File List

Here is a list of all documented files with brief descriptions:

[detail level 123]

► backtracking
generate_parentheses.cpp	Well-formed Generated Parentheses with all combinations
graph_coloring.cpp	Prints the assigned colors using Graph Coloring algorithm
knight_tour.cpp	Knight's tour algorithm
minimax.cpp	Returns which is the longest/shortest number using minimax algorithm
n_queens.cpp	Eight Queens puzzle
n_queens_all_solution_optimised.cpp	N queens all optimized
nqueen_print_all_solutions.cpp	Eight Queens puzzle, printing all solutions
rat_maze.cpp	Implements Rat in a Maze algorithm
subarray_sum.cpp	Subset-sum (only continuous subsets) problem
subset_sum.cpp	Implementation of the Subset Sum problem
sudoku_solver.cpp	Sudoku Solver algorithm
wildcard_matching.cpp	Implementation of the Wildcard Matching problem
► bit_manipulation
count_bits_flip.cpp	Implementation to [Count number of bits to be flipped to convert A to B] (https://www.geeksforgeeks.org/count-number-of-bits-to-be-flipped-to-convert-a-to-b/) in an integer
count_of_set_bits.cpp	Implementation to [count number of set bits of a number] (https://www.geeksforgeeks.org/count-set-bits-in-an-integer/) in an integer
count_of_trailing_ciphers_in_factorial_n.cpp	Count the number of ciphers in n! implementation
find_non_repeating_number.cpp	Implementation to find the non repeating integer in an array of repeating integers. Single Number
hamming_distance.cpp	Returns the Hamming distance between two integers
next_higher_number_with_same_number_of_set_bits.cpp	[Next higher number with same number of set bits] (https://www.geeksforgeeks.org/next-higher-number-with-same-number-of-set-bits/) implementation
power_of_2.cpp	[Find whether a given number is power of 2] (https://www.geeksforgeeks.org/program-to-find-whether-a-given-number-is-power-of-2/) implementation
set_kth_bit.cpp	Implementation to [From the right, set the Kth bit in the binary representation of N] (https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/) in an integer
travelling_salesman_using_bit_manipulation.cpp	Implementation to [Travelling Salesman problem using bit-masking] (https://www.geeksforgeeks.org/travelling-salesman-problem-set-1/)
► ciphers
a1z26_cipher.cpp	Implementation of the A1Z26 cipher
atbash_cipher.cpp	Atbash Cipher implementation
caesar_cipher.cpp	Implementation of Caesar cipher algorithm
elliptic_curve_key_exchange.cpp	Implementation of Elliptic Curve Diffie Hellman Key Exchange
hill_cipher.cpp	Implementation of Hill cipher algorithm
morse_code.cpp	Implementation of [Morse Code] (https://en.wikipedia.org/wiki/Morse_code)
uint128_t.hpp
uint256_t.hpp
vigenere_cipher.cpp	Implementation of Vigenère cipher algorithm
xor_cipher.cpp	Implementation of XOR cipher algorithm
► cpu_scheduling_algorithms
fcfs_scheduling.cpp	Implementation of FCFS CPU scheduling algorithm
► data_structures
► cll
cll.h
avltree.cpp	A simple tree implementation using nodes
binary_search_tree.cpp	A simple tree implementation using structured nodes
binary_search_tree2.cpp	A generic binary search tree implementation. Here you can find more information about the algorithm: Scaler - Binary Search tree
binaryheap.cpp	A C++ program to demonstrate common Binary Heap Operations
bloom_filter.cpp	Bloom Filter generic implementation in C++
disjoint_set.cpp	Disjoint Sets Data Structure (Disjoint Sets)
dsu_path_compression.cpp	DSU (Disjoint sets)
dsu_union_rank.cpp	DSU (Disjoint sets)
linked_list.cpp	Implementation of singly linked list algorithm
linkedlist_implentation_usingarray.cpp	Linked list implementation using Arrays
list_array.cpp	Dynamic Array
node.hpp	Provides Node class and related utilities
queue.hpp
queue_using_array.cpp	Implementation of Linear [Queue using array] (https://www.geeksforgeeks.org/array-implementation-of-queue-simple/)
queue_using_two_stacks.cpp
reverse_a_linked_list.cpp	Implementation of Reversing a single linked list
segment_tree.cpp	A data structure to quickly do operations on ranges: the Segment Tree algorithm implementation
