OpenSoure_Repos/TheAlgorithms-C-Plus-Plus
1
0
Fork 0
mirror of https://hub.njuu.cf/TheAlgorithms/C-Plus-Plus.git synced 2023-10-11 13:05:55 +08:00
Code Issues Packages Projects Releases Wiki Activity

[feat/fix/docs]: Improvements in the backtracking folder (#1553)

Browse Source 
* [feat/fix/docs]: Improvements in the...

...`backtracking` folder, and minor fixes in the `others/iterative_tree_traversals.cpp` and the `math/check_prime.cpp` files.

* clang-format and clang-tidy fixes for 9cc3951d

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Abhinn Mishra <49574460+mishraabhinn@users.noreply.github.com>
This commit is contained in:
David Leal 2021-10-29 13:05:46 -05:00 committed by GitHub
parent a9312b3901
commit 4e3abd4601
No known key found for this signature in database
GPG Key ID: 4AEE18F83AFDEB23
8 changed files with 367 additions and 322 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

40
backtracking/graph_coloring.cpp
View File

@ -17,29 +17,38 @@
* @author [Anup Kumar Panwar](https://github.com/AnupKumarPanwar)
* @author [David Leal](https://github.com/Panquesito7)
*/
#include <array>
#include <iostream>
#include <vector>
#include <array> /// for std::array
#include <iostream> /// for IO operations
#include <vector> /// for std::vector
/**
* @namespace
* @namespace backtracking
* @brief Backtracking algorithms
*/
namespace backtracking {
/** A utility function to print solution
/**
* @namespace graph_coloring
* @brief Functions for the [Graph
* Coloring](https://en.wikipedia.org/wiki/Graph_coloring) algorithm,
*/
namespace graph_coloring {
/**
* @brief A utility function to print the 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;
std::cout << "Following are the assigned colors\n";
for (auto& col : color) {
std::cout << col;
}
std::cout << std::endl;
std::cout << "\n";
}
/** A utility function to check if the current color assignment is safe for
/**
* @brief 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
@ -60,7 +69,8 @@ bool isSafe(int v, const std::array<std::array<int, V>, V>& graph,
return true;
}
/** A recursive utility function to solve m coloring problem
/**
* @brief 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
@ -74,28 +84,30 @@ void graphColoring(const std::array<std::array<int, V>, V>& graph, int m,
// base case:
// If all vertices are assigned a color then return true
if (v == V) {
backtracking::printSolution<V>(color);
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)) {
if (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);
graphColoring<V>(graph, m, color, v + 1);
// If assigning color c doesn't lead to a solution then remove it
color[v] = 0;
}
}
}
} // namespace graph_coloring
} // namespace backtracking
/**
* Main function
* @brief Main function
* @returns 0 on exit
*/
int main() {
// Create following graph and test whether it is 3 colorable
@ -113,6 +125,6 @@ int main() {
int m = 3; // Number of colors
std::array<int, V> color{};
backtracking::graphColoring<V>(graph, m, color, 0);
backtracking::graph_coloring::graphColoring<V>(graph, m, color, 0);
return 0;
}

