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[fix/docs]: Update backtracking folder (#916)
* [fix/docs]: Update backtracking/graph_coloring.cpp * Add CMakeLists.txt in backtracking folder * Add backtracking to CMakeLists.txt * fix: Fix build issues * docs: Various documentation fixes * fix: minimax.cpp issues * fix: sudoku_solve.cpp fixes * formatting source-code for8ffbbb35ce* make he code neat and clean without global variables * fix 2 stars in comment * fix MSVC errors by forcing template parameter in function calls Note: This is identical to passing it as a function parameter, and may not be helpful * Update minimax.cpp * docs: minimax.cpp improvements * docs: Add Wikipedia link in minimax.cpp * fix: minimax.cpp vector fix * docs: fix Wikipedia link in minimax.cpp * docs: fix return statement in minimax.cpp * fix: sudoku_solve.cpp fixes * fix: more sudoku_solve.cpp fixes * fix: sudoku_solve.cpp fixes * fix: sudoku_solve.cpp * formatting source-code for13b5b9b829* docs: update graph_coloring.cpp description * fix: use array instead of vector (minimax.cpp) * feat: add namespace (minimax.cpp) * docs: update namespace description (graph_coloring.cpp) * fix: graph_coloring.cpp * fix: sudoku_solve.cpp fixes * fix: graph_coloring.cpp * fix: minimax.cpp * fix: more sudoku_solve.cpp fixes * fix: more graph_coloring.cpp fixes * fix: graph_coloring.cpp fixes * fix: sudoku_solve.cpp fixes * fix: minimax.cpp * fix: sudoku_solve.cpp fixes * fix: too few template arguments (std::array) * fix: too few template arguments (std::array, minimax.cpp) * fix: narrowing conversion from double to int (minimax.cpp) * fix: excess elements in struct initializer (graph_coloring.cpp) * fix: no matching function (graph_coloring.cpp) * fix: graph_coloring.cpp issues/errors * fix: knight_tour.cpp issues/errors * fix: sudoku_solve.cpp issues/errors * [fix/docs]: Various fixes in graph_coloring.cpp * fix: More graph_coloring.cpp fixes * docs: Add initial comment block (sudoku_solve.cpp) * fix: Add return statement (knight_tour.cpp) * fix: array fixes (graph_coloring.cpp) * docs: documentation improvements (sudoku_solve.cpp) * docs: documentation improvements (knight_tour.cpp) * docs: documentation improvements (sudoku_solve.cpp) * docs: documentation improvements (graph_coloring.cpp) * docs: Documentation improvements (graph_coloring.cpp) Thanks, @kvedala! * docs: Documentation improvements (sudoku_solve.cpp) * docs: Document function parameter (sudoku_solve.cpp) * docs: Documentation improvements (knight_tour.cpp) * docs: Add long description (graph_coloring.cpp) * docs: Add long description (minimax.cpp) * docs: Add long description (sudoku_solve.cpp) * docs: Documentation improvements (knight_tour.cpp) * docs: Documentation improvements (sudoku_solve.cpp) * docs: Documentation improvements (minimax.cpp) * docs: More documentation improvements (minimax.cpp) * docs: Documentation improvements (sudoku_solve.cpp) * fix: sudoku_solve.cpp improvements Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: Krishna Vedala <7001608+kvedala@users.noreply.github.com>
This commit is contained in:
David Leal
@@ -1,91 +1,150 @@
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/**
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* @file
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* @brief [Sudoku Solver](https://en.wikipedia.org/wiki/Sudoku) algorithm.
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*
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* @details
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* Sudoku (数独, sūdoku, digit-single) (/suːˈdoʊkuː/, /-ˈdɒk-/, /sə-/, originally called
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* Number Place) is a logic-based, combinatorial number-placement puzzle.
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* In classic sudoku, the objective is to fill a 9×9 grid with digits so that each column,
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* each row, and each of the nine 3×3 subgrids that compose the grid (also called "boxes", "blocks", or "regions")
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* contain all of the digits from 1 to 9. The puzzle setter provides a
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* partially completed grid, which for a well-posed puzzle has a single solution.