skip_list.cpp	Data structure for fast searching and insertion in \(O(\log n)\) time
sparse_table.cpp	Implementation of Sparse Table for min() function
stack.hpp	This class specifies the basic operation on a stack as a linked list
treap.cpp	A balanced binary search tree (BST) on the basis of binary search tree and heap: the Treap algorithm implementation
tree_234.cpp	A demo 2-3-4 tree implementation
trie_modern.cpp	A basic implementation of trie class to store only lower-case strings
trie_tree.cpp	Implementation of Trie data structure for English alphabets in small characters
trie_using_hashmap.cpp	Implementation of Trie data structure using HashMap for different characters and method for predicting words based on prefix
► divide_and_conquer
karatsuba_algorithm_for_fast_multiplication.cpp	Implementation of the Karatsuba algorithm for fast multiplication
► dynamic_programming
0_1_knapsack.cpp	Implementation of [0-1 Knapsack Problem] (https://en.wikipedia.org/wiki/Knapsack_problem)
abbreviation.cpp	Implementation of Abbrievation
armstrong_number.cpp	Checks whether a number is an Armstrong Number or not
coin_change_topdown.cpp	Minimum coins change problem is a problem used to find the minimum number of coins required to completely reach a target amount
cut_rod.cpp	Implementation of cutting a rod problem
house_robber.cpp	Implementation of House Robber Problem algorithm
kadane2.cpp	Implementation of Kadane Algorithm
longest_common_string.cpp	Definition of the function longest_common_string_length
longest_increasing_subsequence.cpp	Calculate the length of the longest increasing subsequence in an array
longest_palindromic_subsequence.cpp	Program to find the Longest Palindormic Subsequence of a string
maximum_circular_subarray.cpp	C++ program for maximum contiguous circular sum problem using Kadane's Algorithm
minimum_edit_distance.cpp	Implementation of Minimum Edit Distance using Dynamic Programing
palindrome_partitioning.cpp	Implements Palindrome Partitioning algorithm, giving you the minimum number of partitions you need to make
shortest_common_supersequence.cpp	SCS is a string Z which is the shortest supersequence of strings X and Y (may not be continuous in Z, but order is maintained)
subset_sum.cpp	Implements [Sub-set sum problem] (https://en.wikipedia.org/wiki/Subset_sum_problem) algorithm, which tells whether a subset with target sum exists or not
word_break.cpp	Word Break Problem
► games
memory_game.cpp	A simple Memory Game with 3 different sizes and multiple letters
► geometry
graham_scan_functions.hpp
jarvis_algorithm.cpp	Implementation of Jarvis’s algorithm
line_segment_intersection.cpp	Check whether two line segments intersect each other or not
► graph
bidirectional_dijkstra.cpp	[Bidirectional Dijkstra Shortest Path Algorithm] (https://www.coursera.org/learn/algorithms-on-graphs/lecture/7ml18/bidirectional-dijkstra)
breadth_first_search.cpp	Breadth First Search Algorithm (Breadth First Search)
connected_components.cpp	[Graph Connected Components (Connected Components)] (https://en.wikipedia.org/wiki/Component_(graph_theory))
connected_components_with_dsu.cpp	Disjoint union
depth_first_search.cpp	Depth First Search Algorithm (Depth First Search)
depth_first_search_with_stack.cpp	Depth First Search Algorithm using Stack (Depth First Search Algorithm)
dijkstra.cpp	[Graph Dijkstras Shortest Path Algorithm (Dijkstra's Shortest Path)] (https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)
hamiltons_cycle.cpp	The implementation of Hamilton's cycle dynamic solution for vertices number less than 20
hopcroft_karp.cpp	Implementation of Hopcroft–Karp algorithm
is_graph_bipartite.cpp	Algorithm to check whether a graph is bipartite
lowest_common_ancestor.cpp	Data structure for finding the lowest common ancestor of two vertices in a rooted tree using binary lifting
travelling_salesman_problem.cpp	[Travelling Salesman Problem] (https://en.wikipedia.org/wiki/Travelling_salesman_problem) implementation
► graphics
spirograph.cpp	Implementation of Spirograph
► greedy_algorithms
