Algorithms_in_C++: dynamic_programming/shortest_common_supersequence.cpp File Reference
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+ Algorithms_in_C++
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+ Set of algorithms implemented in C++.
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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).
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#include <iostream>#include <string>#include <vector>#include <algorithm>#include <cassert>
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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).
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The idea is to use lookup table method as used in LCS. For example: example 1:- X: 'ABCXYZ', Y: 'ABZ' then Z will be 'ABCXYZ' (y is not continuous but in order)
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For example: example 2:- X: 'AGGTAB', Y: 'GXTXAYB' then Z will be 'AGGXTXAYB'
Author Ridhish Jain
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See also more on SCS
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+related problem Leetcode
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Main function (driver code)
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Function implementing Shortest Common Super-Sequence algorithm using look-up table method.
Parameters
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+ str1 first string 'X' str2 second string 'Y'
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Returns string 'Z', superSequence of X and Y
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49 else if (str1.
empty ()) {
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52 else if (str2.
empty ()) {
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59 for (
int i=1; i <= str1.
length (); i++) {
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60 for (
int j=1; j <= str2.
length (); j++) {
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61 if (str1[i-1] == str2[j-1]) {
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62 lookup[i][j] = lookup[i-1][j-1] + 1;
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65 lookup[i][j] =
std::max (lookup[i-1][j], lookup[i][j-1]);
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81 if (str1[i-1] == str2[j-1]) {
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88 if (lookup[i-1][j] > lookup[i][j-1]) {
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Test Function
Returns void
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129 {
"AGGTAB" ,
"GXTXAYB" },
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136 for (
auto & scsString : scsStrings) {
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139 scsString[0], scsString[1]
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155 for (
int i=0; i < scsStrings.size(); i++) {
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156 assert(expectedOutput[i] == calculatedOutput[i]);
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159 std::cout <<
"All tests passed successfully!\n" ;
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static void test()
Definition: shortest_common_supersequence.cpp:124
ll ans(ll n)
Definition: matrix_exponentiation.cpp:91
std::string scs(const std::string &str1, const std::string &str2)
Definition: shortest_common_supersequence.cpp:42
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diff --git a/d7/d65/shortest__common__supersequence_8cpp_ad2ee8d7e67da9f6eb85146b08dad95e6_cgraph.md5 b/d7/d65/shortest__common__supersequence_8cpp_ad2ee8d7e67da9f6eb85146b08dad95e6_cgraph.md5
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diff --git a/d7/d65/shortest__common__supersequence_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map b/d7/d65/shortest__common__supersequence_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map
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diff --git a/d7/d65/shortest__common__supersequence_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5 b/d7/d65/shortest__common__supersequence_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5
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diff --git a/d7/d65/shortest__common__supersequence_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg b/d7/d65/shortest__common__supersequence_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg
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diff --git a/dd/d24/namespacedynamic__programming.html b/dd/d24/namespacedynamic__programming.html
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+Algorithms_in_C++: dynamic_programming Namespace Reference
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+ Algorithms_in_C++
+ 1.0.0
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+ Set of algorithms implemented in C++.
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Dynamic Programming algorithms.
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Dynamic Programming algorithms.
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+
dynamic_programming Directory Reference
+
+file 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).
