added longest common subsequence algo

src/algorithms/dynamic_programming/lcs.h

@@ -0,0 +1,46 @@
+#ifndef LCS_H
+#define LCS_H
+
+#ifdef __cplusplus
+#include <iostream>
+#include <string>
+#endif
+
+int lcs(std::string a, std::string b) {
+  int m = a.length(), n = b.length();
+  int res[m + 1][n + 1];
+  int trace[20][20];
+
+  for (int i = 0; i < m + 1; i++) {
+    for (int j = 0; j < n + 1; j++) {
+      res[i][j] = 0;
+      trace[i][j] = 0;
+    }
+  }
+
+  for (int i = 0; i < m + 1; ++i) {
+    for (int j = 0; j < n + 1; ++j) {
+      if (i == 0 || j == 0) {
+        res[i][j] = 0;
+        trace[i][j] = 0;
+      }
+
+      else if (a[i - 1] == b[j - 1]) {
+        res[i][j] = 1 + res[i - 1][j - 1];
+        trace[i][j] = 1;
+
+      } else {
+        if (res[i - 1][j] > res[i][j - 1]) {
+          res[i][j] = res[i - 1][j];
+          trace[i][j] = 2;
+        } else {
+          res[i][j] = res[i][j - 1];
+          trace[i][j] = 3;
+        }
+      }
+    }
+  }
+  return res[m][n];
+}
+
+#endif

tests/algorithms/dynamic_programming/lcs.cc

@@ -0,0 +1,11 @@
+#define CATCH_CONFIG_MAIN
+#include "../../../src/algorithms/dynamic_programming/lcs.h"
+#include "../../catch2/catch.hpp"
+
+TEST_CASE("testing longest common subsequence") {
+  std::string a = "AGGTAB", b = "GXTXAYB";
+  REQUIRE(lcs(a, b) == 4);
+  a = "BD";
+  b = "ABCD";
+  REQUIRE(lcs(a, b) == 2);
+}