boruvkas_minimum_spanning_tree.cpp	[Borůvkas Algorithm](https://en.wikipedia.org/wiki/Borůvka's_algorithm) to find the Minimum Spanning Tree
dijkstra.cpp	Dijkstra algorithm implementation
jumpgame.cpp	Implementation of an algorithm to solve the jumping game problem
kruskals_minimum_spanning_tree.cpp	Kruskals Minimum Spanning Tree implementation
► hashing
chaining.cpp	Implementation of hash chains
double_hash_hash_table.cpp	Storage mechanism using double-hashed keys
linear_probing_hash_table.cpp	Storage mechanism using linear probing hash keys
md5.cpp	Simple C++ implementation of the MD5 Hashing Algorithm
quadratic_probing_hash_table.cpp	Storage mechanism using quadratic probing hash keys
sha1.cpp	Simple C++ implementation of the SHA-1 Hashing Algorithm
sha256.cpp	Simple C++ implementation of the [SHA-256 Hashing Algorithm] (https://en.wikipedia.org/wiki/SHA-2)
► machine_learning
adaline_learning.cpp	Adaptive Linear Neuron (ADALINE) implementation
k_nearest_neighbors.cpp	Implementation of [K-Nearest Neighbors algorithm] (https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm)
kohonen_som_topology.cpp	Kohonen self organizing map (topological map)
kohonen_som_trace.cpp	Kohonen self organizing map (data tracing)
neural_network.cpp	Implementation of [Multilayer Perceptron] (https://en.wikipedia.org/wiki/Multilayer_perceptron)
ordinary_least_squares_regressor.cpp	Linear regression example using Ordinary least squares
vector_ops.hpp	Various functions for vectors associated with [NeuralNetwork (aka Multilayer Perceptron)] (https://en.wikipedia.org/wiki/Multilayer_perceptron)
► math
aliquot_sum.cpp	Program to return the Aliquot Sum of a number
approximate_pi.cpp	Implementation to calculate an estimate of the number π (Pi)
area.cpp	Implementations for the area of various shapes
binary_exponent.cpp	C++ Program to find Binary Exponent Iteratively and Recursively
binomial_calculate.cpp	Program to calculate Binomial coefficients
check_amicable_pair.cpp	A C++ Program to check whether a pair of numbers is an amicable pair or not
check_factorial.cpp	A simple program to check if the given number is a factorial of some number or not
check_prime.cpp	A simple program to check if the given number is Prime or not
complex_numbers.cpp	An implementation of Complex Number as Objects
double_factorial.cpp	Compute double factorial: \(n!!\)
eratosthenes.cpp	The Sieve of Eratosthenes
eulers_totient_function.cpp	Implementation of Euler's Totient @description Euler Totient Function is also known as phi function
extended_euclid_algorithm.cpp	GCD using [extended Euclid's algorithm] (https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm)
factorial.cpp	Find the factorial of a given number
fast_power.cpp	Faster computation for \(a^b\)
fibonacci.cpp	Generate fibonacci sequence
fibonacci_fast.cpp	Faster computation of Fibonacci series
fibonacci_large.cpp	Computes N^th Fibonacci number given as input argument. Uses custom build arbitrary integers library to perform additions and other operations
fibonacci_matrix_exponentiation.cpp	This program computes the N^th Fibonacci number in modulo mod input argument
fibonacci_sum.cpp	An algorithm to calculate the sum of Fibonacci Sequence: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\)
finding_number_of_digits_in_a_number.cpp	[Program to count digits in an integer](https://www.geeksforgeeks.org/program-count-digits-integer-3-different-methods)
gcd_iterative_euclidean.cpp	Compute the greatest common denominator of two integers using iterative form of Euclidean algorithm
gcd_of_n_numbers.cpp	This program aims at calculating the GCD of n numbers by division method
gcd_recursive_euclidean.cpp	Compute the greatest common denominator of two integers using recursive form of Euclidean algorithm
integral_approximation.cpp	Compute integral approximation of the function using Riemann sum
integral_approximation2.cpp	Monte Carlo Integration
inv_sqrt.cpp	Implementation of the inverse square root Root
iterative_factorial.cpp	Iterative implementation of Factorial