143
backtracking/knight_tour.cpp
View File

@ -1,6 +1,7 @@
/**
* @file
* @brief [Knight's tour](https://en.wikipedia.org/wiki/Knight%27s_tour) algorithm
* @brief [Knight's tour](https://en.wikipedia.org/wiki/Knight%27s_tour)
* algorithm
*
* @details
* A knight's tour is a sequence of moves of a knight on a chessboard
@ -12,92 +13,102 @@
* @author [Nikhil Arora](https://github.com/nikhilarora068)
* @author [David Leal](https://github.com/Panquesito7)
*/
#include <iostream>
#include <array>
#include <array> /// for std::array
#include <iostream> /// for IO operations
/**
* @namespace backtracking
* @brief Backtracking algorithms
*/
namespace backtracking {
/**
* A utility function to check if i,j are valid indexes for N*N chessboard
* @tparam V number of vertices in array
* @param x current index in rows
* @param y current index in columns
* @param sol matrix where numbers are saved
* @returns `true` if ....
* @returns `false` if ....
*/
template <size_t V>
bool issafe(int x, int y, const std::array <std::array <int, V>, V>& sol) {
return (x < V && x >= 0 && y < V && y >= 0 && sol[x][y] == -1);
}
/**
* Knight's tour algorithm
* @tparam V number of vertices in array
* @param x current index in rows
* @param y current index in columns
* @param mov movement to be done
* @param sol matrix where numbers are saved
* @param xmov next move of knight (x coordinate)
* @param ymov next move of knight (y coordinate)
* @returns `true` if solution exists
* @returns `false` if solution does not exist
*/
template <size_t V>
bool solve(int x, int y, int mov, std::array <std::array <int, V>, V> &sol,
const std::array <int, V> &xmov, std::array <int, V> &ymov) {
int k, xnext, ynext;
if (mov == V * V) {
return true;
}
for (k = 0; k < V; k++) {
xnext = x + xmov[k];
ynext = y + ymov[k];
if (backtracking::issafe<V>(xnext, ynext, sol)) {
sol[xnext][ynext] = mov;
if (backtracking::solve<V>(xnext, ynext, mov + 1, sol, xmov, ymov) == true) {
return true;
}
else {
sol[xnext][ynext] = -1;
}
}
}
return false;
}
} // namespace backtracking
/**
* @namespace knight_tour
* @brief Functions for the [Knight's
* tour](https://en.wikipedia.org/wiki/Knight%27s_tour) algorithm
*/
namespace knight_tour {
/**
* A utility function to check if i,j are valid indexes for N*N chessboard
* @tparam V number of vertices in array
* @param x current index in rows
* @param y current index in columns
* @param sol matrix where numbers are saved
* @returns `true` if ....
* @returns `false` if ....
*/
template <size_t V>
bool issafe(int x, int y, const std::array<std::array<int, V>, V> &sol) {
return (x < V && x >= 0 && y < V && y >= 0 && sol[x][y] == -1);
}
/**
* Main function
* Knight's tour algorithm
* @tparam V number of vertices in array
* @param x current index in rows
* @param y current index in columns
* @param mov movement to be done
* @param sol matrix where numbers are saved
* @param xmov next move of knight (x coordinate)
* @param ymov next move of knight (y coordinate)
* @returns `true` if solution exists
* @returns `false` if solution does not exist
*/
template <size_t V>
bool solve(int x, int y, int mov, std::array<std::array<int, V>, V> &sol,
const std::array<int, V> &xmov, std::array<int, V> &ymov) {
int k = 0, xnext = 0, ynext = 0;
if (mov == V * V) {
return true;
}
for (k = 0; k < V; k++) {
xnext = x + xmov[k];
ynext = y + ymov[k];
if (issafe<V>(xnext, ynext, sol)) {
sol[xnext][ynext] = mov;
if (solve<V>(xnext, ynext, mov + 1, sol, xmov, ymov) == true) {
return true;
} else {
sol[xnext][ynext] = -1;
}
}
}
return false;
}
} // namespace knight_tour
} // namespace backtracking
/**
* @brief Main function
* @returns 0 on exit
*/
int main() {
const int n = 8;
std::array <std::array <int, n>, n> sol = { 0 };
std::array<std::array<int, n>, n> sol = {0};
int i, j;
int i = 0, j = 0;
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) { sol[i][j] = -1; }
for (j = 0; j < n; j++) {
sol[i][j] = -1;
}
}
std::array <int, n> xmov = { 2, 1, -1, -2, -2, -1, 1, 2 };
std::array <int, n> ymov = { 1, 2, 2, 1, -1, -2, -2, -1 };
std::array<int, n> xmov = {2, 1, -1, -2, -2, -1, 1, 2};
std::array<int, n> ymov = {1, 2, 2, 1, -1, -2, -2, -1};
sol[0][0] = 0;
bool flag = backtracking::solve<n>(0, 0, 1, sol, xmov, ymov);
bool flag = backtracking::knight_tour::solve<n>(0, 0, 1, sol, xmov, ymov);
if (flag == false) {
std::cout << "Error: Solution does not exist\n";
}
else {
} else {
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) { std::cout << sol[i][j] << " "; }
for (j = 0; j < n; j++) {
std::cout << sol[i][j] << " ";
}
std::cout << "\n";
}
}

