From dc44631a7ae94734d046aa48c0f8bdd3d4d77c61 Mon Sep 17 00:00:00 2001
From: Rohit Kulkarni <rohitkul247@gmail.com>
Date: Tue, 6 Oct 2020 22:02:36 +0530
Subject: [PATCH] Implemented longest common subsequence in C++

---
 .../Longest_Common_Subsequence.cpp            | 69 +++++++++++++++++++
 1 file changed, 69 insertions(+)
 create mode 100644 Dynamic-Programming/Longest_Common_Subsequence.cpp

diff --git a/Dynamic-Programming/Longest_Common_Subsequence.cpp b/Dynamic-Programming/Longest_Common_Subsequence.cpp
new file mode 100644
index 0000000..4ebebd9
--- /dev/null
+++ b/Dynamic-Programming/Longest_Common_Subsequence.cpp
@@ -0,0 +1,69 @@
+/*
+Name: Longest Common Subsequence
+Time Complexity: O(n*m) where n,m is the length of the strings
+
+Given two sequences, find the length of longest subsequence present in both of them. This code uses the 
+memoization technique to determine the solution*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#define ll long long
+
+typedef pair<int, int> pairii;
+typedef vector<int> veci;
+typedef set<int> seti;
+typedef unordered_set<int> unseti;
+
+const ll MAX1 = 105;
+
+ll dp[MAX1][MAX1];
+
+ll lcs(string s1, string s2, ll n, ll m)
+{
+    if (n == 0 || m == 0)
+        return 0;
+    if (dp[n][m] != -1)
+        return dp[n][m];
+    else
+    {
+        if (s1[n - 1] == s2[m - 1])
+            return dp[n][m] = (1 + lcs(s1, s2, n - 1, m - 1));
+        else
+        {
+            return dp[n][m] = max(lcs(s1, s2, n - 1, m), lcs(s1, s2, n, m - 1));
+        }
+    }
+}
+
+void solve()
+{
+    ll n, m, x, temp = 0, rem = 0, sum = 0, sum1 = 0, sum2 = 0, cnt = 0, in, i, j, k, flag = 1;
+    string s, s1, s2;
+    veci v, e, o, p;
+    cin >> n >> m;
+    cin >> s1 >> s2;
+    memset(dp, -1, sizeof(dp));
+    ll ans = lcs(s1, s2, n, m);
+    cout << ans << "\n";
+}
+
+int main()
+{
+
+    /*#ifndef ONLINE_JUDGE
+      freopen("input.txt", "r", stdin);
+      freopen("output.txt", "w", stdout);
+    #endif*/
+
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+    cout.tie(NULL);
+
+    ll t;
+    cin >> t;
+
+    while (t--)
+        solve();
+    return 0;
+}
\ No newline at end of file