chore(CPlusPlus): add rat in a maze problem (MakeContributions#1051)

Co-authored-by: Arsenic <[email protected]>

algorithms/CPlusPlus/Backtracking/rat-in-a-maze-problem.cpp

@@ -0,0 +1,60 @@
+#include<iostream>
+using namespace std;
+
+bool issafe(int** arr, int x, int y, int n){
+    if(x<n && y<n && arr[x][y]==1){
+        return true;
+    }
+    return false;
+}
+bool ratinMaze(int** arr, int x, int y, int n, int** solArr){
+    if(x==n-1 && y==n-1){
+        solArr[x][y]=1;
+        return true;
+    }
+    if(issafe(arr, x, y, n)){
+        solArr[x][y]=1;
+        if(ratinMaze(arr, x+1, y, n, solArr)){
+            return true;
+        }
+        if(ratinMaze(arr, x, y+1, n, solArr)){
+            return true;
+        }
+        solArr[x][y]=0;
+        return false;
+    }
+    return false;
+}
+
+int main(){
+    int n;
+    cin>>n;
+    int** arr=new int*[n];
+    for(int i=0; i<n; i++){
+        arr[i]=new int[n];
+    }
+    for(int i=0; i<n; i++){
+        for(int j=0; j<n; j++){
+            cin>>arr[i][j];
+        }
+    }
+    int** solArr=new int*[n];
+    for(int i=0; i<n; i++){
+        solArr[i] = new int[n];
+        for(int j=0; j<n; j++){
+            solArr[i][j]=0;
+        }
+    }
+    if(ratinMaze(arr, 0, 0, n, solArr)){
+        for(int i=0; i<n; i++){
+        for(int j=0; j<n; j++){
+            cout<<solArr[i][j];
+        }cout<<endl;
+
+        }
+    }
+    return 0;
+}
+
+/* Time complexity: O(2^(n^2)). The recursion can run upper-bound 2^(n^2) times.
+   Space Complexity: O(n^2). Output matrix is required so an extra space of size n*n is needed. */

algorithms/CPlusPlus/README.md

@@ -216,3 +216,4 @@
 ## Backtracking
 
 - [N-Queens Problem](Backtracking/n-queens.cpp)
+- [Rat In A Maze Problem](Backtracking/rat-in-a-maze-problem.cpp)