36
backtracking/minimax.cpp
View File

@ -6,33 +6,34 @@
* @details
* Minimax (sometimes MinMax, MM or saddle point) is a decision rule used in
* artificial intelligence, decision theory, game theory, statistics,
* and philosophy for minimizing the possible loss for a worst case (maximum loss) scenario.
* When dealing with gains, it is referred to as "maximin"—to maximize the minimum gain.
* Originally formulated for two-player zero-sum game theory, covering both the cases where players take
* alternate moves and those where they make simultaneous moves, it has also been extended to more
* complex games and to general decision-making in the presence of uncertainty.
*
* and philosophy for minimizing the possible loss for a worst case (maximum
* loss) scenario. When dealing with gains, it is referred to as "maximin"—to
* maximize the minimum gain. Originally formulated for two-player zero-sum game
* theory, covering both the cases where players take alternate moves and those
* where they make simultaneous moves, it has also been extended to more complex
* games and to general decision-making in the presence of uncertainty.
*
* @author [Gleison Batista](https://github.com/gleisonbs)
* @author [David Leal](https://github.com/Panquesito7)
*/
#include <algorithm>
#include <cmath>
#include <iostream>
#include <array>
#include <algorithm> /// for std::max, std::min
#include <array> /// for std::array
#include <cmath> /// for log2
#include <iostream> /// for IO operations
/**
/**
* @namespace backtracking
* @brief Backtracking algorithms
*/
namespace backtracking {
/**
* Check which number is the maximum/minimum in the array
* @brief Check which is the maximum/minimum number in the array
* @param depth current depth in game tree
* @param node_index current index in array
* @param is_max if current index is the longest number
* @param scores saved numbers in array
* @param height maximum height for game tree
* @return maximum or minimum number
* @returns the maximum or minimum number
*/
template <size_t T>
int minimax(int depth, int node_index, bool is_max,
@ -46,16 +47,17 @@ int minimax(int depth, int node_index, bool is_max,
return is_max ? std::max(v1, v2) : std::min(v1, v2);
}
} // namespace backtracking
} // namespace backtracking
/**
* Main function
* @brief Main function
* @returns 0 on exit
*/
int main() {
std::array<int, 8> scores = {90, 23, 6, 33, 21, 65, 123, 34423};
double height = log2(scores.size());
std::cout << "Optimal value: " << backtracking::minimax(0, 0, true, scores, height)
<< std::endl;
std::cout << "Optimal value: "
<< backtracking::minimax(0, 0, true, scores, height) << std::endl;
return 0;
}

