0; // Number of elements in the Array
// The size (number of elements) of the array
public int Size() {
return size;
}
// Add an element to the end of the dynamic array
public void Add( Object value ) {
Element e = new Element( value );
// Set the next element of the previous tail to the new element
if ( tail != null )
tail.next = e;
// set the current tail to the new element
tail = e;
// If there is no head (first element), set the head to the new element.
if ( head == null )
head = e;
// Increment the size of the array
size++;
}
// Get the value at the corresponding index
public Object Get( int index ) {
// Check for out of bounds condition
if ( index > size - 1 || index < 0 )
return null;
// Step (linear) to the index position
Element curr = head;
for ( int i = 0; i < index; i++ )
curr = curr.next;
return curr.value;
}
}
// Test Driver
public class dynamic {
public static void main(String[] args) {
DynamicArray d = new DynamicArray();
for ( int i = 0; i < 7; i++ )
d.Add(i);
System.out.println("Expect 0,1,2,3,4,5,6");
for ( int i = 0; i < d.Size(); i++ )
System.out.println( (int) d.Get(i) );
}
</pre>
<pre class='w3-container' ng-show='dyn1[3]'>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script>
$(function() {
var output = $("#output");
function println( text ) {
output.html( output.html() + "<br/>" + text );
}
// Definition for an element in the dynamic array
class Element {
// Constructor
constructor( value ) {
this.value = value; // Element value
this.next = null; // Next element in the array
}
}
// Definition for a Dynamic Array
class DynamicArray {
// constructor
constructor() {
this.head = null; // Head of the Array
this.tail = null; // Tail of the Array
this.size = 0; // Number of elements in the array
}
// The size (number of elements) of the array
Size() {
return this.size;
}
// Add an element to the end of the dynamic array
Add( value ) {
var e = new Element( value );
// Set the next element of the previous tail to the new element
if ( this.tail != null )
this.tail.next = e;
// set the current tail to the new element
this.tail = e;
// If there is no head (first element), set the head to the new element.
if ( this.head == null )
this.head = e;
// Increment the size of the array
this.size++;
}
// Get the value at the corresponding index
Get( index ) {
// Check for out of bounds condition
if ( index > this.size - 1 || index < 0 )
return null;
// Step (linear) to the index position
var curr = this.head;
for ( var i = 0; i < index; i++ )
curr = curr.next;
return curr.value;
}
}
// Test Driver
var d = new DynamicArray();
for ( var i = 0; i < 7; i++ )
d.Add(i);
println("Expect 0,1,2,3,4,5,6");
for ( var i = 0; i < d.Size(); i++ )
println( d.Get(i) );
});
</script>
<body>
<div id='output'></div>
</body>
</pre>
<a name="dynamic2"></a>
<h4>Delete</h4>
<ul class="w3-navbar w3-light-grey" ng-init="dyn2[0] = true; dyn2cls[0] = 'w3-black'">
<li><a href="javascript:void(0)" ng-click="dyn2=[true,false,false,false]; dyn2cls=['w3-black','w3-lightgray','w3-lightgray','w3-lightgray']; Algo('dyn2')" ng-class='dyn2cls[0]'>Algorithm</a></li>
<li><a href="javascript:void(0)" ng-click="dyn2=[false,true,false,false]; dyn2cls=['w3-lightgray','w3-black','w3-lightgray','w3-lightgray']; Python('dyn2')" ng-class='dyn2cls[1]'>Python</a></li>
<li><a href="javascript:void(0)" ng-click="dyn2=[false,false,true,false]; dyn2cls=['w3-lightgray','w3-lightgray','w3-black','w3-lightgray']; Java('dyn2')" ng-class='dyn2cls[2]'>Java</a></li>
<li><a href="javascript:void(0)" ng-click="dyn2=[false,false,false,true]; dyn2cls=['w3-lightgray','w3-lightgray','w3-lightgray','w3-black']; Javascript('dyn2')" ng-class='dyn2cls[3]'>Javascript</a></li>
</ul>