Merge pull request #179 from ndk123-web/main

feat: added countinversions and ratInMaze backtrack approach

Author: admirerr

CPP/Backtracking/backtrack_countInversions.cpp

@@ -0,0 +1,43 @@
+#include <iostream>
+#include <vector>
+using namespace std;
+
+long long mergeAndCount(vector<int>& arr, int l, int m, int r) {
+    int i = l, j = m + 1;
+    vector<int> temp;
+    long long cnt = 0;
+
+    while (i <= m && j <= r) {
+        if (arr[i] <= arr[j]) {
+            temp.push_back(arr[i++]);
+        } else {
+            temp.push_back(arr[j++]);
+            cnt += (m - i + 1); // inversion count
+        }
+    }
+
+    while (i <= m) temp.push_back(arr[i++]);
+    while (j <= r) temp.push_back(arr[j++]);
+
+    // copy back
+    for (int k = l; k <= r; k++) arr[k] = temp[k - l];
+
+    return cnt;
+}
+
+long long countInversion(vector<int>& arr, int l, int r) {
+    long long cnt = 0;
+    if (l < r) {
+        int m = (l + r) / 2;
+        cnt += countInversion(arr, l, m);
+        cnt += countInversion(arr, m + 1, r);
+        cnt += mergeAndCount(arr, l, m, r);
+    }
+    return cnt;
+}
+
+int main() {
+    vector<int> arr = {5, 3, 2, 4, 1};
+    cout << "Inversions: " << countInversion(arr, 0, arr.size() - 1);
+    return 0;
+}

CPP/Backtracking/backtrack_ratInMaze.cpp

@@ -0,0 +1,76 @@
+// Online C++ compiler to run C++ program online
+#include <iostream>
+#include <vector>
+
+using namespace std;
+
+bool canGo(int row, int col, vector<vector<int>>& matrix) {
+    int n = matrix.size();
+    // Check boundaries and validity
+    if (row < 0 || col < 0 || row >= n || col >= n) return false;
+    if (matrix[row][col] == 0 || matrix[row][col] == -1) return false;
+
+    return true;
+}
+
+void solveMaze(int row, int col, vector<vector<int>>& matrix, string& part, int size, vector<string>& ans){
+
+    if (row == size-1 && col == size-1){
+        ans.push_back(part);
+        return;
+    }
+
+    // mark cell as visited
+    matrix[row][col] = -1;
+
+    // check down
+    if (canGo(row+1,col,matrix)){
+        part = part + "D";
+        solveMaze(row+1,col,matrix,part,size,ans);
+        part.pop_back();
+    }
+
+    // check up
+    if (canGo(row-1,col,matrix)){
+        part = part + "U";
+        solveMaze(row-1,col,matrix,part,size,ans);
+        part.pop_back();
+    }
+
+    // check left
+    if(canGo(row,col-1,matrix)){
+        part = part + "L";
+        solveMaze(row,col-1,matrix,part,size,ans);
+        part.pop_back();
+    }
+
+    // check right
+    if(canGo(row,col+1,matrix)){
+        part = part + "R";
+        solveMaze(row,col+1,matrix,part,size,ans);
+        part.pop_back();
+    }
+
+    // unmark
+    matrix[row][col] = 1;
+}
+
+int main() {
+
+    vector<vector<int>> matrix = {
+        {1,0,0,0},
+        {1,1,0,1},
+        {1,1,0,0},
+        {0,1,1,1}
+    };
+    vector<string> ans;
+    string part= "";
+
+    solveMaze(0,0,matrix,part,matrix.size(),ans);
+
+    for (auto i : ans){
+        cout << i << " ";
+    }
+
+    return 0;
+}