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*
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* @author [DarthCoder3200](https://github.com/DarthCoder3200)
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* @author [David Leal](https://github.com/Panquesito7)
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*/
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#include <iostream>
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using namespace std;
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/// N=9;
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int n = 9;
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#include <array>
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bool isPossible(int mat[][9], int i, int j, int no) {
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/// Row or col nahin hona chahiye
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for (int x = 0; x < n; x++) {
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if (mat[x][j] == no || mat[i][x] == no) {
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return false;
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}
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}
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/// Subgrid mein nahi hona chahiye
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int sx = (i / 3) * 3;
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int sy = (j / 3) * 3;
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for (int x = sx; x < sx + 3; x++) {
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for (int y = sy; y < sy + 3; y++) {
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if (mat[x][y] == no) {
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/**
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* @namespace backtracking
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* @brief Backtracking algorithms
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*/
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namespace backtracking {
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/**
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* Checks if it's possible to place a 'no'
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* @tparam V number of vertices in the array
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* @param mat matrix where numbers are saved
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* @param i current index in rows
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* @param j current index in columns
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* @param no number to be added in matrix
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* @param n number of times loop will run
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* @returns `true` if 'mat' is different from 'no'
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* @returns `false` if 'mat' equals to 'no'
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*/
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template <size_t V>
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bool isPossible(const std::array <std::array <int, V>, V> &mat, int i, int j, int no, int n) {
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/// Row or col nahin hona chahiye
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for (int x = 0; x < n; x++) {
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if (mat[x][j] == no || mat[i][x] == no) {
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return false;
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}
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}
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}
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return true;
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}
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void printMat(int mat[][9]) {
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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cout << mat[i][j] << " ";
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if ((j + 1) % 3 == 0) {
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cout << '\t';
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/// Subgrid mein nahi hona chahiye
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int sx = (i / 3) * 3;
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int sy = (j / 3) * 3;
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for (int x = sx; x < sx + 3; x++) {
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for (int y = sy; y < sy + 3; y++) {
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if (mat[x][y] == no) {
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return false;
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}
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}
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}
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if ((i + 1) % 3 == 0) {
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cout << endl;
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}
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cout << endl;
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}
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}
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bool solveSudoku(int mat[][9], int i, int j) {
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/// Base Case
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if (i == 9) {
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/// Solve kr chuke hain for 9 rows already
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printMat(mat);
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return true;
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}
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/// Crossed the last Cell in the row
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if (j == 9) {
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return solveSudoku(mat, i + 1, 0);
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}
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/// Blue Cell - Skip
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if (mat[i][j] != 0) {
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return solveSudoku(mat, i, j + 1);
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}
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/// White Cell
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/// Try to place every possible no
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for (int no = 1; no <= 9; no++) {
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if (isPossible(mat, i, j, no)) {
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/// Place the no - assuming solution aa jayega
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mat[i][j] = no;
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bool aageKiSolveHui = solveSudoku(mat, i, j + 1);
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if (aageKiSolveHui) {
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return true;
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/**
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* Utility function to print matrix
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* @tparam V number of vertices in array
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* @param mat matrix where numbers are saved
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* @param n number of times loop will run
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* @return void
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*/
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template <size_t V>
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void printMat(const std::array <std::array <int, V>, V> &mat, int n) {
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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std::cout << mat[i][j] << " ";
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if ((j + 1) % 3 == 0) {
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std::cout << '\t';
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}
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}
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/// Nahin solve hui
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/// loop will place the next no.
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if ((i + 1) % 3 == 0) {
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std::cout << std::endl;
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}
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std::cout << std::endl;
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}
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}
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/// Sare no try kr liey, kisi se bhi solve nahi hui
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mat[i][j] = 0;
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return false;
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}
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/**
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* Sudoku algorithm
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* @tparam V number of vertices in array
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* @param mat matrix where numbers are saved
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* @param i current index in rows
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* @param j current index in columns
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* @returns `true` if 'no' was placed
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* @returns `false` if 'no' was not placed
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*/
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template <size_t V>
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bool solveSudoku(std::array <std::array <int, V>, V> &mat, int i, int j) {
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/// Base Case
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if (i == 9) {
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/// Solve kr chuke hain for 9 rows already
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backtracking::printMat<V>(mat, 9);
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return true;
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}
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/// Crossed the last Cell in the row
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if (j == 9) {
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return backtracking::solveSudoku<V>(mat, i + 1, 0);
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}
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/// Blue Cell - Skip
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if (mat[i][j] != 0) {
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return backtracking::solveSudoku<V>(mat, i, j + 1);
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}
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/// White Cell
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/// Try to place every possible no
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for (int no = 1; no <= 9; no++) {
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if (backtracking::isPossible<V>(mat, i, j, no, 9)) {
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/// Place the no - assuming solution aa jayega
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mat[i][j] = no;
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bool aageKiSolveHui = backtracking::solveSudoku<V>(mat, i, j + 1);
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if (aageKiSolveHui) {
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return true;
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}
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/// Nahin solve hui
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/// loop will place the next no.
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}
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}
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/// Sare no try kr liey, kisi se bhi solve nahi hui
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mat[i][j] = 0;
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return false;
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}
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} // namespace backtracking
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/**
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* Main function
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*/
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int main() {
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int mat[9][9] = {{5, 3, 0, 0, 7, 0, 0, 0, 0}, {6, 0, 0, 1, 9, 5, 0, 0, 0},
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{0, 9, 8, 0, 0, 0, 0, 6, 0}, {8, 0, 0, 0, 6, 0, 0, 0, 3},
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{4, 0, 0, 8, 0, 3, 0, 0, 1}, {7, 0, 0, 0, 2, 0, 0, 0, 6},
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{0, 6, 0, 0, 0, 0, 2, 8, 0}, {0, 0, 0, 4, 1, 9, 0, 0, 5},
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{0, 0, 0, 0, 8, 0, 0, 7, 9}};
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const int V = 9;
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std::array <std::array <int, V>, V> mat = {
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std::array <int, V> {5, 3, 0, 0, 7, 0, 0, 0, 0},
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std::array <int, V> {6, 0, 0, 1, 9, 5, 0, 0, 0},
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std::array <int, V> {0, 9, 8, 0, 0, 0, 0, 6, 0},
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std::array <int, V> {8, 0, 0, 0, 6, 0, 0, 0, 3},
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std::array <int, V> {4, 0, 0, 8, 0, 3, 0, 0, 1},
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std::array <int, V> {7, 0, 0, 0, 2, 0, 0, 0, 6},
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std::array <int, V> {0, 6, 0, 0, 0, 0, 2, 8, 0},
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std::array <int, V> {0, 0, 0, 4, 1, 9, 0, 0, 5},
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std::array <int, V> {0, 0, 0, 0, 8, 0, 0, 7, 9}
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};
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printMat(mat);
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cout << "Solution " << endl;
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solveSudoku(mat, 0, 0);
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backtracking::printMat<V>(mat, 9);
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std::cout << "Solution " << std::endl;
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backtracking::solveSudoku<V>(mat, 0, 0);
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return 0;
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}
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