157
backtracking/n_queens.cpp
View File

@ -15,115 +15,114 @@
* @author [David Leal](https://github.com/Panquesito7)
*
*/
#include <iostream>
#include <array>
#include <iostream>
/**
* @namespace backtracking
* @brief Backtracking algorithms
*/
namespace backtracking {
/**
* @namespace n_queens
* @brief Functions for [Eight Queens](https://en.wikipedia.org/wiki/Eight_queens_puzzle) puzzle.
*/
namespace n_queens {
/**
* Utility function to print matrix
* @tparam n number of matrix size
* @param board matrix where numbers are saved
*/
template <size_t n>
void printSolution(const std::array<std::array<int, n>, n> &board) {
std::cout << "\n";
for (int i = 0; i < n; i++) {
/**
* @namespace n_queens
* @brief Functions for [Eight
* Queens](https://en.wikipedia.org/wiki/Eight_queens_puzzle) puzzle.
*/
namespace n_queens {
/**
* Utility function to print matrix
* @tparam n number of matrix size
* @param board matrix where numbers are saved
*/
template <size_t n>
void printSolution(const std::array<std::array<int, n>, n> &board) {
std::cout << "\n";
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
std::cout << "" << board[i][j] << " ";
std::cout << "" << board[i][j] << " ";
}
std::cout << "\n";
}
}
}
/**
* Check if a queen can be placed on matrix
* @tparam n number of matrix size
* @param board matrix where numbers are saved
* @param row current index in rows
* @param col current index in columns
* @returns `true` if queen can be placed on matrix
* @returns `false` if queen can't be placed on matrix
*/
template <size_t n>
bool isSafe(const std::array<std::array<int, n>, n> &board, const int &row,
const int &col) {
int i = 0, j = 0;
/**
* Check if a queen can be placed on matrix
* @tparam n number of matrix size
* @param board matrix where numbers are saved
* @param row current index in rows
* @param col current index in columns
* @returns `true` if queen can be placed on matrix
* @returns `false` if queen can't be placed on matrix
*/
template <size_t n>
bool isSafe(const std::array<std::array<int, n>, n> &board, const int &row,
const int &col) {
int i = 0, j = 0;
// Check this row on left side
for (i = 0; i < col; i++) {
// Check this row on left side
for (i = 0; i < col; i++) {
if (board[row][i]) {
return false;
return false;
}
}
// Check upper diagonal on left side
for (i = row, j = col; i >= 0 && j >= 0; i--, j--) {
if (board[i][j]) {
return false;
}
}
// Check lower diagonal on left side
for (i = row, j = col; j >= 0 && i < n; i++, j--) {
if (board[i][j]) {
return false;
}
}
return true;
}
/**
* Solve n queens problem
* @tparam n number of matrix size
* @param board matrix where numbers are saved
* @param col current index in columns
*/
template <size_t n>
void solveNQ(std::array<std::array<int, n>, n> board, const int &col) {
if (col >= n) {
// Check upper diagonal on left side
for (i = row, j = col; i >= 0 && j >= 0; i--, j--) {
if (board[i][j]) {
return false;
}
}
// Check lower diagonal on left side
for (i = row, j = col; j >= 0 && i < n; i++, j--) {
if (board[i][j]) {
return false;
}
}
return true;
}
/**
* Solve n queens problem
* @tparam n number of matrix size
* @param board matrix where numbers are saved
* @param col current index in columns
*/
template <size_t n>
void solveNQ(std::array<std::array<int, n>, n> board, const int &col) {
if (col >= n) {
printSolution<n>(board);
return;
}
}
// Consider this column and try placing
// this queen in all rows one by one
for (int i = 0; i < n; i++) {
// Consider this column and try placing
// this queen in all rows one by one
for (int i = 0; i < n; i++) {
// Check if queen can be placed
// on board[i][col]
if (isSafe<n>(board, i, col)) {
// Place this queen in matrix
board[i][col] = 1;
// Place this queen in matrix
board[i][col] = 1;
// Recursive to place rest of the queens
solveNQ<n>(board, col + 1);
// Recursive to place rest of the queens
solveNQ<n>(board, col + 1);
board[i][col] = 0; // backtrack
board[i][col] = 0; // backtrack
}
}
}
} // namespace n_queens
} // namespace backtracking
}
} // namespace n_queens
} // namespace backtracking
/**
* Main function
* @brief Main function
* @returns 0 on exit
*/
int main() {
const int n = 4;
std::array<std::array<int, n>, n> board = {
std::array<int, n>({0, 0, 0, 0}),
std::array<int, n>({0, 0, 0, 0}),
std::array<int, n>({0, 0, 0, 0}),
std::array<int, n>({0, 0, 0, 0})
};
const int n = 4;
std::array<std::array<int, n>, n> board = {
std::array<int, n>({0, 0, 0, 0}), std::array<int, n>({0, 0, 0, 0}),
std::array<int, n>({0, 0, 0, 0}), std::array<int, n>({0, 0, 0, 0})};
backtracking::n_queens::solveNQ<n>(board, 0);
return 0;
backtracking::n_queens::solveNQ<n>(board, 0);
return 0;
}