skip_list.cpp Data structure for fast searching and insertion in \(O(\log n)\) time stack.h This class specifies the basic operation on a stack as a linked list trie_modern.cpp A basic implementation of trie class to store only lower-case strings ► geometry jarvis_algorithm.cpp Implementation of Jarvis’s algorithm line_segment_intersection.cpp Check whether two line segments intersect each other or not ► graph breadth_first_search.cpp Breadth First Search Algorithm (Breadth First Search) connected_components.cpp Graph Connected Components (Connected Components) dijkstra.cpp Graph Dijkstras Shortest Path Algorithm (Dijkstra's Shortest Path) hamiltons_cycle.cpp The implementation of Hamilton's cycle dynamic solution for vertices number less than 20 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 ► graphics spirograph.cpp Implementation of Spirograph ► 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 quadratic_probing_hash_table.cpp Storage mechanism using quadratic probing hash keys ► machine_learning adaline_learning.cpp Adaptive Linear Neuron (ADALINE) implementation kohonen_som_topology.cpp Kohonen self organizing map (topological map) kohonen_som_trace.cpp Kohonen self organizing map (data tracing) ordinary_least_squares_regressor.cpp Linear regression example using Ordinary least squares ► math armstrong_number.cpp Program to check if a number is an Armstrong/Narcissistic number in decimal system binary_exponent.cpp C++ Program to find Binary Exponent Iteratively and Recursively check_amicable_pair.cpp A C++ Program to check whether a pair of number is amicable pair or not check_prime.cpp Reduced all possibilities of a number which cannot be prime. Eg: No even number, except 2 can be a prime number, hence we will increment our loop with i+2 jumping on all odd numbers only. If number is <= 1 or if it is even except 2, break the loop and return false telling number is not prime complex_numbers.cpp An implementation of Complex Number as Objects double_factorial.cpp Compute double factorial : \(n!!\) eulers_totient_function.cpp C++ Program to find Euler's Totient function extended_euclid_algorithm.cpp GCD using extended Euclid's algorithm factorial.cpp C++ program to find factorial of 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 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 large_factorial.cpp Compute factorial of any arbitratily large number/ large_number.h Library to perform arithmatic operations on arbitrarily large numbers least_common_multiple.cpp miller_rabin.cpp modular_inverse_fermat_little_theorem.cpp C++ Program to find the modular inverse using Fermat's Little Theorem number_of_positive_divisors.cpp C++ Program to calculate the number of positive divisors power_for_huge_numbers.cpp Compute powers of large numbers 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 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_digits.cpp A C++ Program to find the Sum of Digits of input integer ► numerical_methods 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 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 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 lu_decompose.cpp LU decomposition of a square matrix lu_decomposition.h Functions associated with LU Decomposition of a square matrix 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 successive_approximation.cpp Method of successive approximations using fixed-point iteration method ► 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_interger_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 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 primality_test.cpp Primality test implementation 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() ► probability addition_rule.cpp Addition rule of probabilities bayes_theorem.cpp Bayes' theorem binomial_dist.cpp Binomial distribution example poisson_dist.cpp Poisson statistics ► range_queries fenwick_tree.cpp Fenwick tree ► search binary_search.cpp Binary search algorithm exponential_search.cpp Exponential search algorithm fibonacci_search.cpp Fibonacci search algorithm hash_search.cpp Hash Search Algorithm - Best Time Complexity Ω(1) interpolation_search.cpp Interpolation search algorithm interpolation_search2.cpp Interpolation search algorithm jump_search.cpp C++ program to implement Jump Search linear_search.cpp Linear search algorithm median_search.cpp Median search algorithm ternary_search.cpp Ternary search algorithm text_search.cpp Search for words in a long textual paragraph ► sorting bogo_sort.cpp Implementation of Bogosort algorithm bubble_sort.cpp Bubble sort algorithm comb_sort.cpp Comb Sort Algorithm (Comb Sort) 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_sort.cpp Merege Sort Algorithm (MEREGE SORT) implementation non_recursive_merge_sort.cpp quick_sort.cpp Quick sort algorithm quick_sort_3.cpp Implementation Details shell_sort2.cpp Shell sort algorithm ► strings brute_force_string_searching.cpp String pattern search - brute force knuth_morris_pratt.cpp The Knuth-Morris-Pratt Algorithm for finding a pattern within a piece of text with complexity O(n + m) rabin_karp.cpp The Rabin-Karp Algorithm for finding