diff --git a/Backtracking/Graph Coloring.cpp b/Backtracking/Graph Coloring.cpp
new file mode 100644
index 000000000..fdf50b288
--- /dev/null
+++ b/Backtracking/Graph Coloring.cpp	
@@ -0,0 +1,81 @@
+#include<stdio.h>
+ 
+// Number of vertices in the graph
+#define V 4
+ 
+void printSolution(int color[]);
+ 
+/* A utility function to check if the current color assignment
+   is safe for vertex v */
+bool isSafe (int v, bool graph[V][V], int color[], int c)
+{
+    for (int i = 0; i < V; i++)
+        if (graph[v][i] && c == color[i])
+            return false;
+    return true;
+}
+ 
+/* A recursive utility function to solve m coloring problem */
+void graphColoring(bool graph[V][V], int m, int color[], int v)
+{
+    /* base case: If all vertices are assigned a color then
+       return true */
+    if (v == V){
+    	printSolution(color);
+        return;
+    }
+ 
+    /* Consider this vertex v and try different colors */
+    for (int c = 1; c <= m; c++)
+    {
+        /* Check if assignment of color c to v is fine*/
+        if (isSafe(v, graph, color, c))
+        {
+           color[v] = c;
+ 
+           /* recur to assign colors to rest of the vertices */
+           graphColoring (graph, m, color, v+1);
+            
+ 
+            /* If assigning color c doesn't lead to a solution
+               then remove it */
+           color[v] = 0;
+        }
+    }
+ 
+}
+
+/* A utility function to print solution */
+void printSolution(int color[])
+{
+    printf(" Following are the assigned colors \n");
+    for (int i = 0; i < V; i++)
+      printf(" %d ", color[i]);
+    printf("\n");
+}
+ 
+// driver program to test above function
+int main()
+{
+    /* Create following graph and test whether it is 3 colorable
+      (3)---(2)
+       |   / |
+       |  /  |
+       | /   |
+      (0)---(1)
+    */
+    bool graph[V][V] = {{0, 1, 1, 1},
+        {1, 0, 1, 0},
+        {1, 1, 0, 1},
+        {1, 0, 1, 0},
+    };
+    int m = 3; // Number of colors
+
+	int color[V];
+
+	for (int i = 0; i < V; i++)
+        color[i] = 0;
+    
+    graphColoring(graph, m, color, 0);
+    return 0;
+}
diff --git a/Backtracking/N Queens.cpp b/Backtracking/N Queens.cpp
new file mode 100644
index 000000000..f070c5803
--- /dev/null
+++ b/Backtracking/N Queens.cpp	
@@ -0,0 +1,82 @@
+#include<iostream>
+#define N 4
+using namespace std;
+
+void printSolution(int board[N][N])
+{
+    cout<<"\n";
+    for (int i = 0; i < N; i++)
+    {
+        for (int j = 0; j < N; j++)
+            cout<<""<<board[i][j];
+        cout<<"\n";
+    }
+}
+ 
+
+bool isSafe(int board[N][N], int row, int col)
+{
+    int i, j;
+ 
+    /* Check this row on left side */
+    for (i = 0; i < col; i++)
+        if (board[row][i])
+            return false;
+ 
+    /* Check upper diagonal on left side */
+    for (i=row, j=col; i>=0 && j>=0; i--, j--)
+        if (board[i][j])
+            return false;
+ 
+    /* Check lower diagonal on left side */
+    for (i=row, j=col; j>=0 && i<N; i++, j--)
+        if (board[i][j])
+            return false;
+ 
+    return true;
+}
+ 
+
+void solveNQ(int board[N][N], int col)
+{
+    
+    if (col >= N){
+        printSolution(board);
+        return;
+    }
+ 
+    /* Consider this column and try placing
+       this queen in all rows one by one */
