From 76d718f5630a63b7cce27ad0fde7d8a2867e230c Mon Sep 17 00:00:00 2001 From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Date: Fri, 30 Oct 2020 16:31:57 +0000 Subject: [PATCH] Documentation for 15ce8ac92df6f4a89fe590b4623761d0f64919dd --- d1/da6/rungekutta_8cpp.html | 391 ++++++++++++++ d1/da6/rungekutta_8cpp.js | 7 + ...b9f40c7b5e9749cc550f19be3dc8856_cgraph.map | 5 + ...b9f40c7b5e9749cc550f19be3dc8856_cgraph.md5 | 1 + ...b9f40c7b5e9749cc550f19be3dc8856_cgraph.svg | 59 +++ ...66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map | 4 + ...66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5 | 1 + ...66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg | 37 ++ d1/de0/namespacenumerical__methods.html | 1 + d1/df3/hash__search_8cpp.html | 2 + d2/de7/namespacerunge__kutta.html | 112 ++++ d3/d40/graph__coloring_8cpp.html | 10 +- d5/d88/md__d_i_r_e_c_t_o_r_y.html | 1 + dc/d5a/rat__maze_8cpp.html | 2 +- ...ical_methods_2rungekutta_8cpp-example.html | 251 +++++++++ dc/dc7/rungekutta_8cpp__incl.map | 6 + 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create mode 100644 d1/da6/rungekutta_8cpp_a7b9f40c7b5e9749cc550f19be3dc8856_cgraph.svg create mode 100644 d1/da6/rungekutta_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map create mode 100644 d1/da6/rungekutta_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5 create mode 100644 d1/da6/rungekutta_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg create mode 100644 d2/de7/namespacerunge__kutta.html create mode 100644 dc/dc4/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2numerical_methods_2rungekutta_8cpp-example.html create mode 100644 dc/dc7/rungekutta_8cpp__incl.map create mode 100644 dc/dc7/rungekutta_8cpp__incl.md5 create mode 100644 dc/dc7/rungekutta_8cpp__incl.svg diff --git a/d1/da6/rungekutta_8cpp.html b/d1/da6/rungekutta_8cpp.html new file mode 100644 index 000000000..baac09907 --- /dev/null +++ b/d1/da6/rungekutta_8cpp.html @@ -0,0 +1,391 @@ + + + + + + + +Algorithms_in_C++: numerical_methods/rungekutta.cpp File Reference + + + + + + + + + + + + + + + +
+
+ + + + + + +
+
Algorithms_in_C++ +  1.0.0 +
+
Set of algorithms implemented in C++.
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+
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+ +
+ +
+
+ + +
+ +
+ +
+ +
+
rungekutta.cpp File Reference
+
+
+ +

Runge Kutta fourth order method implementation +More...

+
#include <iostream>
+#include <vector>
+#include <cassert>
+
+Include dependency graph for rungekutta.cpp:
+
+
+
+
+
+ + + + + + + +

+Namespaces

 numerical_methods
 for io operations
 
 runge_kutta
 Functions for Runge Kutta fourth order method.
 
+ + + + + + + + + + + + + + +

+Functions

double numerical_methods::runge_kutta::rungeKutta (double init_x, const double &init_y, const double &x, const double &h)
 the Runge Kutta method finds the value of integration of a function in the given limits. the lower limit of integration as the initial value and the upper limit is the given x More...
 
static double change (double x, double y)
 asserting the test functions More...
 
static void test ()
 Tests to check algorithm implementation. More...
 
int main ()
 Main function. More...
 
+

Detailed Description

+

Runge Kutta fourth order method implementation

+
Author
Rudra Prasad Das
+

It solves the unknown value of y for a given value of x only first order differential equations can be solved

+

Function Documentation

+ +

◆ change()

+ +
+
+ + + + + +
+ + + + + + + + + + + + + + + + + + +
static double change (double x,
double y 
)
+
+static
+
+ +

asserting the test functions

+

for io operations for using the vector container

+

The change() function is used to return the updated iterative value corresponding to the given function

Parameters
+ + + +
xis the value corresponding to the x coordinate
yis the value corresponding to the y coordinate
+
+
+
Returns
the computed function value at that call
+
Examples
/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp.
+
+
32 {
+
33  return ((x - y)/2.0);
+
34 
+
35 }
+
+
+
+ +

◆ main()

+ +
+
+ + + + + + + + +
int main (void )
+
+ +

Main function.

+
Returns
0 on exit
+
131 {
+
132 
+
133  test(); // Execute the tests
+
134  return 0;
+
135 }
+
+Here is the call graph for this function:
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+
+
+
+ +
+
+ +

◆ rungeKutta()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
double numerical_methods::runge_kutta::rungeKutta (double init_x,
const double & init_y,
const double & x,
const double & h 
)
+
+ +

the Runge Kutta method finds the value of integration of a function in the given limits. the lower limit of integration as the initial value and the upper limit is the given x

+
Parameters
+ + + + + +
init_xis the value of initial x and is updated after each call
init_yis the value of initial x and is updated after each call
xis current iteration at which the function needs to be evaluated
his the step value
+
+
+
Returns
the value of y at thr required value of x from the initial conditions
+
Examples
/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp.
+
+
57 {
+
58 
+
59  // Count number of iterations
+
60  // using step size or
+
61  // step height h
+
62 
+
63 
+
64  // n calucates the number of iterations
+
65  // k1, k2, k3, k4 are the Runge Kutta variables
+
66  // used for calculation of y at each iteration
+
67 
+
68  auto n = static_cast<uint64_t>((x - init_x) / h);
+
69  // used a vector container for the variables
+
70  std::vector<double> k(4,0.0);
+
71 
+
72 
+
73  // Iterate for number of iterations
+
74 
+
75  double y = init_y;
+
76  for (int i=1; i<=n; ++i)
+
77  {
+
78 
+
79  // Apply Runge Kutta Formulas
+
80  // to find next value of y
+
81  k[0] = h*change(init_x, y);
+
82  k[1] = h*change(init_x + 0.5*h, y + 0.5*k[0]);
+
83  k[2] = h*change(init_x + 0.5*h, y + 0.5*k[1]);
+
84  k[3] = h*change(init_x + h, y + k[2]);
+
85 
+
86 
+
87  // Update next value of y
+
88 
+
89  y += (1.0/6.0)*(k[0] + 2*k[1] + 2*k[2] + k[3]);
+
90 
+
91  // Update next value of x
+
92 
+
93  init_x += h;
+
94  }
+
95 
+
96  return y;
+
97 }
+
+Here is the call graph for this function:
+
+
+
+
+ +
+
+ +

◆ test()

+ +
+
+ + + + + +
+ + + + + + + +
static void test ()
+
+static
+
+ +

Tests to check algorithm implementation.

