Rat in a maze problem

Algorithms/Backtracking/Rat_in_a_maze.cpp

@@ -0,0 +1,72 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+#define N 4 
+
+bool solveMazeUtil(int maze[N][N], int x, int y, int sol[N][N]); 
+
+void printSolution(int sol[N][N]) 
+{ 
+    for (int i = 0; i < N; i++) { 
+        for (int j = 0; j < N; j++) 
+            cout<<sol[i][j]; 
+        cout<<endl; 
+    } 
+} 
+
+bool isSafe(int maze[N][N], int x, int y) 
+{ 
+    if (x >= 0 && x < N && y >= 0 && y < N && maze[x][y] == 1) 
+        return true; 
+
+    return false; 
+} 
+
+bool solveMaze(int maze[N][N]) 
+{ 
+    int sol[N][N] = { { 0, 0, 0, 0 }, 
+                      { 0, 0, 0, 0 }, 
+                      { 0, 0, 0, 0 }, 
+                      { 0, 0, 0, 0 } }; 
+
+    if (solveMazeUtil(maze, 0, 0, sol) == false) { 
+        cout<<"Solution doesn't exist"<<endl; 
+        return false; 
+    } 
+
+    printSolution(sol); 
+    return true; 
+} 
+
+bool solveMazeUtil(int maze[N][N], int x, int y, int sol[N][N]) 
+{ 
+    if (x == N - 1 && y == N - 1) { 
+        sol[x][y] = 1; 
+        return true; 
+    } 
+
+    if (isSafe(maze, x, y) == true) { 
+        sol[x][y] = 1; 
+
+        if (solveMazeUtil(maze, x + 1, y, sol) == true) 
+            return true; 
+
+        if (solveMazeUtil(maze, x, y + 1, sol) == true) 
+            return true; 
+        sol[x][y] = 0; 
+        return false; 
+    } 
+
+    return false; 
+} 
+
+int main() 
+{ 
+    int maze[N][N] = { { 0, 1, 1, 0 }, 
+                       { 1, 0, 1, 1 }, 
+                       { 0, 1, 1, 0 }, 
+                       { 1, 0, 0, 1 } }; 
+
+    solveMaze(maze); 
+    return 0; 
+} 

Algorithms/Dynamic Programming/subset_sum.cpp

@@ -0,0 +1,37 @@
+#include<bits/stdc++.h> 
+
+bool isSubsetSum(int set[], int n, int sum) 
+{
+    bool subset[n+1][sum+1]; 
+
+    for (int i = 0; i <= n; i++) 
+      subset[i][0] = true; 
+
+    for (int i = 1; i <= sum; i++) 
+      subset[0][i] = false; 
+
+     for (int i = 1; i <= n; i++) 
+     { 
+       for (int j = 1; j <= sum; j++) 
+       { 
+         if(j<set[i-1]) 
+         subset[i][j] = subset[i-1][j]; 
+         if (j >= set[i-1]) 
+           subset[i][j] = subset[i-1][j] ||  
+                                 subset[i - 1][j-set[i-1]]; 
+       } 
+     }
+     return subset[n][sum]; 
+}
+
+int main() 
+{ 
+  int set[] = {13, 34, 44, 18, 9, 23};
+  int sum = 56; 
+  int n = sizeof(set)/sizeof(set[0]); 
+  if (isSubsetSum(set, n, sum) == true) 
+     cout<<"Found a subset with given sum"<<endl; 
+  else
+     cout<<"No subset with given sum"<<endl; 
+  return 0; 
+}