large_factorial.cpp	Compute factorial of any arbitratily large number/
large_number.h	Library to perform arithmatic operations on arbitrarily large numbers
largest_power.cpp	Algorithm to find largest x such that p^x divides n! (factorial) using Legendre's Formula
lcm_sum.cpp	An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\)
least_common_multiple.cpp
magic_number.cpp	A simple program to check if the given number is a magic number or not. A number is said to be a magic number, if the sum of its digits are calculated till a single digit recursively by adding the sum of the digits after every addition. If the single digit comes out to be 1,then the number is a magic number
miller_rabin.cpp
modular_division.cpp	An algorithm to divide two numbers under modulo p Modular Division
modular_exponentiation.cpp	C++ Program for Modular Exponentiation Iteratively
modular_inverse_fermat_little_theorem.cpp	C++ Program to find the modular inverse using Fermat's Little Theorem
modular_inverse_simple.cpp	Simple implementation of modular multiplicative inverse
n_bonacci.cpp	Implementation of the N-bonacci series
n_choose_r.cpp	Combinations n choose r function implementation
ncr_modulo_p.cpp	This program aims at calculating nCr modulo p
number_of_positive_divisors.cpp	C++ Program to calculate the number of positive divisors
perimeter.cpp	Implementations for the perimeter of various shapes
power_for_huge_numbers.cpp	Compute powers of large numbers
power_of_two.cpp	Implementation to check whether a number is a power of 2 or not
prime_factorization.cpp	Prime factorization of positive integers
prime_numbers.cpp	Get list of prime numbers
primes_up_to_billion.cpp	Compute prime numbers upto 1 billion
quadratic_equations_complex_numbers.cpp	Calculate quadratic equation with complex roots, i.e. b^2 - 4ac < 0
realtime_stats.cpp	Compute statistics for data entered in rreal-time
sieve_of_eratosthenes.cpp	Get list of prime numbers using Sieve of Eratosthenes
sqrt_double.cpp	Calculate the square root of any positive real number in \(O(\log N)\) time, with precision fixed using bisection method of root-finding
string_fibonacci.cpp	This Programme returns the Nth fibonacci as a string
sum_of_binomial_coefficient.cpp	Algorithm to find sum of binomial coefficients of a given positive integer
sum_of_digits.cpp	A C++ Program to find the Sum of Digits of input integer
vector_cross_product.cpp	Calculates the Cross Product and the magnitude of two mathematical 3D vectors
volume.cpp	Implmentations for the volume of various 3D shapes
► numerical_methods
babylonian_method.cpp	A babylonian method (BM) is an algorithm that computes the square root
bisection_method.cpp	Solve the equation \(f(x)=0\) using bisection method
brent_method_extrema.cpp	Find real extrema of a univariate real function in a given interval using Brent's method
composite_simpson_rule.cpp	Implementation of the Composite Simpson Rule for the approximation
durand_kerner_roots.cpp	Compute all possible approximate roots of any given polynomial using Durand Kerner algorithm
false_position.cpp	Solve the equation \(f(x)=0\) using false position method, also known as the Secant method
fast_fourier_transform.cpp	A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT)
gaussian_elimination.cpp	Gaussian elimination method
golden_search_extrema.cpp	Find extrema of a univariate real function in a given interval using golden section search algorithm
gram_schmidt.cpp	Gram Schmidt Orthogonalisation Process
inverse_fast_fourier_transform.cpp	An inverse fast Fourier transform (IFFT) is an algorithm that computes the inverse fourier transform
lu_decompose.cpp	LU decomposition of a square matrix
lu_decomposition.h	Functions associated with LU Decomposition of a square matrix
midpoint_integral_method.cpp	A numerical method for easy approximation of integrals
newton_raphson_method.cpp	Solve the equation \(f(x)=0\) using Newton-Raphson method for both real and complex solutions
ode_forward_euler.cpp	Solve a multivariable first order ordinary differential equation (ODEs) using forward Euler method