a pattern within a piece of text with complexity O(n + m) ► dynamic_programming 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) ► geometry jarvis_algorithm.cpp Implementation of Jarvis’s algorithm line_segment_intersection.cpp Check whether two line segments intersect each other or not ► graph breadth_first_search.cpp Breadth First Search Algorithm (Breadth First Search) connected_components.cpp Graph Connected Components (Connected Components) dijkstra.cpp Graph Dijkstras Shortest Path Algorithm (Dijkstra's Shortest Path) hamiltons_cycle.cpp The implementation of Hamilton's cycle dynamic solution for vertices number less than 20 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 ► graphics spirograph.cpp Implementation of Spirograph ► 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 quadratic_probing_hash_table.cpp Storage mechanism using quadratic probing hash keys ► machine_learning adaline_learning.cpp Adaptive Linear Neuron (ADALINE) implementation kohonen_som_topology.cpp Kohonen self organizing map (topological map) kohonen_som_trace.cpp Kohonen self organizing map (data tracing) ordinary_least_squares_regressor.cpp Linear regression example using Ordinary least squares ► math armstrong_number.cpp Program to check if a number is an Armstrong/Narcissistic number in decimal system binary_exponent.cpp C++ Program to find Binary Exponent Iteratively and Recursively check_amicable_pair.cpp A C++ Program to check whether a pair of number is amicable pair or not check_prime.cpp Reduced all possibilities of a number which cannot be prime. Eg: No even number, except 2 can be a prime number, hence we will increment our loop with i+2 jumping on all odd numbers only. If number is <= 1 or if it is even except 2, break the loop and return false telling number is not prime complex_numbers.cpp An implementation of Complex Number as Objects double_factorial.cpp Compute double factorial : \(n!!\) eulers_totient_function.cpp C++ Program to find Euler's Totient function extended_euclid_algorithm.cpp GCD using extended Euclid's algorithm factorial.cpp C++ program to find factorial of 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 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 large_factorial.cpp Compute factorial of any arbitratily large number/ large_number.h Library to perform arithmatic operations on arbitrarily large numbers least_common_multiple.cpp miller_rabin.cpp modular_inverse_fermat_little_theorem.cpp C++ Program to find the modular inverse using Fermat's Little Theorem number_of_positive_divisors.cpp C++ Program to calculate the number of positive divisors power_for_huge_numbers.cpp Compute powers of large numbers 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 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_digits.cpp A C++ Program to find the Sum of Digits of input integer ► numerical_methods 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 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 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 lu_decompose.cpp LU decomposition of a square matrix lu_decomposition.h Functions associated with LU Decomposition of a square matrix 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 successive_approximation.cpp Method of successive approximations using fixed-point iteration method ► 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_interger_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 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 primality_test.cpp Primality test implementation 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() ► probability addition_rule.cpp Addition rule of probabilities bayes_theorem.cpp Bayes' theorem binomial_dist.cpp Binomial distribution example poisson_dist.cpp Poisson statistics ► range_queries fenwick_tree.cpp Fenwick tree ► search binary_search.cpp Binary search algorithm exponential_search.cpp Exponential search algorithm fibonacci_search.cpp Fibonacci search algorithm hash_search.cpp Hash Search Algorithm - Best Time Complexity Ω(1) interpolation_search.cpp Interpolation search algorithm interpolation_search2.cpp Interpolation search algorithm jump_search.cpp C++ program to implement Jump Search linear_search.cpp Linear search algorithm median_search.cpp Median search algorithm ternary_search.cpp Ternary search algorithm text_search.cpp Search for words in a long textual paragraph ► sorting bogo_sort.cpp Implementation of Bogosort algorithm bubble_sort.cpp Bubble sort algorithm comb_sort.cpp Comb Sort Algorithm (Comb Sort) 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_sort.cpp Merege Sort Algorithm (MEREGE SORT) implementation non_recursive_merge_sort.cpp quick_sort.cpp Quick sort algorithm quick_sort_3.cpp Implementation Details shell_sort2.cpp Shell sort algorithm ► strings brute_force_string_searching.cpp String pattern search - brute force knuth_morris_pratt.cpp The Knuth-Morris-Pratt Algorithm for finding a pattern within a piece of text with complexity O(n + m) rabin_karp.cpp The Rabin-Karp Algorithm for finding a pattern within a piece of text with complexity O(n + m) 
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