From c7b69429c1218d9844b4bc9d46c0b83cd666c564 Mon Sep 17 00:00:00 2001
From: Nikhil Arora <nikhilarora068@gmail.com>
Date: Tue, 2 Oct 2018 01:05:40 +0530
Subject: [PATCH] added knight tour to backtracking and longest common string
 to dynamic

---
 Backtracking/knight-tour.cpp                  | 59 +++++++++++++++++
 Dynamic Programming/longest_common_string.cpp | 65 +++++++++++++++++++
 2 files changed, 124 insertions(+)
 create mode 100644 Backtracking/knight-tour.cpp
 create mode 100644 Dynamic Programming/longest_common_string.cpp

diff --git a/Backtracking/knight-tour.cpp b/Backtracking/knight-tour.cpp
new file mode 100644
index 000000000..978a2d34b
--- /dev/null
+++ b/Backtracking/knight-tour.cpp
@@ -0,0 +1,59 @@
+#include<bits/stdc++.h>
+# define n 8
+using namespace std;
+bool issafe(int x,int y,int sol[n][n])
+{
+    return (x<n && x>=0 && y<n && y>=0 && sol[x][y]==-1);
+
+}
+bool solve(int x,int y, int mov, int sol[n][n], int xmov[n], int ymov[n])
+{
+    int k,xnext,ynext;
+
+    if(mov == n*n)
+        return true;
+
+    for(k=0;k<8;k++)
+    {
+        xnext=x+xmov[k];
+        ynext=y+ymov[k];
+
+        if(issafe(xnext,ynext,sol))
+            {
+                sol[xnext][ynext]=mov;
+
+                if(solve(xnext,ynext,mov+1,sol,xmov,ymov)==true)
+                    return true;
+                else
+                    sol[xnext][ynext]=-1;
+            }
+    }
+    return false;
+}
+int main()
+{
+    //initialize();
+
+    int sol[n][n];
+    int i,j;
+    for(i=0;i<n;i++)
+        for(j=0;j<n;j++)
+            sol[i][j]=-1;
+
+    int xmov[8] = {  2, 1, -1, -2, -2, -1,  1,  2 };
+    int ymov[8] = {  1, 2,  2,  1, -1, -2, -2, -1 };
+    sol[0][0]=0;
+
+    bool flag=solve(0,0,1,sol,xmov,ymov);
+    if(flag==false)
+        cout<<"solution doesnot exist \n";
+    else
+    {
+        for(i=0;i<n;i++)
+        {
+            for(j=0;j<n;j++)
+                cout<<sol[i][j]<<"  ";
+            cout<<"\n";
+        }
+    }
+}
diff --git a/Dynamic Programming/longest_common_string.cpp b/Dynamic Programming/longest_common_string.cpp
new file mode 100644
index 000000000..e18b9eb01
--- /dev/null
+++ b/Dynamic Programming/longest_common_string.cpp	
@@ -0,0 +1,65 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+int max(int a,int b)
+{
+    return (a > b) ? a : b;
+}
+
+int main()
+{
+    char str1[]="DEFBCD";
+    char str2[]="ABDEFJ";
+    int i,j,k;
+    int n=strlen(str1)+1;
+    int m=strlen(str2)+1;
+    //cout<<n<<" "<<m<<"\n";
+    int a[m][n];
+
+    for(i=0;i<m;i++)
+    {
+        for(j=0;j<n;j++)
+        {
+            if(i==0 || j==0)
+                a[i][j]=0;
+
+            else if(str1[i-1] == str2[j-1])
+                    a[i][j]=a[i-1][j-1]+1;
+
+            else
+                a[i][j]=0;
+        }
+    }
+
+
+/*for(i=0;i<m;i++)
+    {
+        for(j=0;j<n;j++)
+            cout<<a[i][j]<<" ";
+        cout<<"\n";
+    }*/
+
+
+int ma=-1;
+int indi,indj;
+for(i=0;i<m;i++)
+    {
+        for(j=0;j<n;j++)
+        {
+            if(a[i][j]>ma)
+            {
+                ma=a[i][j];
+                indi=i;
+                indj=j;
+            }
+        }
+    }
+
+    cout<<str1<<"\n";
+    cout<<str2<<"\n";
+
+    cout<<"longest string size = "<<ma/*<<" "<<indi<<" "<<indj*/<<"\n";
+    for(i=indi-3;i<indi;i++)
+        cout<<str1[i];
+    cout<<"\n";
+}