LCS.cpp

LCS.cpp

@@ -0,0 +1,132 @@
+//LCS --> Longest common subsequence
+#include<bits/stdc++.h>
+using namespace std;
+
+// DP
+int lcs_DP(string s,string t)
+{
+    int m = s.size();
+    int n = t.size();
+
+    int **output = new int*[m+1];
+    for(int i=0;i<=m;i++)
+    {
+        output[i] = new int[n+1];
+    }
+
+    // Fill first row
+    for(int j=0;j<=n;j++)
+    {
+        output[0][j] = 0;
+    }
+
+    // Fill first column
+    for(int i=1;i<=m;i++)
+    {
+        output[i][0] = 0;
+    }
+
+    // Fill remaining cells
+    for(int i=1;i<=m;i++)
+    {
+        for(int j=1;j<=n;j++)
+        {
+            if(s[m-i]==t[n-j])
+            {
+                output[i][j] = output[i-1][j-1]+1;
+            }
+            else
+            {
+                int a = output[i-1][j];
+                int b = output[i][j-1];
+                int c = output[i-1][j-1];
+
+                output[i][j] = max(a,max(b,c));
+            }
+        }
+    }
+    return output[m][n];
+}
+
+//MEMOIZATION
+int lcs_mem(string s,string t,int **output)
+{
+    int x = s.size();
+    int y = t.size();
+    //Base Case
+    if(x==0 || y==0)
+        return 0;
+
+    //If ans already exists
+    if(output[x][y]!=-1) return output[x][y];
+
+    //Recursive call
+    int ans;
+    if(s[0]==t[0])
+    {
+        ans = 1+lcs_mem(s.substr(1),t.substr(1),output);
+    }
+    else{
+        int x = lcs_mem(s.substr(1),t,output);
+        int y = lcs_mem(s,t.substr(1),output);
+        int z = lcs_mem(s.substr(1),t.substr(1),output);
+
+        ans = max(x,max(y,z));
+    }
+    //save our ans and return
+    output[x][y] = ans;
+    return ans;
+}
+
+int lcs_mem(string s,string t)
+{
+    int x = s.size();
+    int y = t.size();
+    int **output = new int*[x+1];
+    for(int i=0;i<=x;i++)
+    {
+        output[i] = new int[y+1];
+        for(int j=0;j<=y;j++)
+        {
+            output[i][j] = -1;
+        }
+    }
+    lcs_mem(s,t,output);
+    int ans = output[x][y];
+    for(int i=0;i<=x;i++)
+    {
+        delete [] output[i];
+    }
+    delete []output;
+    return ans;
+}
+
+//BRUTE FORCE
+int lcs(string s,string t)
+{
+    //Base Case
+    if(s.size()==0 || t.size()==0)
+        return 0;
+
+    //Recursive call
+    if(s[0]==t[0])
+    {
+        return 1+lcs(s.substr(1),t.substr(1));
+    }
+    else{
+        int x = lcs(s.substr(1),t);
+        int y = lcs(s,t.substr(1));
+        int z = lcs(s.substr(1),t.substr(1));
+
+        return max(x,max(y,z));
+    }
+}
+
+int main()
+{
+    string s,t;
+    cin>>s>>t;
+    cout<<lcs(s,t)<<endl;
+    cout<<lcs_mem(s,t)<<endl;
+    cout<<lcs_DP(s,t)<<endl;
+}