feat: updated LCS problem

longest-common-subsequence/src/ac.cpp

@@ -2,25 +2,50 @@
 
 using namespace std;
 
-int memo[1011][1011];
-
-int solve(string &s1, string &s2, int i = 0, int j = 0)
+int main()
 {
-   if (i == s1.size() || j == s2.size()) return 0;
-   if (memo[i][j] != - 1) return memo[i][j];
-   
-   if (s1[i] == s2[j]) {
-      return memo[i][j] = (solve(s1, s2, i + 1, j + 1) + 1);
+   int n, m;
+   cin >> n >> m;
+   string s1, s2;
+   cin >> s1 >> s2;
+
+   /*
+      let dp[i][j] represent the length of the longest common subsequence using the first i characters
+      of s1 and the first j characters of s2
+
+      if s1[i] == s2[j]
+         dp[i][j] = dp[i - 1][j - 1] + 1
+      else
+         dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
+   */
+
+   vector<vector<int>> dp(n + 1, vector<int>(m + 1, 0));
+   for (int i = 1; i <= n; i++) {
+      for (int j = 1; j <= m; j++) {
+         if (s1[i - 1] == s2[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 memo[i][j] = max(solve(s1, s2, i, j + 1), solve(s1, s2, i + 1, j));
-}
 
-int main(){
-   int n, m; cin >> n >> m;
-   string s1, s2; cin >> s1 >> s2;
-   memset(memo, -1, sizeof(memo));
-
-   cout << solve(s1, s2) << endl;
+   int row = n, col = m;
+   string sub = "";
+   while (dp[row][col]) {
+      if (s1[row - 1] == s2[col - 1]) {
+         sub = string(1, s1[row - 1]) + sub;
+         row--, col--;
+      } else if (dp[row - 1][col] > dp[row][col - 1]) {
+         row--;
+      } else {
+         col--;
+      }
+   }
+   
+   int size = dp[n][m];
+   cout << size << endl;
+   cout << sub << endl;
 
    return 0;
 }