4
backtracking/n_queens_all_solution_optimised.cpp
View File

@ -111,7 +111,7 @@ int main() {
std::array<std::array<int, n>, n> board{};
if (n % 2 == 0) {
for (int i = 0; i <= n / 2 - 1; i++) { // 😎
for (int i = 0; i <= n / 2 - 1; i++) {
if (backtracking::n_queens_optimized::CanIMove(board, i, 0)) {
board[i][0] = 1;
backtracking::n_queens_optimized::NQueenSol(board, 1);
@ -119,7 +119,7 @@ int main() {
}
}
} else {
for (int i = 0; i <= n / 2; i++) { // 😏
for (int i = 0; i <= n / 2; i++) {
if (backtracking::n_queens_optimized::CanIMove(board, i, 0)) {
board[i][0] = 1;
backtracking::n_queens_optimized::NQueenSol(board, 1);

25
backtracking/nqueen_print_all_solutions.cpp
View File

@ -1,14 +1,14 @@
/**
* @file
* @brief [Eight Queens](https://en.wikipedia.org/wiki/Eight_queens_puzzle)
* @brief [Eight Queens](https://en.wikipedia.org/wiki/Eight_queens_puzzle)
* puzzle, printing all solutions
*
* @author [Himani Negi](https://github.com/Himani2000)
* @author [David Leal](https://github.com/Panquesito7)
*
*/
#include <iostream>
#include <array>
#include <array> /// for std::array
#include <iostream> /// for IO operations
/**
* @namespace backtracking
@ -17,12 +17,13 @@
namespace backtracking {
/**
* @namespace n_queens_all_solutions
* @brief Functions for [Eight
* Queens](https://en.wikipedia.org/wiki/Eight_queens_puzzle) puzzle with all solutions.
* @brief Functions for the [Eight
* Queens](https://en.wikipedia.org/wiki/Eight_queens_puzzle) puzzle with all
* solutions.
*/
namespace n_queens_all_solutions {
/**
* Utility function to print matrix
* @brief Utility function to print matrix
* @tparam n number of matrix size
* @param board matrix where numbers are saved
*/
@ -38,7 +39,7 @@ void PrintSol(const std::array<std::array<int, n>, n>& board) {
}
/**
* Check if a queen can be placed on matrix
* @brief Check if a queen can be placed on the matrix
* @tparam n number of matrix size
* @param board matrix where numbers are saved
* @param row current index in rows
@ -47,7 +48,8 @@ void PrintSol(const std::array<std::array<int, n>, n>& board) {
* @returns `false` if queen can't be placed on matrix
*/
template <size_t n>
bool CanIMove(const std::array<std::array<int, n>, n>& board, int row, int col) {
bool CanIMove(const std::array<std::array<int, n>, n>& board, int row,
int col) {
/// check in the row
for (int i = 0; i < col; i++) {
if (board[row][i] == 1) {
@ -70,7 +72,7 @@ bool CanIMove(const std::array<std::array<int, n>, n>& board, int row, int col)
}
/**
* Solve n queens problem
* @brief Main function to solve the N Queens problem
* @tparam n number of matrix size
* @param board matrix where numbers are saved
* @param col current index in columns
@ -89,11 +91,12 @@ void NQueenSol(std::array<std::array<int, n>, n> board, int col) {
}
}
}
} // namespace n_queens_all_solutions
} // namespace n_queens_all_solutions
} // namespace backtracking
/**
* Main function
* @brief Main function
* @returns 0 on exit
*/
int main() {
const int n = 4;

