added sudoku to backtracking folder

Backtracking/sudoku.cpp

@@ -0,0 +1,155 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+#define NIL 0
+
+int FULL;
+vector<map<int,int>> rowsMap(9);
+vector<map<int,int>> colsMap(9);
+vector<map<int,int>> internalMap(9);
+vector<vector<int>> board(9, vector<int>(9, 0));
+vector<vector<int>> empty;
+void getEmptyPositions(vector<vector<int>>);
+void initialiseMaps(vector<vector<int>>);
+bool isBoardValid();
+bool isMoveValid();
+void assignToMaps(int, int, int);
+void removeFromMaps(int, int, int);
+void solve();
+
+void assignToMaps(int row, int col, int val){
+    int pos = (row/3)*3+col/3;
+    rowsMap[row][val]++;
+    colsMap[col][val]++;
+    internalMap[pos][val]++;
+}
+
+void removeFromMaps(int row, int col, int val){
+    int pos = (row/3)*3+col/3;
+    rowsMap[row][val]--;
+    colsMap[col][val]--;
+    internalMap[pos][val]--;
+}
+
+bool isBoardValid(){
+    for(int i = 0; i < 9; i++){
+        for(int j = 0; j < 9; j++){
+            int val = board[i][j]-1;
+            if(val > 0){
+                int pos = (i/3)*3+j/3;
+                if(rowsMap[i][val] > 1 || colsMap[j][val] > 1 || internalMap[pos][val] > 1) return false;
+            }
+        }
+    }
+    return true;
+}
+
+bool isMoveValid(int row, int col, int val){
+    int pos = (row/3)*3+col/3;
+    if(rowsMap[row][val] > 1 || colsMap[col][val] > 1 || internalMap[pos][val] > 1) return false;
+    return true;
+}
+
+void getEmptyPositions(vector<vector<int>> start){
+    for(int i = 0; i < 9; i++){
+        for(int j = 0; j < 9; j++){
+            if(start[i][j] == NIL) empty.push_back({i, j});
+        }
+    }
+}
+
+void initialiseMaps(vector<vector<int>> board){
+    for(int i = 0; i < 9; i++){
+        for(int j = 0; j < 9; j++){
+            if(board[i][j] != NIL){
+                assignToMaps(i, j, board[i][j]-1);
+            }
+        }
+    }
+}
+
+bool solve(int pos){
+    if(pos < 0) return false;
+    if(pos == FULL) return true;
+    int row = empty[pos][0], col = empty[pos][1];
+    for(int i = 1; i <= 9; i++){
+        board[row][col] = i;
+        assignToMaps(row, col, i-1);
+        if(isMoveValid(row, col, i-1)){
+            if(solve(pos+1)) return true;
+            else{
+                board[row][col] = NIL;
+                removeFromMaps(row, col, i-1);
+            }
+        }
+        else{
+            board[row][col] = NIL;
+            removeFromMaps(row, col, i-1);
+        }
+    }
+    return false;
+}
+
+bool printFormatted(){
+    cout<<"{";
+    for(int i = 0; i < 9; i++){
+        cout<<"{";
+        for(int j = 0; j < 9; j++){
+            if(j == 8) cout<<"'"<<board[i][j]<<"'";
+            else cout<<"'"<<board[i][j]<<"', ";
+        }
+        if(i < 8)
+            cout<<"},\n";
+        else cout<<"}";
+    }
+    cout<<"};\n";
+}
+
+int main(){ 
+    vector<vector<int> > startConfig = {{0, 6, 7, 0, 0, 0, 0, 9, 0},  
+                                        {9, 0, 0, 5, 0, 0, 6, 8, 7},  
+                                        {0, 0, 0, 0, 6, 7, 0, 0, 0},  
+                                        {0, 1, 9, 4, 0, 0, 0, 0, 0},  
+                                        {0, 7, 6, 3, 0, 2, 0, 0, 0},  
+                                        {0, 0, 0, 0, 0, 6, 4, 7, 0},  
+                                        {0, 0, 0, 8, 2, 0, 0, 0, 0},  
+                                        {6, 9, 0, 0, 0, 3, 0, 0, 2},  
+                                        {7, 4, 0, 6, 0, 0, 3, 5, 0}};  
+    board = startConfig;
+    getEmptyPositions(board);
+    initialiseMaps(board);
+    if(!isBoardValid()){
+        cout<<"Initial board not correct\n";
+        return 0;
+    }
+    else{
+        cout<<"Initial Config                  Final Ans\n";
+    }
+    FULL = empty.size();
+    bool flag = solve(0);
+    if(flag){
+        for(int i = 0; i < 9; i++){
+            for(int j = 0; j < 9; j++){
+                if(startConfig[i][j] == 0) cout<<". ";
+                else cout<<startConfig[i][j]<<" ";
+            }
+            if( i == 4) cout<<"   --->    ";
+            else cout<<"           ";
+            for(int j = 0; j < 9; j++){
+                if(startConfig[i][j] == 0) cout<<board[i][j]<<" ";
+                else cout<<board[i][j]<<" ";
+            }
+            cout<<endl;
+        } cout<<endl;
+        if(isBoardValid()){
+            cout<<"Verified solution\n";
+        }
+        else{
+            cout<<"Not valid\n";
+        }
+    }
+    else{
+        cout<<"Not Solvable\n";
+    }
+}
+