+
Returns
void
+
106  {
+
107  std::cout << "The Runge Kutta function will be tested on the basis of precomputed values\n";
+
108 
+
109  std::cout << "Test 1...." << "\n";
+
110  double valfirst=numerical_methods::runge_kutta::rungeKutta(2,3,4,0.2); // Tests the function with pre calculated values
+
111  assert(valfirst==3.10363932323749570);
+
112  std::cout << "Passed Test 1\n";
+
113 
+
114  std::cout << "Test 2...." << "\n";
+
115  double valsec=numerical_methods::runge_kutta::rungeKutta(1,2,5,0.1); // The value of step changed
+
116  assert(valsec==3.40600589380261409);
+
117  std::cout << "Passed Test 2\n";
+
118 
+
119  std::cout << "Test 3...." << "\n";
+
120  double valthird=numerical_methods::runge_kutta::rungeKutta(-1,3,4,0.1); // Tested with negative value
+
121  assert(valthird==2.49251005860244268);
+
122  std::cout << "Passed Test 3\n";
+
123  }
+
+
+
+
+
+
std::vector< double >
+
std::cout
+
h
int h(int key)
Definition: hash_search.cpp:45
+
change
static double change(double x, double y)
asserting the test functions
Definition: rungekutta.cpp:31
+
numerical_methods::runge_kutta::rungeKutta
double rungeKutta(double init_x, const double &init_y, const double &x, const double &h)
the Runge Kutta method finds the value of integration of a function in the given limits....
Definition: rungekutta.cpp:56
+
test
static void test()
Tests to check algorithm implementation.
Definition: rungekutta.cpp:105
+ + + + diff --git a/d1/da6/rungekutta_8cpp.js b/d1/da6/rungekutta_8cpp.js new file mode 100644 index 000000000..d81c25c45 --- /dev/null +++ b/d1/da6/rungekutta_8cpp.js @@ -0,0 +1,7 @@ +var rungekutta_8cpp = +[ + [ "change", "d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579", null ], + [ "main", "d1/da6/rungekutta_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4", null ], + [ "rungeKutta", "d1/da6/rungekutta_8cpp.html#a7b9f40c7b5e9749cc550f19be3dc8856", null ], + [ "test", "d1/da6/rungekutta_8cpp.html#aa8dca7b867074164d5f45b0f3851269d", null ] +]; \ No newline at end of file diff --git a/d1/da6/rungekutta_8cpp_a7b9f40c7b5e9749cc550f19be3dc8856_cgraph.map b/d1/da6/rungekutta_8cpp_a7b9f40c7b5e9749cc550f19be3dc8856_cgraph.map new file mode 100644 index 000000000..faaec39af --- /dev/null +++ b/d1/da6/rungekutta_8cpp_a7b9f40c7b5e9749cc550f19be3dc8856_cgraph.map @@ -0,0 +1,5 @@ + + + + + diff --git a/d1/da6/rungekutta_8cpp_a7b9f40c7b5e9749cc550f19be3dc8856_cgraph.md5 b/d1/da6/rungekutta_8cpp_a7b9f40c7b5e9749cc550f19be3dc8856_cgraph.md5 new file mode 100644 index 000000000..62ffa7090 --- /dev/null +++ b/d1/da6/rungekutta_8cpp_a7b9f40c7b5e9749cc550f19be3dc8856_cgraph.md5 @@ -0,0 +1 @@ +b6f029e30ef280b3989d6def4d5f776b \ No newline at end of file diff --git a/d1/da6/rungekutta_8cpp_a7b9f40c7b5e9749cc550f19be3dc8856_cgraph.svg b/d1/da6/rungekutta_8cpp_a7b9f40c7b5e9749cc550f19be3dc8856_cgraph.svg new file mode 100644 index 000000000..7665e857e --- /dev/null +++ b/d1/da6/rungekutta_8cpp_a7b9f40c7b5e9749cc550f19be3dc8856_cgraph.svg @@ -0,0 +1,59 @@ + + + + + + +numerical_methods::runge_kutta::rungeKutta + + + +Node1 + + +numerical_methods:: +runge_kutta::rungeKutta + + + + + +Node1->Node1 + + + + + +Node2 + + +change + + + + + +Node1->Node2 + + + + + +Node3 + + +h + + + + + +Node1->Node3 + + + + + diff --git a/d1/da6/rungekutta_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map b/d1/da6/rungekutta_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map new file mode 100644 index 000000000..6a6f8f0bf --- /dev/null +++ b/d1/da6/rungekutta_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map @@ -0,0 +1,4 @@ + + + + diff --git a/d1/da6/rungekutta_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5 b/d1/da6/rungekutta_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5 new file mode 100644 index 000000000..78248fb4a --- /dev/null +++ b/d1/da6/rungekutta_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5 @@ -0,0 +1 @@ +edb7409d59319402656d568b23b8d3f1 \ No newline at end of file diff --git a/d1/da6/rungekutta_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg b/d1/da6/rungekutta_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg new file mode 100644 index 000000000..121a8da97 --- /dev/null +++ b/d1/da6/rungekutta_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg @@ -0,0 +1,37 @@ + + + + + + +main + + + +Node1 + + +main + + + + + +Node2 + + +test + + + + + +Node1->Node2 + + + + + diff --git a/d1/de0/namespacenumerical__methods.html b/d1/de0/namespacenumerical__methods.html index 0d5d04c80..64881d12c 100644 --- a/d1/de0/namespacenumerical__methods.html +++ b/d1/de0/namespacenumerical__methods.html @@ -99,6 +99,7 @@ $(document).ready(function(){initNavTree('d1/de0/namespacenumerical__methods.htm More...