24
backtracking/rat_maze.cpp
View File

@ -16,9 +16,9 @@
* @author [David Leal](https://github.com/Panquesito7)
*/
#include <array>
#include <iostream>
#include <cassert>
#include <array> /// for std::array
#include <cassert> /// for assert
#include <iostream> /// for IO operations
/**
* @namespace backtracking
@ -39,12 +39,14 @@ namespace rat_maze {
* @param currposcol current position in columns
* @param maze matrix where numbers are saved
* @param soln matrix to problem solution
* @returns 0 on end
* @returns `true` if there exists a solution to move one step ahead in a column
* or in a row
* @returns `false` for the backtracking part
*/
template <size_t size>
bool solveMaze(int currposrow, int currposcol,
const std::array<std::array<int, size>, size> &maze,
std::array<std::array<int, size>, size> soln) {
const std::array<std::array<int, size>, size> &maze,
std::array<std::array<int, size>, size> soln) {
if ((currposrow == size - 1) && (currposcol == size - 1)) {
soln[currposrow][currposcol] = 1;
for (int i = 0; i < size; ++i) {
@ -78,10 +80,10 @@ bool solveMaze(int currposrow, int currposcol,
} // namespace backtracking
/**
* @brief Test implementations
* @brief Self-test implementations
* @returns void
*/
static void test(){
static void test() {
const int size = 4;
std::array<std::array<int, size>, size> maze = {
std::array<int, size>{1, 0, 1, 0}, std::array<int, size>{1, 0, 1, 1},
@ -96,8 +98,8 @@ static void test(){
}
}
int currposrow = 0; // Current position in rows
int currposcol = 0; // Current position in columns
int currposrow = 0; // Current position in the rows
int currposcol = 0; // Current position in the columns
assert(backtracking::rat_maze::solveMaze<size>(currposrow, currposcol, maze,
soln) == 1);
@ -108,6 +110,6 @@ static void test(){
* @returns 0 on exit
*/
int main() {
test(); // run the tests
test(); // run self-test implementations
return 0;
}

