title: Space Optimized Solution Lcs
signature: function spaceOptimizedSolutionLcs($x, $y) {
test_code: <?php
  
  
  // SOLUTION CODE 
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  function validateSolution($actual, $expected){
      return serialize($actual) == serialize($expected);
  }
  
  function driver($x, $y, $expected){
      try{
        if (validateSolution(PLACEHOLDER_FN_NAME($x, $y), $expected)){
          return "PASSED";
        }
        return "FAILED";
      }
      catch (Exception $exception_obj) {
        return get_class($exception_obj);
      }
  }
  
  function main(){
      printf("TEST-0...%s\n",driver(
        "YNpjSv", "qtUkJn", 
        0));
      
      printf("TEST-1...%s\n",driver(
        "736519", "07592", 
        2));
      
      printf("TEST-2...%s\n",driver(
        "11010000100010", "0", 
        1));
      
      printf("TEST-3...%s\n",driver(
        "v ", "qGBQT", 
        0));
      
      printf("TEST-4...%s\n",driver(
        "8311172", "157219329531", 
        3));
      
      printf("TEST-5...%s\n",driver(
        "100011101011", "1000001111", 
        7));
      
      printf("TEST-6...%s\n",driver(
        "u", "YzkubTqLhP", 
        0));
      
      printf("TEST-7...%s\n",driver(
        "3943042", "3859", 
        1));
      
      printf("TEST-8...%s\n",driver(
        "101", "00010000101010", 
        2));
      
      printf("TEST-9...%s\n",driver(
        "MpbfF OsizevaM", "WgsFGaQwtp", 
        2));
      
  }
  
  main();
  ?>
source_py: def space_optimized_solution_lcs(X, Y):
      m = len(X)
      n = len(Y)
      L = [[0 for i in range((n + 1))] for j in range(2)]
      bi = bool
      for i in range(m):
          bi = (i & 1)
          for j in range((n + 1)):
              if ((i == 0) or (j == 0)):
                  L[bi][j] = 0
              elif (X[i] == Y[(j - 1)]):
                  L[bi][j] = (L[(1 - bi)][(j - 1)] + 1)
              else:
                  L[bi][j] = max(L[(1 - bi)][j], L[bi][(j - 1)])
      return L[bi][n]
source_cpp: int space_optimized_solution_lcs(string & X, string & Y) {
    int m = X . length ( ), n = Y . length ( );
    int L [ 2 ] [ n + 1 ];
    bool bi;
    for ( int i = 0;
    i <= m;
    i ++ ) {
      bi = i & 1;
      for ( int j = 0;
      j <= n;
      j ++ ) {
        if ( i == 0 || j == 0 ) L [ bi ] [ j ] = 0;
        else if ( X [ i - 1 ] == Y [ j - 1 ] ) L [ bi ] [ j ] = L [ 1 - bi ] [ j - 1 ] + 1;
        else L [ bi ] [ j ] = max ( L [ 1 - bi ] [ j ], L [ bi ] [ j - 1 ] );
      }
    }
    return L [ bi ] [ n ];
  }