Detailed Description

for io operations

+

Numerical Methods.

for math operations

Numerical methods

diff --git a/d1/df3/hash__search_8cpp.html b/d1/df3/hash__search_8cpp.html index e4a055f85..096654bd9 100644 --- a/d1/df3/hash__search_8cpp.html +++ b/d1/df3/hash__search_8cpp.html @@ -251,6 +251,8 @@ Here is the call graph for this function:
Returns
hash value for key
+
Examples
/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp.
+
45 { return key % HASHMAX; }
diff --git a/d2/de7/namespacerunge__kutta.html b/d2/de7/namespacerunge__kutta.html new file mode 100644 index 000000000..846fb030f --- /dev/null +++ b/d2/de7/namespacerunge__kutta.html @@ -0,0 +1,112 @@ + + + + + + + +Algorithms_in_C++: runge_kutta Namespace Reference + + + + + + + + + + + + + + + +
+
+ + + + + + +
+
Algorithms_in_C++ +  1.0.0 +
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Set of algorithms implemented in C++.
+
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+ +
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+ +
+ +
+
+ + +
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+ +
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+
runge_kutta Namespace Reference
+
+
+ +

Functions for Runge Kutta fourth order method. +More...

+

Detailed Description

+

Functions for Runge Kutta fourth order method.

+
+
+ + + + diff --git a/d3/d40/graph__coloring_8cpp.html b/d3/d40/graph__coloring_8cpp.html index e82a77194..66ad71c06 100644 --- a/d3/d40/graph__coloring_8cpp.html +++ b/d3/d40/graph__coloring_8cpp.html @@ -154,7 +154,7 @@ Functions

Main function

Driver Code

-
Examples
/Users/runner/work/C-Plus-Plus/C-Plus-Plus/sorting/wiggle_sort.cpp.
+
Examples
/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp, and /Users/runner/work/C-Plus-Plus/C-Plus-Plus/sorting/wiggle_sort.cpp.
96  {
97  // Create following graph and test whether it is 3 colorable
@@ -218,6 +218,7 @@ Functions
void heapSort(T *arr, int n)
Definition: heap_sort.cpp:84
int t_root
the root of the tree
Definition: heavy_light_decomposition.cpp:91
+
for io operations
T move(T... args)
int main()
Definition: binomial_dist.cpp:84
double addition_rule_dependent(double A, double B, double B_given_A)
Definition: addition_rule.cpp:25
@@ -234,7 +235,7 @@ Functions
void update(int p, X v)
Update the value at a node.
Definition: heavy_light_decomposition.cpp:293
Tree(int nodes)
Class parameterized constructor, resizes the and initializes the data members.
Definition: heavy_light_decomposition.cpp:140
bool random_tests()
random tests which cover cases when we have one, multiple or zero occurences of the value we're looki...
Definition: fibonacci_search.cpp:96
-
STL class.
+
T find(T... args)
X sret_init
inital query return value
Definition: heavy_light_decomposition.cpp:264
T size(T... args)
@@ -364,6 +365,7 @@ Functions
char opening(char ch)
Definition: paranthesis_matching.cpp:36
T c_str(T... args)
void dfs_hc(int u, int p=-1)
Utility function to assign heavy child to each node (-1 for a leaf node)
Definition: heavy_light_decomposition.cpp:350
+
Functions for Runge Kutta fourth order method.
bool is_happy(T n)
Definition: happy_number.cpp:14
bool check_if_equal(const std::string &str1, const std::string &str2, int start1, int end1, int start2, int end2)
Definition: rabin_karp.cpp:60
static void displayElements(const std::vector< T > &arr)
Utility function used for printing the elements. Prints elements of the array after they're sorted us...
Definition: wiggle_sort.cpp:84
@@ -472,6 +474,7 @@ Functions
int main()
Definition: spiral_print.cpp:69
#define MAX
Definition: paranthesis_matching.cpp:16
Definition: stack.h:26
+
static double change(double x, double y)
asserting the test functions
Definition: rungekutta.cpp:31
vector< vector< ll > > power(const vector< vector< ll >> &A, ll p)
Definition: matrix_exponentiation.cpp:76
static void InsertionSort(std::array< T, N > *A, size_t start, size_t end)
Insertion merge algorithm.
Definition: merge_insertion_sort.cpp:37
Graph algorithms.
@@ -506,6 +509,7 @@ Functions
node< Type > * stackTop
Definition: stack.h:146
#define LIMS
Definition: qr_eigen_values.cpp:20
T end(T... args)
+
double rungeKutta(double init_x, const double &init_y, const double &x, const double &h)
the Runge Kutta method finds the value of integration of a function in the given limits....
Definition: rungekutta.cpp:56
char stack[MAX]
Definition: paranthesis_matching.cpp:20
double bayes_AgivenB(double BgivenA, double A, double B)
Definition: bayes_theorem.cpp:14
int sum(int id)
Definition: fenwick_tree.cpp:54
@@ -515,6 +519,7 @@ Functions
static void test()
Function to test code using random arrays.
Definition: merge_insertion_sort.cpp:132
void change_root(int new_root)
Set the root for the tree.
Definition: heavy_light_decomposition.cpp:167
FenwickTree(int x)
Definition: fenwick_tree.cpp:39
+
static void test()
Tests to check algorithm implementation.
Definition: rungekutta.cpp:105
Point(double a=0.f, double b=0.f)
Definition: smallest_circle.cpp:23
int main()
Definition: primality_test.cpp:31
std::vector< int > h_label
stores the label of a node
Definition: heavy_light_decomposition.cpp:339
@@ -523,6 +528,7 @@ Functions
Definition: line_segment_intersection.cpp:12
void TH(int n, tower *From, tower *Using, tower *To)
Definition: tower_of_hanoi.cpp:52
int interpolation_search(int arr[], int value, int len)
Definition: interpolation_search.cpp:15
+
int main()
Main function.
Definition: rungekutta.cpp:130
void push(char ch)
push byte to stack variable
Definition: paranthesis_matching.cpp:26
int main()
Definition: bogo_sort.cpp:104
static void test_2()
Definition: pigeonhole_sort.cpp:88
diff --git a/d5/d88/md__d_i_r_e_c_t_o_r_y.html b/d5/d88/md__d_i_r_e_c_t_o_r_y.html index c9ac28991..5da5d3b68 100644 --- a/d5/d88/md__d_i_r_e_c_t_o_r_y.html +++ b/d5/d88/md__d_i_r_e_c_t_o_r_y.html @@ -296,6 +296,7 @@ Numerical Methods
  • Qr Decompose
  • Qr Decomposition
  • Qr Eigen Values
  • +
  • Rungekutta
  • Successive Approximation
  • diff --git a/dc/d5a/rat__maze_8cpp.html b/dc/d5a/rat__maze_8cpp.html index 97b5df7c7..07ed192e5 100644 --- a/dc/d5a/rat__maze_8cpp.html +++ b/dc/d5a/rat__maze_8cpp.html @@ -294,7 +294,7 @@ Here is the call graph for this function:

    Test implementations.

    Returns
    void
    -
    Examples
    /Users/runner/work/C-Plus-Plus/C-Plus-Plus/sorting/wiggle_sort.cpp.
    +
    Examples
    /Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp, and /Users/runner/work/C-Plus-Plus/C-Plus-Plus/sorting/wiggle_sort.cpp.
    84  {
    85  const int size = 4;
    diff --git a/dc/dc4/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2numerical_methods_2rungekutta_8cpp-example.html b/dc/dc4/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2numerical_methods_2rungekutta_8cpp-example.html new file mode 100644 index 000000000..ebddfffcb --- /dev/null +++ b/dc/dc4/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2numerical_methods_2rungekutta_8cpp-example.html @@ -0,0 +1,251 @@ + + + + + + + +Algorithms_in_C++: /Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp + + + + + + + + + + + + + + + +
    +
    + + + + + + +
    +
    Algorithms_in_C++ +  1.0.0 +
    +
    Set of algorithms implemented in C++.
    +
    +
    + + + + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    /Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp
    +
    +
    +

    it solves \frac{\mathrm{d} y}{\mathrm{d} x}= \frac{\left ( x-y \right )}{2} given x for given initial conditions There can be many such equations

    +
    /**
    +
    * @{
    +
    * \file
    +
    * \brief [Runge Kutta fourth order](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods) method implementation
    +
    *
    +
    * \author [Rudra Prasad Das](http://github.com/rudra697)
    +
    *
    +
    * \details
    +
    * It solves the unknown value of y
    +
    * for a given value of x
    +
    * only first order differential equations
    +
    * can be solved
    +
    * \example
    +
    * it solves \frac{\mathrm{d} y}{\mathrm{d} x}= \frac{\left ( x-y \right )}{2}
    +
    * given x for given initial
    +
    * conditions
    +
    * There can be many such equations
    +
    */
    +
    #include <iostream> /// for io operations
    +
    #include <vector> /// for using the vector container
    +
    #include <cassert> /// asserting the test functions
    +
    +
    /**
    +
    * @brief The change() function is used
    +
    * to return the updated iterative value corresponding
    +
    * to the given function
    +
    * @param x is the value corresponding to the x coordinate
    +
    * @param y is the value corresponding to the y coordinate
    +
    * @returns the computed function value at that call
    +
    */
    +
    static double change(double x, double y)
    +
    {
    +
    return ((x - y)/2.0);
    +
    +
    }
    +
    +
    /**
    +
    * @namespace numerical_methods
    +
    * @brief Numerical Methods
    +
    */
    +
    namespace numerical_methods {
    +
    /**
    +
    * @namespace runge_kutta
    +
    * @brief Functions for [Runge Kutta fourth order](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods) method
    +
    */
    +
    namespace runge_kutta {
    +
    /**
    +
    * @brief the Runge Kutta method finds the value of integration of a function in the given limits.
    +
    * the lower limit of integration as the initial value and the upper limit is the given x
    +
    * @param init_x is the value of initial x and is updated after each call
    +
    * @param init_y is the value of initial x and is updated after each call
    +
    * @param x is current iteration at which the function needs to be evaluated
    +
    * @param h is the step value
    +
    * @returns the value of y at thr required value of x from the initial conditions
    +
    */
    +
    double rungeKutta(double init_x, const double &init_y, const double &x, const double &h)
    +
    {
    +
    +
    // Count number of iterations
    +
    // using step size or
    +
    // step height h
    +
    +
    +
    // n calucates the number of iterations
    +
    // k1, k2, k3, k4 are the Runge Kutta variables
    +
    // used for calculation of y at each iteration
    +
    +
    auto n = static_cast<uint64_t>((x - init_x) / h);
    +
    // used a vector container for the variables
    + +
    +
    +
    // Iterate for number of iterations
    +
    +
    double y = init_y;
    +
    for (int i=1; i<=n; ++i)
    +
    {
    +
    +
    // Apply Runge Kutta Formulas
    +
    // to find next value of y
    +
    k[0] = h*change(init_x, y);
    +
    k[1] = h*change(init_x + 0.5*h, y + 0.5*k[0]);
    +
    k[2] = h*change(init_x + 0.5*h, y + 0.5*k[1]);
    +
    k[3] = h*change(init_x + h, y + k[2]);
    +
    +
    +
    // Update next value of y
    +
    +
    y += (1.0/6.0)*(k[0] + 2*k[1] + 2*k[2] + k[3]);
    +
    +
    // Update next value of x
    +
    +
    init_x += h;
    +
    }
    +
    +
    return y;
    +
    }
    +
    } // namespace runge_kutta
    +
    } // namespace numerical_methods
    +
    +
    /**
    +
    * @brief Tests to check algorithm implementation.
    +
    * @returns void
    +
    */
    +
    static void test()
    +
    {
    +