ode_midpoint_euler.cpp	Solve a multivariable first order ordinary differential equation (ODEs) using midpoint Euler method
ode_semi_implicit_euler.cpp	Solve a multivariable first order ordinary differential equation (ODEs) using semi implicit Euler method
qr_decompose.h	Library functions to compute QR decomposition of a given matrix
qr_decomposition.cpp	Program to compute the QR decomposition of a given matrix
qr_eigen_values.cpp	Compute real eigen values and eigen vectors of a symmetric matrix using QR decomposition method
rungekutta.cpp	Runge Kutta fourth order method implementation
successive_approximation.cpp	Method of successive approximations using fixed-point iteration method
► operations_on_datastructures
array_left_rotation.cpp	Implementation for the Array Left Rotation algorithm
array_right_rotation.cpp	Implementation for the Array right Rotation algorithm
circular_linked_list.cpp	Implementation for a Circular Linked List
inorder_successor_of_bst.cpp	An implementation for finding the Inorder successor of a binary search tree Inorder successor of a node is the next node in Inorder traversal of the Binary Tree. Inorder Successor is NULL for the last node in Inorder traversal
intersection_of_two_arrays.cpp	Implementation for the Intersection of two sorted Arrays algorithm
reverse_binary_tree.cpp	Implementation for the Reversing a Binary Tree recursively algorithm
trie_multiple_search.cpp	Trie datastructure with search variants
union_of_two_arrays.cpp	Implementation for the Union of two sorted Arrays algorithm
► others
buzz_number.cpp	A buzz number is a number that is either divisible by 7 or has last digit as 7
decimal_to_binary.cpp	Function to convert decimal number to binary representation
decimal_to_hexadecimal.cpp	Convert decimal number to hexadecimal representation
decimal_to_roman_numeral.cpp	This Programme Converts a given decimal number in the range [0,4000) to both Lower case and Upper case Roman Numeral
fast_integer_input.cpp	Read integers from stdin continuously as they are entered without waiting for the \n character
happy_number.cpp	A happy number is a number whose sum of digits is calculated until the sum is a single digit, and this sum turns out to be 1
iterative_tree_traversals.cpp	Iterative version of Preorder, Postorder, and preorder [Traversal of the Tree] (https://en.wikipedia.org/wiki/Tree_traversal)
kadanes3.cpp	Efficient implementation for maximum contiguous subarray sum by Kadane's algorithm
kelvin_to_celsius.cpp	Conversion from Kelvin to Celsius degrees
lru_cache.cpp	An implementation of LRU Cache. Lru is a part of cache algorithms (also frequently called cache replacement algorithms or cache replacement policies)
matrix_exponentiation.cpp	Matrix Exponentiation
palindrome_of_number.cpp	Check if a number is palindrome or not
paranthesis_matching.cpp	Perform paranthesis matching
pascal_triangle.cpp	Pascal's triangle implementation
postfix_evaluation.cpp	Evaluation of Postfix Expression
primality_test.cpp	Primality test implementation
recursive_tree_traversal.cpp	Recursive version of Inorder, Preorder, and Postorder [Traversal of the Tree] (https://en.wikipedia.org/wiki/Tree_traversal)
smallest_circle.cpp	Get centre and radius of the smallest circle that circumscribes given set of points
sparse_matrix.cpp
spiral_print.cpp	Print the elements of a matrix traversing it spirally
stairs_pattern.cpp	This program is use to print the following pattern
tower_of_hanoi.cpp	Solve the Tower of Hanoi problem
vector_important_functions.cpp	A C++ program to demonstrate working of std::sort(), std::reverse()
► physics
ground_to_ground_projectile_motion.cpp	Ground to ground projectile motion equation implementations
► probability
addition_rule.cpp	Addition rule of probabilities
bayes_theorem.cpp	Bayes' theorem
binomial_dist.cpp	Binomial distribution example
geometric_dist.cpp	Geometric Distribution
poisson_dist.cpp	Poisson statistics
windowed_median.cpp	An implementation of a median calculation of a sliding window along a data stream