+    for (int i = 0; i < N; i++)
+    {
+        /* Check if queen can be placed on
+          board[i][col] */
+        if ( isSafe(board, i, col) )
+        {
+            /* Place this queen in board[i][col] */
+//            cout<<"\n"<<col<<"can place"<<i;
+            board[i][col] = 1;
+ 
+            /* recur to place rest of the queens */
+            solveNQ(board, col + 1);
+                
+
+            board[i][col] = 0; // BACKTRACK
+        }
+    }
+ 
+}
+ 
+ 
+int main()
+{
+    
+   int board[N][N] = { {0, 0, 0, 0},
+       {0, 0, 0, 0},
+       {0, 0, 0, 0},
+       {0, 0, 0, 0}
+   };
+   
+	solveNQ(board, 0);
+    return 0;
+}
diff --git a/Dynamic Programming/Knapsack.cpp b/Dynamic Programming/0-1 Knapsack.cpp
similarity index 58%
rename from Dynamic Programming/Knapsack.cpp
rename to Dynamic Programming/0-1 Knapsack.cpp
index a06d042f8..4bed36fb2 100644
--- a/Dynamic Programming/Knapsack.cpp	
+++ b/Dynamic Programming/0-1 Knapsack.cpp	
@@ -1,8 +1,35 @@
 //0-1 Knapsack problem - Dynamic programming
-#include <bits/stdc++.h>
+//#include <bits/stdc++.h>
+#include<iostream>
 using namespace std;
+
+//void Print(int res[20][20], int i, int j, int capacity)
+//{
+//	if(i==0 || j==0)
+//	{
+//		return;
+//	}
+//	if(res[i-1][j]==res[i][j-1])
+//	{
+//		if(i<=capacity)
+//		{
+//			cout<<i<<" ";
+//		}
+//		
+//		Print(res, i-1, j-1, capacity-i);
+//	}
+//	else if(res[i-1][j]>res[i][j-1])
+//	{
+//		Print(res, i-1,j, capacity);
+//	}
+//	else if(res[i][j-1]>res[i-1][j])
+//	{
+//		Print(res, i,j-1, capacity);
+//	}
+//}
+
 int Knapsack(int capacity,int n,int weight[],int value[]){
-	int res[n+1][capacity+1];
+	int res[20][20];
 	for (int i = 0; i < n+1; ++i)
 	{
 		for (int j = 0; j < capacity+1; ++j)
@@ -15,9 +42,11 @@ int Knapsack(int capacity,int n,int weight[],int value[]){
 				res[i][j] = res[i-1][j];
 		}
 	}
+//	Print(res, n, capacity, capacity);
+//	cout<<"\n";
 	return res[n][capacity];
 }
-int main(int argc, char const *argv[])
+int main()
 {
 	int n;
 	cout<<"Enter number of items: ";
@@ -38,4 +67,4 @@ int main(int argc, char const *argv[])
 	cin>>capacity;
 	cout<<Knapsack(capacity,n,weight,value);
 	return 0;
-}
\ No newline at end of file
+}
diff --git a/Dynamic Programming/Longest Common Subsequence.cpp b/Dynamic Programming/Longest Common Subsequence.cpp
index 04800f223..2b0d00f9d 100644
--- a/Dynamic Programming/Longest Common Subsequence.cpp	
+++ b/Dynamic Programming/Longest Common Subsequence.cpp	
@@ -1,27 +1,75 @@
 //Longest common subsequence - Dynamic Programming
 #include <iostream>
 using namespace std;
+
+void Print(int trace[20][20], int m, int n, string a)
+{
+	if (m==0 || n==0)
+	{
+		return;
+	}
+	if (trace[m][n]==1)
+	{
+		Print(trace, m-1, n-1, a);
+		cout<<a[m-1];
+	}
+	else if(trace[m][n]==2)
+	{
+		Print(trace, m-1,n, a);
+	}
+	else if (trace[m][n]==3)
+	{
+		Print(trace, m,n-1, a);
+	}
+}
+
+
+
 int lcs(string a, string b){
 	int m = a.length(), n = b.length();
 	int res[m+1][n+1];
+	int trace[20][20];
 	for (int i = 0; i < m+1; ++i)
 	{
 		for (int j = 0; j < n+1; ++j)
 		{
 			if(i==0||j==0)
-				res[i][j] = 0;
+				{
+					res[i][j] = 0;	
+					trace[i][j]=0;
+				}
+				
 			else if(a[i-1]==b[j-1])
+			{
 				res[i][j] = 1 + res[i-1][j-1];
+				trace[i][j]=1;			// 1 means trace the matrix in upper left diagonal direction.