    std::cout << "The Runge Kutta function will be tested on the basis of precomputed values\n";
    +
    +
    std::cout << "Test 1...." << "\n";
    +
    double valfirst=numerical_methods::runge_kutta::rungeKutta(2,3,4,0.2); // Tests the function with pre calculated values
    +
    assert(valfirst==3.10363932323749570);
    +
    std::cout << "Passed Test 1\n";
    +
    +
    std::cout << "Test 2...." << "\n";
    +
    double valsec=numerical_methods::runge_kutta::rungeKutta(1,2,5,0.1); // The value of step changed
    +
    assert(valsec==3.40600589380261409);
    +
    std::cout << "Passed Test 2\n";
    +
    +
    std::cout << "Test 3...." << "\n";
    +
    double valthird=numerical_methods::runge_kutta::rungeKutta(-1,3,4,0.1); // Tested with negative value
    +
    assert(valthird==2.49251005860244268);
    +
    std::cout << "Passed Test 3\n";
    +
    }
    +
    +
    +
    /**
    +
    * @brief Main function
    +
    * @returns 0 on exit
    +
    */
    +
    int main()
    +
    {
    +
    +
    test(); // Execute the tests
    +
    return 0;
    +
    }
    +
    +
    +
    static void test()
    Test implementations.
    Definition: rat_maze.cpp:84
    +
    for io operations
    + +
    int main()
    Definition: graph_coloring.cpp:96
    + +
    int h(int key)
    Definition: hash_search.cpp:45
    +
    Functions for Runge Kutta fourth order method.
    +
    static double change(double x, double y)
    asserting the test functions
    Definition: rungekutta.cpp:31
    +
    double rungeKutta(double init_x, const double &init_y, const double &x, const double &h)
    the Runge Kutta method finds the value of integration of a function in the given limits....
    Definition: rungekutta.cpp:56
    + + + + diff --git a/dc/dc7/rungekutta_8cpp__incl.map b/dc/dc7/rungekutta_8cpp__incl.map new file mode 100644 index 000000000..fa985c5f9 --- /dev/null +++ b/dc/dc7/rungekutta_8cpp__incl.map @@ -0,0 +1,6 @@ + + + + + + diff --git a/dc/dc7/rungekutta_8cpp__incl.md5 b/dc/dc7/rungekutta_8cpp__incl.md5 new file mode 100644 index 000000000..d294e2ebf --- /dev/null +++ b/dc/dc7/rungekutta_8cpp__incl.md5 @@ -0,0 +1 @@ +71964ee4e0ecca036604e5639b0cff75 \ No newline at end of file diff --git a/dc/dc7/rungekutta_8cpp__incl.svg b/dc/dc7/rungekutta_8cpp__incl.svg new file mode 100644 index 000000000..5e5a04293 --- /dev/null +++ b/dc/dc7/rungekutta_8cpp__incl.svg @@ -0,0 +1,67 @@ + + + + + + +numerical_methods/rungekutta.cpp + + + +Node1 + + +numerical_methods/rungekutta.cpp + + + + + +Node2 + + +iostream + + + + + +Node1->Node2 + + + + + +Node3 + + +vector + + + + + +Node1->Node3 + + + + + +Node4 + + +cassert + + + + + +Node1->Node4 + + + + + diff --git a/dir_9c6faab82c22511b50177aa2e38e2780.html b/dir_9c6faab82c22511b50177aa2e38e2780.html index e77804b5e..42dcd3a9d 100644 --- a/dir_9c6faab82c22511b50177aa2e38e2780.html +++ b/dir_9c6faab82c22511b50177aa2e38e2780.html @@ -142,6 +142,9 @@ Files file  qr_eigen_values.cpp  Compute real eigen values and eigen vectors of a symmetric matrix using QR decomposition method.
      +file  rungekutta.cppRunge Kutta fourth order method implementation
    +  file  successive_approximation.cpp  Method of successive approximations using fixed-point iteration method.
      diff --git a/dir_9c6faab82c22511b50177aa2e38e2780.js b/dir_9c6faab82c22511b50177aa2e38e2780.js index 8f05fb60a..ef6c1a60d 100644 --- a/dir_9c6faab82c22511b50177aa2e38e2780.js +++ b/dir_9c6faab82c22511b50177aa2e38e2780.js @@ -15,5 +15,6 @@ var dir_9c6faab82c22511b50177aa2e38e2780 = [ "qr_decompose.h", "d4/d68/qr__decompose_8h.html", "d4/d68/qr__decompose_8h" ], [ "qr_decomposition.cpp", "d3/d24/qr__decomposition_8cpp.html", "d3/d24/qr__decomposition_8cpp" ], [ "qr_eigen_values.cpp", "de/d75/qr__eigen__values_8cpp.html", "de/d75/qr__eigen__values_8cpp" ], + [ "rungekutta.cpp", "d1/da6/rungekutta_8cpp.html", "d1/da6/rungekutta_8cpp" ], [ "successive_approximation.cpp", "df/dc8/successive__approximation_8cpp.html", "df/dc8/successive__approximation_8cpp" ] ]; \ No newline at end of file diff --git a/examples.html b/examples.html index 977c43e20..22b605ca9 100644 --- a/examples.html +++ b/examples.html @@ -95,6 +95,8 @@ $(document).ready(function(){initNavTree('examples.html',''); initResizable(); }
    Here is a list of all examples:
    diff --git a/examples.js b/examples.js index f3d2fb900..3148360af 100644 --- a/examples.js +++ b/examples.js @@ -1,4 +1,5 @@ var examples = [ + [ "/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp", "dc/dc4/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2numerical_methods_2rungekutta_8cpp-example.html", null ], [ "/Users/runner/work/C-Plus-Plus/C-Plus-Plus/sorting/wiggle_sort.cpp", "dd/db0/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2sorting_2wiggle_sort_8cpp-example.html", null ] ]; \ No newline at end of file diff --git a/files.html b/files.html index e50fd02b0..dc522578c 100644 --- a/files.html +++ b/files.html @@ -216,7 +216,8 @@ solve-a-rat-in-a-maze-c-java-pytho/">Rat in a Maze algorithm  qr_decompose.hLibrary functions to compute QR decomposition of a given matrix  qr_decomposition.cppProgram to compute the QR decomposition of a given matrix  qr_eigen_values.cppCompute real eigen values and eigen vectors of a symmetric matrix using QR decomposition method - successive_approximation.cppMethod of successive approximations using fixed-point iteration method + rungekutta.cppRunge Kutta fourth order method implementation + successive_approximation.cppMethod of successive approximations using fixed-point iteration method   others  buzz_number.cppA buzz number is a number that is either divisible by 7 or has last digit as 7  decimal_to_binary.cppFunction to convert decimal number to binary representation diff --git a/globals_c.html b/globals_c.html index 33586e52d..100f27615 100644 --- a/globals_c.html +++ b/globals_c.html @@ -96,6 +96,9 @@ $(document).ready(function(){initNavTree('globals_c.html',''); initResizable();
  • canJump() : jumpgame.cpp
  • +
  • change() +: rungekutta.cpp +
  • check_termination() : durand_kerner_roots.cpp
  • diff --git a/globals_func_c.html b/globals_func_c.html index c1444f9f6..c75f89808 100644 --- a/globals_func_c.html +++ b/globals_func_c.html @@ -96,6 +96,9 @@ $(document).ready(function(){initNavTree('globals_func_c.html',''); initResizabl
  • canJump() : jumpgame.cpp
  • +
  • change() +: rungekutta.cpp +
  • check_termination() : durand_kerner_roots.cpp
  • diff --git a/globals_func_i.html b/globals_func_i.html index abdeb1215..036092ccf 100644 --- a/globals_func_i.html +++ b/globals_func_i.html @@ -123,12 +123,12 @@ $(document).ready(function(){initNavTree('globals_func_i.html',''); initResizabl
  • is_square() : ordinary_least_squares_regressor.cpp
  • -
  • isPrime() -: modular_inverse_fermat_little_theorem.cpp -
  • IsPrime() : primality_test.cpp
  • +
  • isPrime() +: modular_inverse_fermat_little_theorem.cpp +
  • it_ternary_search() : ternary_search.cpp
  • diff --git a/globals_func_m.html b/globals_func_m.html index 0bfe918c3..a72b3e5d7 100644 --- a/globals_func_m.html +++ b/globals_func_m.html @@ -101,14 +101,14 @@ $(document).ready(function(){initNavTree('globals_func_m.html',''); initResizabl , linked_list.cpp , depth_first_search.cpp , gcd_recursive_euclidean.cpp +, ternary_search.cpp , text_search.cpp -, bogo_sort.cpp , large_factorial.cpp +, bogo_sort.cpp , comb_sort.cpp -, cycle_sort.cpp , dijkstra.cpp , lcm_sum.cpp -, gnome_sort.cpp +, cycle_sort.cpp , rabin_karp.cpp , knuth_morris_pratt.cpp , horspool.cpp @@ -120,15 +120,15 @@ $(document).ready(function(){initNavTree('globals_func_m.html',''); initResizabl , pigeonhole_sort.cpp , pancake_sort.cpp , merge_sort.cpp -, heap_sort.cpp -, least_common_multiple.cpp -, insertion_sort.cpp , merge_insertion_sort.cpp +, gnome_sort.cpp +, least_common_multiple.cpp +, heap_sort.cpp +, insertion_sort.cpp , linkedlist_implentation_usingarray.cpp , hamiltons_cycle.cpp , magic_number.cpp , miller_rabin.cpp -, ternary_search.cpp , median_search.cpp , linear_search.cpp , interpolation_search2.cpp @@ -161,6 +161,7 @@ $(document).ready(function(){initNavTree('globals_func_m.html',''); initResizabl , decimal_to_hexadecimal.cpp , buzz_number.cpp , successive_approximation.cpp +, rungekutta.cpp , qr_eigen_values.cpp , qr_decomposition.cpp , ode_semi_implicit_euler.cpp diff --git a/globals_func_s.html b/globals_func_s.html index 874162f4f..99011104b 100644 --- a/globals_func_s.html +++ b/globals_func_s.html @@ -126,12 +126,12 @@ $(document).ready(function(){initNavTree('globals_func_s.html',''); initResizabl
  • show_pascal() : pascal_triangle.cpp
  • -
  • sieve() -: sieve_of_eratosthenes.cpp -
  • Sieve() : primes_up_to_billion.cpp
  • +
  • sieve() +: sieve_of_eratosthenes.cpp +
  • SieveOfEratosthenes() : prime_factorization.cpp
  • diff --git a/globals_func_t.html b/globals_func_t.html index 681b1869b..d0fbbf2a6 100644 --- a/globals_func_t.html +++ b/globals_func_t.html @@ -101,13 +101,14 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl , morse_code.cpp , 0_1_knapsack.cpp , neural_network.cpp +, merge_insertion_sort.cpp , pancake_sort.cpp -, strand_sort.cpp , armstrong_number.cpp +, strand_sort.cpp , wiggle_sort.cpp -, horspool.cpp , cut_rod.cpp , check_amicable_pair.cpp +, horspool.cpp , double_factorial.cpp , vigenere_cipher.cpp , palindrome_partitioning.cpp @@ -120,17 +121,17 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl , xor_cipher.cpp , word_break.cpp , sum_of_digits.cpp -, smallest_circle.cpp +, rungekutta.cpp , jarvis_algorithm.cpp +, smallest_circle.cpp , median_search.cpp -, bogo_sort.cpp , trie_tree.cpp , is_graph_bipartite.cpp +, bogo_sort.cpp , cycle_sort.cpp -, gnome_sort.cpp , jumpgame.cpp +, gnome_sort.cpp , heap_sort.cpp -, merge_insertion_sort.cpp
  • test1() : hill_cipher.cpp @@ -147,28 +148,28 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl , qr_eigen_values.cpp