► range_queries
fenwick_tree.cpp	Fenwick Tree algorithm implementation
heavy_light_decomposition.cpp	Heavy Light Decomposition implementation
persistent_seg_tree_lazy_prop.cpp	Persistent segment tree with range updates (lazy propagation)
prefix_sum_array.cpp	Prefix Sum Array data structure implementation
segtree.cpp	Implementation of [Segment Tree] (https://en.wikipedia.org/wiki/Segment_tree) data structure
sparse_table.cpp	Implementation of Sparse Table data structure
► search
exponential_search.cpp	Exponential search algorithm
fibonacci_search.cpp	Fibonacci search algorithm
floyd_cycle_detection_algo.cpp	Implementation of Floyd's Cycle Detection algorithm
hash_search.cpp	Hash Search Algorithm - Best Time Complexity Ω(1)
interpolation_search2.cpp	Interpolation search algorithm
jump_search.cpp	C++ program to implement Jump Search
linear_search.cpp	Linear search algorithm
median_search.cpp	Implementation of Median search algorithm. @cases from here
median_search2.cpp	Given a linked list L[0,....,n] of n numbers, find the middle node
saddleback_search.cpp	Implementation of Saddleback Algorithm for 2D arrays
sublist_search.cpp	Implementation of the Sublist Search Algorithm
ternary_search.cpp	Ternary search algorithm
text_search.cpp	Search for words in a long textual paragraph
► sorting
binary_insertion_sort.cpp	Binary Insertion Sort Algorithm (Insertion Sort)
bogo_sort.cpp	Implementation of Bogosort algorithm
bubble_sort.cpp	Bubble sort algorithm
comb_sort.cpp	Comb Sort Algorithm (Comb Sort)
count_inversions.cpp	Counting Inversions using Merge Sort
cycle_sort.cpp	Implementation of Cycle sort algorithm
dnf_sort.cpp	Implementation of the DNF sort implementation
gnome_sort.cpp	Implementation of gnome sort algorithm
heap_sort.cpp	Heap Sort Algorithm (heap sort) implementation
insertion_sort.cpp	Insertion Sort Algorithm (Insertion Sort)
merge_insertion_sort.cpp	Algorithm that combines insertion sort and merge sort. Wiki link
merge_sort.cpp	Merege Sort Algorithm (MEREGE SORT) implementation
non_recursive_merge_sort.cpp
pancake_sort.cpp	Pancake sort sorts a disordered stack of pancakes by flipping any number of pancakes using a spatula using minimum number of flips
pigeonhole_sort.cpp	Implementation of [Pigeonhole Sort algorithm] (https://en.wikipedia.org/wiki/Pigeonhole_sort)
quick_sort.cpp	Quick sort implementation in C++
quick_sort_3.cpp	Implementation Details
radix_sort2.cpp	Algorithm of Radix sort
random_pivot_quick_sort.cpp	Implementation of the Random Pivot Quick Sort algorithm
recursive_bubble_sort.cpp	This is an implementation of a recursive version of the Bubble sort algorithm
selection_sort_recursive.cpp	Implementation of the Selection sort implementation using recursion
shell_sort2.cpp	Shell sort algorithm
stooge_sort.cpp	Stooge sort implementation in C++
strand_sort.cpp	Implementation of Strand Sort algorithm
wave_sort.cpp	Implementation of the Wave sort algorithm
wiggle_sort.cpp	[Wiggle Sort Algorithm] (https://leetcode.com/problems/wiggle-sort-ii/) Implementation
► strings
boyer_moore.cpp	The Boyer–Moore algorithm searches for occurrences of pattern P in text T by performing explicit character comparisons at different alignments. Instead of a brute-force search of all alignments (of which there are n - m + 1), Boyer–Moore uses information gained by preprocessing P to skip as many alignments as possible
brute_force_string_searching.cpp	String pattern search - brute force
horspool.cpp	Horspool's algorithm that finds if a string contains a substring (https://en.wikipedia.org/wiki/Boyer%E2%80%93Moore%E2%80%93Horspool_algorithm)
knuth_morris_pratt.cpp	The Knuth-Morris-Pratt Algorithm for finding a pattern within a piece of text with complexity O(n + m)
manacher_algorithm.cpp	Implementation of Manacher's Algorithm
rabin_karp.cpp	The Rabin-Karp Algorithm for finding a pattern within a piece of text with complexity O(n + m)
z_function.cpp	The Z function for finding occurences of a pattern within a piece of text with time and space complexity O(n + m)