+			}
 			else
-				res[i][j] = max(res[i-1][j], res[i][j-1]);
+			{
+				if (res[i-1][j]>res[i][j-1])
+				{
+					res[i][j]=res[i-1][j];
+					trace[i][j]=2;		// 2 means trace the matrix in upwards direction.
+				}
+				else
+				{
+					res[i][j]=res[i][j-1];
+					trace[i][j]=3;		//  means trace the matrix in left direction.
+				}	
+			}
 		}
 	}
+	Print(trace, m, n, a);
 	return res[m][n];
 }
-int main(int argc, char const *argv[])
+
+
+
+
+int main()
 {
 	string a,b;
 	cin>>a>>b;
 	cout<<lcs(a,b);
 	return 0;
-}
\ No newline at end of file
+}
diff --git a/Greedy Algorithms/Knapsack.cpp b/Greedy Algorithms/Knapsack.cpp
index 661e5774a..41ce4cc9b 100644
--- a/Greedy Algorithms/Knapsack.cpp	
+++ b/Greedy Algorithms/Knapsack.cpp	
@@ -10,7 +10,6 @@ struct Item
 
 float profitPerUnit(Item x)
 {
-//	cout<<(float)x.profit/(float)x.weight<<"\n";
 	return (float)x.profit/(float)x.weight;
 }
 
@@ -53,13 +52,6 @@ void quickSort(Item arr[], int low, int high)
 
 
 
-// void show(Item arr[], int size)
-// {
-//     for (int i=0; i < size; i++)
-//     cout<<arr[i].weight<<"\t"<<arr[i].profit<<"\n";
-// }
-
-
 int main()
 {
 	cout<<"\nEnter the capacity of the knapsack : ";
diff --git a/Greedy Algorithms/Knapsack.exe b/Greedy Algorithms/Knapsack.exe
new file mode 100644
index 000000000..5789ed978
Binary files /dev/null and b/Greedy Algorithms/Knapsack.exe differ
diff --git a/Strassen Matrix Multiplication.cpp b/Strassen Matrix Multiplication.cpp
new file mode 100644
index 000000000..1cb398a62
--- /dev/null
+++ b/Strassen Matrix Multiplication.cpp	
@@ -0,0 +1,60 @@
+#include <iostream>
+using namespace std;
+
+Multiply(int A[][], int B[][], int n)
+{
+	if (n==2)
+	{
+		int p1= (a[0][0] + a[1][1])*(b[0][0]+b[1][1]);
+	  	int p2= (a[1][0]+a[1][1])*b[0][0];
+	 	int p3= a[0][0]*(b[0][1]-b[1][1]);
+	 	int p4= a[1][1]*(b[1][0]-b[0][0]);
+	 	int p5= (a[0][0]+a[0][1])*b[1][1];
+	 	int p6= (a[1][0]-a[0][0])*(b[0][0]+b[0][1]);
+	 	int p7= (a[0][1]-a[1][1])*(b[1][0]+b[1][1]);
+
+
+	 	int c[n][n];
+		c[0][0]=p1+p4-p5+p7;
+ 		c[0][1]=p3+p5;
+ 		c[1][0]=p2+p4;
+ 		c[1][1]=p1-p2+p3+p6;
+
+ 	 	return c[][];
+	}
+	else
+	{
+		
+	}
+
+}
+
+int main()
+{
+	int p,q,r,s;
+	cout<<"Enter the dimensions of Matrices";
+	cin>>n;
+	int A[n][n],;
+	int B[n][n],;
+	cout<<"Enter the elements of Matrix A";
+	for (int i = 0; i < n; i++)
+	{
+		for (int j = 0; j <n ; j++)
+		{
+			cin>>A[i][j];
+		}
+	}
+
+
+	cout<<"Enter the elements of Matrix B";
+	for (int i = 0; i < n; i++)
+	{
+		for (int j = 0; j <n ; j++)
+		{
+			cin>>B[i][j];
+		}
+	}
+
+	Multiply(A, B, n);
+	return 0;
+}
\ No newline at end of file