  • test2() -: qr_eigen_values.cpp +: lu_decompose.cpp , hill_cipher.cpp , hamiltons_cycle.cpp , adaline_learning.cpp -, brent_method_extrema.cpp , kohonen_som_topology.cpp , kohonen_som_trace.cpp , large_factorial.cpp , sum_of_digits.cpp +, brent_method_extrema.cpp , durand_kerner_roots.cpp , golden_search_extrema.cpp -, lu_decompose.cpp +, qr_eigen_values.cpp , smallest_circle.cpp
  • test3() -: kohonen_som_trace.cpp +: kohonen_som_topology.cpp +, kohonen_som_trace.cpp , brent_method_extrema.cpp , golden_search_extrema.cpp , smallest_circle.cpp -, kohonen_som_topology.cpp -, hamiltons_cycle.cpp , adaline_learning.cpp +, hamiltons_cycle.cpp
  • test_1() : heavy_light_decomposition.cpp @@ -182,8 +183,8 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl : kohonen_som_topology.cpp
  • test_3() -: pigeonhole_sort.cpp -, heavy_light_decomposition.cpp +: heavy_light_decomposition.cpp +, pigeonhole_sort.cpp
  • test_3d_classes() : kohonen_som_trace.cpp @@ -213,28 +214,28 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl : postfix_evaluation.cpp
  • test_int() -: quick_sort_3.cpp -, shell_sort2.cpp +: shell_sort2.cpp +, quick_sort_3.cpp
  • test_lamniscate() : kohonen_som_trace.cpp
  • tests() -: magic_number.cpp -, double_factorial.cpp -, insertion_sort.cpp -, sieve_of_eratosthenes.cpp -, hopcroft_karp.cpp -, complex_numbers.cpp -, comb_sort.cpp -, connected_components.cpp -, dijkstra.cpp -, lowest_common_ancestor.cpp -, check_factorial.cpp -, miller_rabin.cpp -, number_of_positive_divisors.cpp -, breadth_first_search.cpp +: double_factorial.cpp , least_common_multiple.cpp +, check_factorial.cpp +, sieve_of_eratosthenes.cpp +, comb_sort.cpp +, complex_numbers.cpp +, number_of_positive_divisors.cpp +, dijkstra.cpp +, miller_rabin.cpp +, hopcroft_karp.cpp +, breadth_first_search.cpp +, connected_components.cpp +, magic_number.cpp +, insertion_sort.cpp +, lowest_common_ancestor.cpp
  • TH() : tower_of_hanoi.cpp diff --git a/globals_i.html b/globals_i.html index cb81baa60..5227c1b2e 100644 --- a/globals_i.html +++ b/globals_i.html @@ -123,14 +123,14 @@ $(document).ready(function(){initNavTree('globals_i.html',''); initResizable();
  • is_square() : ordinary_least_squares_regressor.cpp
  • -
  • IsPrime() -: primality_test.cpp +
  • isPrime() +: modular_inverse_fermat_little_theorem.cpp
  • isprime : prime_factorization.cpp
  • -
  • isPrime() -: modular_inverse_fermat_little_theorem.cpp +
  • IsPrime() +: primality_test.cpp
  • it_ternary_search() : ternary_search.cpp diff --git a/globals_m.html b/globals_m.html index 40d7eb8a4..0918437fc 100644 --- a/globals_m.html +++ b/globals_m.html @@ -101,35 +101,36 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable(); , linked_list.cpp , depth_first_search.cpp , gcd_recursive_euclidean.cpp +, ternary_search.cpp , text_search.cpp -, bogo_sort.cpp , large_factorial.cpp +, bogo_sort.cpp , comb_sort.cpp -, cycle_sort.cpp , dijkstra.cpp , lcm_sum.cpp +, cycle_sort.cpp , gnome_sort.cpp -, heap_sort.cpp , least_common_multiple.cpp +, heap_sort.cpp , insertion_sort.cpp -, merge_insertion_sort.cpp , linkedlist_implentation_usingarray.cpp , hamiltons_cycle.cpp , magic_number.cpp +, merge_insertion_sort.cpp , merge_sort.cpp -, pancake_sort.cpp , miller_rabin.cpp , rabin_karp.cpp , knuth_morris_pratt.cpp , horspool.cpp , brute_force_string_searching.cpp , strand_sort.cpp +, shell_sort2.cpp +, pancake_sort.cpp , pigeonhole_sort.cpp -, quick_sort.cpp , hopcroft_karp.cpp , modular_exponentiation.cpp +, quick_sort.cpp , quick_sort_3.cpp -, shell_sort2.cpp , modular_inverse_fermat_little_theorem.cpp , caesar_cipher.cpp , queue_using_two_stacks.cpp @@ -138,7 +139,6 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable(); , power_for_huge_numbers.cpp , lowest_common_ancestor.cpp , prime_factorization.cpp -, ternary_search.cpp , median_search.cpp , linear_search.cpp , interpolation_search2.cpp @@ -171,6 +171,7 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable(); , decimal_to_hexadecimal.cpp , buzz_number.cpp , successive_approximation.cpp +, rungekutta.cpp , qr_eigen_values.cpp , qr_decomposition.cpp , ode_semi_implicit_euler.cpp diff --git a/globals_s.html b/globals_s.html index 00646dddf..52b61c89b 100644 --- a/globals_s.html +++ b/globals_s.html @@ -126,12 +126,12 @@ $(document).ready(function(){initNavTree('globals_s.html',''); initResizable();
  • show_pascal() : pascal_triangle.cpp
  • -
  • Sieve() -: primes_up_to_billion.cpp -
  • sieve() : sieve_of_eratosthenes.cpp
  • +
  • Sieve() +: primes_up_to_billion.cpp +
  • SieveOfEratosthenes() : prime_factorization.cpp
  • diff --git a/globals_t.html b/globals_t.html index d14c9f637..390e7565c 100644 --- a/globals_t.html +++ b/globals_t.html @@ -101,13 +101,14 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable(); , morse_code.cpp , 0_1_knapsack.cpp , neural_network.cpp +, merge_insertion_sort.cpp , pancake_sort.cpp -, strand_sort.cpp , armstrong_number.cpp +, strand_sort.cpp , wiggle_sort.cpp -, horspool.cpp , cut_rod.cpp , check_amicable_pair.cpp +, horspool.cpp , double_factorial.cpp , vigenere_cipher.cpp , palindrome_partitioning.cpp @@ -120,17 +121,17 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable(); , xor_cipher.cpp , word_break.cpp , sum_of_digits.cpp -, smallest_circle.cpp +, rungekutta.cpp , jarvis_algorithm.cpp +, smallest_circle.cpp , median_search.cpp -, bogo_sort.cpp , trie_tree.cpp , is_graph_bipartite.cpp +, bogo_sort.cpp , cycle_sort.cpp -, gnome_sort.cpp , jumpgame.cpp +, gnome_sort.cpp , heap_sort.cpp -, merge_insertion_sort.cpp
