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feat: Add the Subarray Sum implementation (#1527)

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* Create subarray_sum.cpp

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* Update backtracking/subarray_sum.cpp

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* Update backtracking/subarray_sum.cpp

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* Update backtracking/subarray_sum.cpp

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* Update subarray_sum.cpp

* clang-format and clang-tidy fixes for 9b0b5f87

* Update backtracking/subarray_sum.cpp

* Update backtracking/subarray_sum.cpp

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* Update backtracking/subarray_sum.cpp

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* Update backtracking/subarray_sum.cpp

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* clang-format and clang-tidy fixes for 047366a8

* Update subarray_sum.cpp

* clang-format and clang-tidy fixes for 512b1887

* Update backtracking/subarray_sum.cpp

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* Update backtracking/subarray_sum.cpp

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* Update backtracking/subarray_sum.cpp

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* Update backtracking/subarray_sum.cpp

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This commit is contained in:
Swastika Gupta
2021-07-22 00:52:16 +05:30
committed by GitHub
parent 0e0ba5fc89
commit f34f93e77a
5 changed files with 549 additions and 362 deletions
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151
backtracking/graph_coloring.cpp
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@@ -1,22 +1,24 @@
/**
* @file
* @brief prints the assigned colors
* using [Graph Coloring](https://en.wikipedia.org/wiki/Graph_coloring) algorithm
* using [Graph Coloring](https://en.wikipedia.org/wiki/Graph_coloring)
* algorithm
*
* @details
* In graph theory, graph coloring is a special case of graph labeling;
* it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.
* In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color;
* this is called a vertex coloring. Similarly, an edge coloring assigns
* a color to each edge so that no two adjacent edges are of the same color,
* and a face coloring of a planar graph assigns a color to each face or
* In graph theory, graph coloring is a special case of graph labeling;
* it is an assignment of labels traditionally called "colors" to elements of a
* graph subject to certain constraints. In its simplest form, it is a way of
* coloring the vertices of a graph such that no two adjacent vertices are of
* the same color; this is called a vertex coloring. Similarly, an edge coloring
* assigns a color to each edge so that no two adjacent edges are of the same
* color, and a face coloring of a planar graph assigns a color to each face or
* region so that no two faces that share a boundary have the same color.
*
* @author [Anup Kumar Panwar](https://github.com/AnupKumarPanwar)
* @author [David Leal](https://github.com/Panquesito7)
*/
#include <iostream>
#include <array>
#include <iostream>
#include <vector>
/**
@@ -24,70 +26,72 @@
* @brief Backtracking algorithms
*/
namespace backtracking {
/** A utility function to print solution
* @tparam V number of vertices in the graph
* @param color array of colors assigned to the nodes
*/
template <size_t V>
void printSolution(const std::array <int, V>& color) {
std::cout << "Following are the assigned colors" << std::endl;
for (auto &col : color) {
std::cout << col;
}
std::cout << std::endl;
/** A utility function to print solution
* @tparam V number of vertices in the graph
* @param color array of colors assigned to the nodes
*/
template <size_t V>
void printSolution(const std::array<int, V>& color) {
std::cout << "Following are the assigned colors" << std::endl;
for (auto& col : color) {
std::cout << col;
}
std::cout << std::endl;
}
/** A utility function to check if the current color assignment is safe for
* vertex v
* @tparam V number of vertices in the graph
* @param v index of graph vertex to check
* @param graph matrix of graph nonnectivity
* @param color vector of colors assigned to the graph nodes/vertices
* @param c color value to check for the node `v`
* @returns `true` if the color is safe to be assigned to the node
* @returns `false` if the color is not safe to be assigned to the node
*/
template <size_t V>
bool isSafe(int v, const std::array<std::array <int, V>, V>& graph, const std::array <int, V>& color, int c) {
for (int i = 0; i < V; i++) {
if (graph[v][i] && c == color[i]) {
return false;
}
}
return true;
}
/** A recursive utility function to solve m coloring problem
* @tparam V number of vertices in the graph
* @param graph matrix of graph nonnectivity
* @param m number of colors
* @param [in,out] color description // used in,out to notify in documentation
* that this parameter gets modified by the function
* @param v index of graph vertex to check
*/
template <size_t V>
void graphColoring(const std::array<std::array <int, V>, V>& graph, int m, std::array <int, V> color, int v) {
// base case:
// If all vertices are assigned a color then return true
if (v == V) {
backtracking::printSolution<V>(color);
return;
}
// Consider this vertex v and try different colors
for (int c = 1; c <= m; c++) {
// Check if assignment of color c to v is fine
if (backtracking::isSafe<V>(v, graph, color, c)) {
color[v] = c;
// recur to assign colors to rest of the vertices
backtracking::graphColoring<V>(graph, m, color, v + 1);
// If assigning color c doesn't lead to a solution then remove it
color[v] = 0;
}
/** A utility function to check if the current color assignment is safe for
* vertex v
* @tparam V number of vertices in the graph
* @param v index of graph vertex to check
* @param graph matrix of graph nonnectivity
* @param color vector of colors assigned to the graph nodes/vertices
* @param c color value to check for the node `v`
* @returns `true` if the color is safe to be assigned to the node
* @returns `false` if the color is not safe to be assigned to the node
*/
template <size_t V>
bool isSafe(int v, const std::array<std::array<int, V>, V>& graph,
const std::array<int, V>& color, int c) {
for (int i = 0; i < V; i++) {
if (graph[v][i] && c == color[i]) {
return false;
}
}
return true;
}
/** A recursive utility function to solve m coloring problem
* @tparam V number of vertices in the graph
* @param graph matrix of graph nonnectivity
* @param m number of colors
* @param [in,out] color description // used in,out to notify in documentation
* that this parameter gets modified by the function
* @param v index of graph vertex to check
*/
template <size_t V>
void graphColoring(const std::array<std::array<int, V>, V>& graph, int m,
std::array<int, V> color, int v) {
// base case:
// If all vertices are assigned a color then return true
if (v == V) {
backtracking::printSolution<V>(color);
return;
}
// Consider this vertex v and try different colors
for (int c = 1; c <= m; c++) {
// Check if assignment of color c to v is fine
if (backtracking::isSafe<V>(v, graph, color, c)) {
color[v] = c;
// recur to assign colors to rest of the vertices
backtracking::graphColoring<V>(graph, m, color, v + 1);
// If assigning color c doesn't lead to a solution then remove it
color[v] = 0;
}
}
}
} // namespace backtracking
/**
@@ -102,15 +106,12 @@ int main() {
// (0)---(1)
const int V = 4; // number of vertices in the graph
std::array <std::array <int, V>, V> graph = {
std::array <int, V>({0, 1, 1, 1}),
std::array <int, V>({1, 0, 1, 0}),
std::array <int, V>({1, 1, 0, 1}),
std::array <int, V>({1, 0, 1, 0})
};
std::array<std::array<int, V>, V> graph = {
std::array<int, V>({0, 1, 1, 1}), std::array<int, V>({1, 0, 1, 0}),
std::array<int, V>({1, 1, 0, 1}), std::array<int, V>({1, 0, 1, 0})};
int m = 3; // Number of colors
std::array <int, V> color{};
std::array<int, V> color{};
backtracking::graphColoring<V>(graph, m, color, 0);
return 0;