Added Print The Longest Common Subsequence under classical_algorithms/c++/

Author: srajantiwari

classical_algorithms/c++/longestCommonSubsequencePrinting.cpp

@@ -0,0 +1,49 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+int main(){
+    // take input
+    string s,t;
+    cin>>s>>t;
+
+    int sLength = s.length();
+    int tLength = t.length();
+
+    // create dp table
+    int dp[sLength][tLength];
+    memset(dp, 0, sizeof dp);
+    for(int i=0;i<sLength;i++){
+        for(int j=0;j<tLength;j++){
+            // if the characters are same
+            if(s[i] == t[j])
+                dp[i][j] = ((i>0 && j>0) ? dp[i-1][j-1] : 0) + 1;
+            // if characters are not same
+            // choose the largest common subsequence
+            // which could be made with string s[0..i-1] and t[0..j-1]
+            else
+                dp[i][j] = max(((i>0) ? dp[i-1][j] : 0), ((j>0) ? dp[i][j-1] : 0));
+        }
+    }
+
+    // now run a backward loop
+    // from bottom right corner to the top left corner
+    string answer="";
+    int i = sLength-1, j = tLength-1;
+    while(i>=0 && j>=0){
+        // you have chosen the common character
+        // thus should have come to the current cell from top left diagonal direction
+        // so move in opposite direction of that
+        if(dp[i][j] == (((i>0 && j>0) ? dp[i-1][j-1] : 0) + 1) && s[i] == t[j])
+            answer+=s[i], i--, j--;
+        else if(i>0 && j>0 && dp[i-1][j] > dp[i][j-1])
+            i--;
+        else if(i>0 && j>0 && dp[i-1][j] < dp[i][j-1])
+            j--;
+        else{
+            if(i>j)i--;
+            else j--;
+        }
+    }
+    reverse(answer.begin(), answer.end());
+    cout<<answer;
+}