DP: Longest Common Subsequence

Cpp/Dynamic Programming/longest_common_subsequence.cpp

@@ -0,0 +1,68 @@
+#include <algorithm>
+#include <iostream>
+#include <vector>
+using namespace std;
+
+int lcs(int i, int j, string &s, string &t, vector<vector<int>> &dp)
+{
+  if (i < 0 || j < 0)
+    return 0;
+  if (dp[i][j] != -1)
+    return dp[i][j];
+
+  if (s[i - 1] == t[j - 1])
+    return dp[i][j] = 1 + lcs(i - 1, j - 1, s, t, dp);
+  else
+    return dp[i][j] = max(lcs(i - 1, j, s, t, dp), lcs(i, j - 1, s, t, dp));
+}
+
+int lcsfunCall(string s, string t)
+{
+  int n = s.size();
+  int m = t.size();
+  vector<vector<int>> dp(n, vector<int>(m, -1));
+  return lcs(n, m, s, t, dp);
+}
+
+int lcsTabultion(string s, string t)
+{
+  int n = s.size();
+  int m = t.size();
+  vector<vector<int>> dp(n, vector<int>(m, 0));
+  for (int i = 0; i < n; i++)
+    dp[i][0] = 0;
+  for (int j = 0; j < m; j++)
+    dp[0][j] = 0;
+  for (int i = 1; i < n; i++)
+  {
+    for (int j = 1; j < m; j++)
+    {
+      if (s[i - 1] == t[j - 1])
+        dp[i][j] = 1 + dp[i - 1][j - 1];
+      else
+        dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);
+    }
+  }
+  return dp[n][m];
+}
+
+int lcsSpaceOptimization(string s, string t)
+{
+  int n = s.size();
+  int m = t.size();
+  vector<int> cur(m + 1, 0), prev(m + 1, 0);
+  for (int j = 0; j < m; j++)
+    prev[j] = 0;
+  for (int i = 1; i < n; i++)
+  {
+    for (int j = 1; j < m; j++)
+    {
+      if (s[i - 1] == t[j - 1])
+        cur[j] = 1 + prev[j - 1];
+      else
+        cur[j] = max(prev[j], prev[j - 1]);
+    }
+    prev = cur;
+  }
+  return prev[m];
+}