chore(CPlusPlus): add longest common subsequence and topological sort (#388)

Co-authored-by: Ujjwal <75884061+UG-SEP@users.noreply.github.com>

algorithms/CPlusPlus/Dynamic-Programming/longest-common-subsequence.cpp

@@ -0,0 +1,88 @@
+/*
+Printing longest common subseqeunce from 2 subsequences using dp bottom-up approach
+*/
+
+#include<bits/stdc++.h>
+
+using namespace std;
+
+void longestCommonSubsequence(vector < int > a, vector < int > b) {
+  int n = a.size();
+  int m = b.size();
+  int i, j;
+  vector < vector < int >> dp(n + 1, vector < int > (m + 1, 0)); //creating lookup table to keep track of subsequnces 
+  vector < int > result; //result vector
+  for (i = 1; i <= n; i++) {
+    for (j = 1; j <= m; j++) //iterating through all subsequences, if common then increment value of dp[i][j] else consider max from previous
+    {
+      if (a[i - 1] == b[j - 1]) {
+        dp[i][j] = dp[i - 1][j - 1] + 1;
+      } else {
+        dp[i][j] = max(dp[i][j - 1], dp[i - 1][j]);
+      }
+    }
+  }
+  i = n, j = m;
+
+  while (i > 0 && j > 0) { //traversing dp vector and finding the same elements in both to print result
+    if (a[i - 1] == b[j - 1]) {
+      result.push_back(a[i - 1]);
+      i--;
+      j--;
+    } else if (dp[i][j - 1] > dp[i - 1][j]) {
+      j--;
+    } else
+      i--;
+
+  }
+
+  cout << "Length of lcs " << result.size() << '\n';
+  reverse(result.begin(), result.end()); //reversing to get correct order
+  cout << "\nLongest common subsequence ";
+  for (auto it: result) {
+    cout << it;
+  }
+  cout << "\n";
+}
+
+int main() {
+
+  int n, m;
+  cout << "\nEnter no of elements in first sequence"; //Input and output
+  cin >> n;
+  cout << "\nEnter no of elements in second sequence";
+  cin >> m;
+  vector < int > a(n);
+  vector < int > b(m);
+  cout << "\nEnter elements in first sequence\n";
+  for (int i = 0; i < n; i++) {
+    cin >> a[i];
+  }
+  cout << "\nEnter elements in second sequence\n";
+  for (int i = 0; i < m; i++) {
+    cin >> b[i];
+  }
+
+  longestCommonSubsequence(a, b);
+
+  return 0;
+}
+
+/*
+Time and space complexity for subsequence-O(m*n)
+
+SAMPLE INPUT-
+Enter no of elements in first sequence5
+
+Enter no of elements in second sequence3
+
+Enter elements in first sequence
+1 2 3 4 5
+
+Enter elements in second sequence
+1 3 4
+Length of lcs 3
+
+Longest common subsequence 134
+
+*/

algorithms/CPlusPlus/README.md

@@ -12,6 +12,11 @@
 8. [Sorted-Rotated Search Array](Arrays/search-sorted-rotated.cpp)
 9. [Fractional Knapsack](Arrays/fractional-knapsack.cpp)
 
+## Dynamic-Programming
+
+1. [Longest Common Subsequence](Dynamic-Programming/longest-common-subsequence.cpp)
+
+
 ## Graphs
 
 1. [Bellman Ford Algorithm](Graphs/bellmam-ford.cpp)