260
backtracking/sudoku_solve.cpp
View File

@ -3,155 +3,171 @@
* @brief [Sudoku Solver](https://en.wikipedia.org/wiki/Sudoku) algorithm.
*
* @details
* Sudoku (数独, sūdoku, digit-single) (/suːˈdoʊkuː/, /-ˈdɒk-/, /sə-/, originally called
* Number Place) is a logic-based, combinatorial number-placement puzzle.
* In classic sudoku, the objective is to fill a 9×9 grid with digits so that each column,
* each row, and each of the nine 3×3 subgrids that compose the grid (also called "boxes", "blocks", or "regions")
* Sudoku (数独, sūdoku, digit-single) (/suːˈdoʊkuː/, /-ˈdɒk-/, /sə-/,
* originally called Number Place) is a logic-based, combinatorial
* number-placement puzzle. In classic sudoku, the objective is to fill a 9×9
* grid with digits so that each column, each row, and each of the nine 3×3
* subgrids that compose the grid (also called "boxes", "blocks", or "regions")
* contain all of the digits from 1 to 9. The puzzle setter provides a
* partially completed grid, which for a well-posed puzzle has a single solution.
* partially completed grid, which for a well-posed puzzle has a single
* solution.
*
* @author [DarthCoder3200](https://github.com/DarthCoder3200)
* @author [David Leal](https://github.com/Panquesito7)
*/
#include <iostream>
#include <array>
#include <array> /// for assert
#include <iostream> /// for IO operations
/**
* @namespace backtracking
* @brief Backtracking algorithms
*/
namespace backtracking {
/**
* Checks if it's possible to place a number 'no'
* @tparam V number of vertices in the array
* @param mat matrix where numbers are saved
* @param i current index in rows
* @param j current index in columns
* @param no number to be added in matrix
* @param n number of times loop will run
* @returns `true` if 'mat' is different from 'no'
* @returns `false` if 'mat' equals to 'no'
*/
template <size_t V>
bool isPossible(const std::array <std::array <int, V>, V> &mat, int i, int j, int no, int n) {
/// 'no' shouldn't be present in either row i or column j
for (int x = 0; x < n; x++) {
if (mat[x][j] == no || mat[i][x] == no) {
/**
* @namespace sudoku_solver
* @brief Functions for the [Sudoku
* Solver](https://en.wikipedia.org/wiki/Sudoku) implementation
*/
namespace sudoku_solver {
/**
* @brief Check if it's possible to place a number (`no` parameter)
* @tparam V number of vertices in the array
* @param mat matrix where numbers are saved
* @param i current index in rows
* @param j current index in columns
* @param no number to be added in matrix
* @param n number of times loop will run
* @returns `true` if 'mat' is different from 'no'
* @returns `false` if 'mat' equals to 'no'
*/
template <size_t V>
bool isPossible(const std::array<std::array<int, V>, V> &mat, int i, int j,
int no, int n) {
/// `no` shouldn't be present in either row i or column j
for (int x = 0; x < n; x++) {
if (mat[x][j] == no || mat[i][x] == no) {
return false;
}
}
/// `no` shouldn't be present in the 3*3 subgrid
int sx = (i / 3) * 3;
int sy = (j / 3) * 3;
for (int x = sx; x < sx + 3; x++) {
for (int y = sy; y < sy + 3; y++) {
if (mat[x][y] == no) {
return false;
}
}
}
/// 'no' shouldn't be present in the 3*3 subgrid
int sx = (i / 3) * 3;
int sy = (j / 3) * 3;
for (int x = sx; x < sx + 3; x++) {
for (int y = sy; y < sy + 3; y++) {
if (mat[x][y] == no) {
return false;
}
return true;
}
/**
* @brief Utility function to print the matrix
* @tparam V number of vertices in array
* @param mat matrix where numbers are saved
* @param starting_mat copy of mat, required by printMat for highlighting the
* differences
* @param n number of times loop will run
* @return void
*/
template <size_t V>
void printMat(const std::array<std::array<int, V>, V> &mat,
const std::array<std::array<int, V>, V> &starting_mat, int n) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (starting_mat[i][j] != mat[i][j]) {
std::cout << "\033[93m" << mat[i][j] << "\033[0m"
<< " ";
} else {
std::cout << mat[i][j] << " ";
}
if ((j + 1) % 3 == 0) {
std::cout << '\t';
}
}
return true;
}
/**
* Utility function to print matrix
* @tparam V number of vertices in array
* @param mat matrix where numbers are saved
* @param starting_mat copy of mat, required by printMat for highlighting the differences
* @param n number of times loop will run
* @return void
*/
template <size_t V>
void printMat(const std::array <std::array <int, V>, V> &mat, const std::array <std::array <int, V>, V> &starting_mat, int n) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (starting_mat[i][j] != mat[i][j]) {