  • test1() : hill_cipher.cpp @@ -148,7 +149,7 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
  • test2() : hill_cipher.cpp -, qr_eigen_values.cpp +, lu_decompose.cpp , hamiltons_cycle.cpp , adaline_learning.cpp , kohonen_som_topology.cpp @@ -158,25 +159,25 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable(); , brent_method_extrema.cpp , durand_kerner_roots.cpp , golden_search_extrema.cpp -, lu_decompose.cpp +, qr_eigen_values.cpp , smallest_circle.cpp
  • test3() -: kohonen_som_trace.cpp +: kohonen_som_topology.cpp +, kohonen_som_trace.cpp , brent_method_extrema.cpp , golden_search_extrema.cpp , smallest_circle.cpp -, kohonen_som_topology.cpp -, hamiltons_cycle.cpp , adaline_learning.cpp +, hamiltons_cycle.cpp
  • test_1() : heavy_light_decomposition.cpp , pigeonhole_sort.cpp
  • test_2() -: heavy_light_decomposition.cpp -, pigeonhole_sort.cpp +: pigeonhole_sort.cpp +, heavy_light_decomposition.cpp
  • test_2d_classes() : kohonen_som_topology.cpp @@ -223,21 +224,21 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable(); : brute_force_string_searching.cpp
  • tests() -: sieve_of_eratosthenes.cpp -, dijkstra.cpp -, insertion_sort.cpp +: hopcroft_karp.cpp , comb_sort.cpp +, sieve_of_eratosthenes.cpp +, connected_components.cpp , number_of_positive_divisors.cpp +, breadth_first_search.cpp , check_factorial.cpp , least_common_multiple.cpp -, connected_components.cpp -, complex_numbers.cpp -, miller_rabin.cpp -, breadth_first_search.cpp , double_factorial.cpp -, magic_number.cpp +, miller_rabin.cpp , lowest_common_ancestor.cpp -, hopcroft_karp.cpp +, magic_number.cpp +, insertion_sort.cpp +, complex_numbers.cpp +, dijkstra.cpp
  • TH() : tower_of_hanoi.cpp diff --git a/namespacemembers.html b/namespacemembers.html index acae6b1b5..a73e89a61 100644 --- a/namespacemembers.html +++ b/namespacemembers.html @@ -214,12 +214,12 @@ $(document).ready(function(){initNavTree('namespacemembers.html',''); initResiza
  • isPossible() : backtracking
  • -
  • issafe() -: backtracking -
  • isSafe() : backtracking
  • +
  • issafe() +: backtracking +
  • @@ -341,12 +341,12 @@ $(document).ready(function(){initNavTree('namespacemembers.html',''); initResiza
  • quadraticProbe() : quadratic_probing
  • -
  • quicksort() -: sorting -
  • quickSort() : sorting
  • +
  • quicksort() +: sorting +
  • diff --git a/namespacemembers_func.html b/namespacemembers_func.html index ccb35f241..daa5dc1da 100644 --- a/namespacemembers_func.html +++ b/namespacemembers_func.html @@ -214,12 +214,12 @@ $(document).ready(function(){initNavTree('namespacemembers_func.html',''); initR
  • isPossible() : backtracking
  • -
  • issafe() -: backtracking -
  • isSafe() : backtracking
  • +
  • issafe() +: backtracking +
  • @@ -332,12 +332,12 @@ $(document).ready(function(){initNavTree('namespacemembers_func.html',''); initR
  • quadraticProbe() : quadratic_probing
  • -
  • quicksort() -: sorting -
  • quickSort() : sorting
  • +
  • quicksort() +: sorting +
  • diff --git a/namespaces.html b/namespaces.html index 0f41372a8..996ab64f3 100644 --- a/namespaces.html +++ b/namespaces.html @@ -136,21 +136,22 @@ $(document).ready(function(){initNavTree('namespaces.html',''); initResizable();  Nrange_queriesAlgorithms and Data Structures that support range queries and updates  Nrat_mazeFunctions for Rat in a Maze algorithm - NsearchSearch algorithms - Nshortest_common_supersequenceShortest Common Super Sequence algorithm - NsortingSorting algorithms - Nsparse_tableRange queries using sparse-tables - Nspirograph - NstatisticsStatistical algorithms - NstdSTL namespace - NstrandFunctions for Strand Sort algorithm - Nstring_searchString search algorithms - NstringsAlgorithms with strings - Nutil_functionsVarious utility functions used in Neural network - NvigenereFunctions for vigenère cipher algorithm - Nwiggle_sortFunctions for Wiggle Sort algorithm - Nword_breakFunctions for Word Break problem - NXORFunctions for XOR cipher algorithm + Nrunge_kuttaFunctions for Runge Kutta fourth order method + NsearchSearch algorithms + Nshortest_common_supersequenceShortest Common Super Sequence algorithm + NsortingSorting algorithms + Nsparse_tableRange queries using sparse-tables + Nspirograph + NstatisticsStatistical algorithms + NstdSTL namespace + NstrandFunctions for Strand Sort algorithm + Nstring_searchString search algorithms + NstringsAlgorithms with strings + Nutil_functionsVarious utility functions used in Neural network + NvigenereFunctions for vigenère cipher algorithm + Nwiggle_sortFunctions for Wiggle Sort algorithm + Nword_breakFunctions for Word Break problem + NXORFunctions for XOR cipher algorithm
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