std::cout << "\033[93m" << mat[i][j] << "\033[0m" << " ";
} else {
std::cout << mat[i][j] << " ";
}
if ((j + 1) % 3 == 0) {
std::cout << '\t';
}
}
if ((i + 1) % 3 == 0) {
std::cout << std::endl;
}
if ((i + 1) % 3 == 0) {
std::cout << std::endl;
}
std::cout << std::endl;
}
/**
* Sudoku algorithm
* @tparam V number of vertices in array
* @param mat matrix where numbers are saved
* @param starting_mat copy of mat, required by printMat for highlighting the differences
* @param i current index in rows
* @param j current index in columns
* @returns `true` if 'no' was placed
* @returns `false` if 'no' was not placed
*/
template <size_t V>
bool solveSudoku(std::array <std::array <int, V>, V> &mat, const std::array <std::array <int, V>, V> &starting_mat, int i, int j) {
/// Base Case
if (i == 9) {
/// Solved for 9 rows already
backtracking::printMat<V>(mat, starting_mat, 9);
return true;
}
/// Crossed the last Cell in the row
if (j == 9) {
return backtracking::solveSudoku<V>(mat, starting_mat, i + 1, 0);
}
/// Blue Cell - Skip
if (mat[i][j] != 0) {
return backtracking::solveSudoku<V>(mat, starting_mat, i, j + 1);
}
/// White Cell
/// Try to place every possible no
for (int no = 1; no <= 9; no++) {
if (backtracking::isPossible<V>(mat, i, j, no, 9)) {
/// Place the 'no' - assuming a solution will exist
mat[i][j] = no;
bool solution_found = backtracking::solveSudoku<V>(mat, starting_mat, i, j + 1);
if (solution_found) {
return true;
}
/// Couldn't find a solution
/// loop will place the next no.
}
}
/// Solution couldn't be found for any of the numbers provided
mat[i][j] = 0;
return false;
}
} // namespace backtracking
}
/**
* Main function
* @brief Main function to implement the Sudoku algorithm
* @tparam V number of vertices in array
* @param mat matrix where numbers are saved
* @param starting_mat copy of mat, required by printMat for highlighting the
* differences
* @param i current index in rows
* @param j current index in columns
* @returns `true` if 'no' was placed
* @returns `false` if 'no' was not placed
*/
template <size_t V>
bool solveSudoku(std::array<std::array<int, V>, V> &mat,
const std::array<std::array<int, V>, V> &starting_mat, int i,
int j) {
/// Base Case
if (i == 9) {
/// Solved for 9 rows already
printMat<V>(mat, starting_mat, 9);
return true;
}
/// Crossed the last Cell in the row
if (j == 9) {
return solveSudoku<V>(mat, starting_mat, i + 1, 0);
}
/// Blue Cell - Skip
if (mat[i][j] != 0) {
return solveSudoku<V>(mat, starting_mat, i, j + 1);
}
/// White Cell
/// Try to place every possible no
for (int no = 1; no <= 9; no++) {
if (isPossible<V>(mat, i, j, no, 9)) {
/// Place the 'no' - assuming a solution will exist
mat[i][j] = no;
bool solution_found = solveSudoku<V>(mat, starting_mat, i, j + 1);
if (solution_found) {
return true;
}
/// Couldn't find a solution
/// loop will place the next `no`.
}
}
/// Solution couldn't be found for any of the numbers provided
mat[i][j] = 0;
return false;
}
} // namespace sudoku_solver
} // namespace backtracking
/**
* @brief Main function
* @returns 0 on exit
*/
int main() {
const int V = 9;
std::array <std::array <int, V>, V> mat = {
std::array <int, V> {5, 3, 0, 0, 7, 0, 0, 0, 0},
std::array <int, V> {6, 0, 0, 1, 9, 5, 0, 0, 0},
std::array <int, V> {0, 9, 8, 0, 0, 0, 0, 6, 0},
std::array <int, V> {8, 0, 0, 0, 6, 0, 0, 0, 3},
std::array <int, V> {4, 0, 0, 8, 0, 3, 0, 0, 1},
std::array <int, V> {7, 0, 0, 0, 2, 0, 0, 0, 6},
std::array <int, V> {0, 6, 0, 0, 0, 0, 2, 8, 0},
std::array <int, V> {0, 0, 0, 4, 1, 9, 0, 0, 5},
std::array <int, V> {0, 0, 0, 0, 8, 0, 0, 7, 9}
};
std::array<std::array<int, V>, V> mat = {
std::array<int, V>{5, 3, 0, 0, 7, 0, 0, 0, 0},
std::array<int, V>{6, 0, 0, 1, 9, 5, 0, 0, 0},
std::array<int, V>{0, 9, 8, 0, 0, 0, 0, 6, 0},
std::array<int, V>{8, 0, 0, 0, 6, 0, 0, 0, 3},
std::array<int, V>{4, 0, 0, 8, 0, 3, 0, 0, 1},
std::array<int, V>{7, 0, 0, 0, 2, 0, 0, 0, 6},
std::array<int, V>{0, 6, 0, 0, 0, 0, 2, 8, 0},
std::array<int, V>{0, 0, 0, 4, 1, 9, 0, 0, 5},
std::array<int, V>{0, 0, 0, 0, 8, 0, 0, 7, 9}};
backtracking::printMat<V>(mat, mat, 9);
backtracking::sudoku_solver::printMat<V>(mat, mat, 9);
std::cout << "Solution " << std::endl;
std::array <std::array <int, V>, V> starting_mat = mat;
backtracking::solveSudoku<V>(mat, starting_mat, 0, 0);
std::array<std::array<int, V>, V> starting_mat = mat;
backtracking::sudoku_solver::solveSudoku<V>(mat, starting_mat, 0, 0);
return 0;
}