title: Longest Palindrome Subsequence Space
signature: longest_palindrome_subsequence_space <- function(s) {
test_code: 
  
  
  # SOLUTION CODE
  # ============================================
  PLACEHOLDER_CODE_BODY
  
  # TESTING CODE 
  # ============================================
  validate_solution <- function(actual, expected) {
      toString(actual)==toString(expected)
  }
  
  driver <- function(s, expected){
      if (validate_solution(PLACEHOLDER_FN_NAME(s), expected)){
          "PASSED"
      } else{
          "FAILED"
      }
  }
  
  main <- function() {
      cat(sprintf("TEST-0...%s\n",driver(
          " E", 
          1L
      )))
  
      cat(sprintf("TEST-1...%s\n",driver(
          "0845591950", 
          7L
      )))
  
      cat(sprintf("TEST-2...%s\n",driver(
          "00101011", 
          5L
      )))
  
      cat(sprintf("TEST-3...%s\n",driver(
          "pLSvlwrACvFaoT", 
          3L
      )))
  
      cat(sprintf("TEST-4...%s\n",driver(
          "7246", 
          1L
      )))
  
      cat(sprintf("TEST-5...%s\n",driver(
          "1010101100000", 
          8L
      )))
  
      cat(sprintf("TEST-6...%s\n",driver(
          "obPkcLSFp", 
          1L
      )))
  
      cat(sprintf("TEST-7...%s\n",driver(
          "914757557818", 
          7L
      )))
  
      cat(sprintf("TEST-8...%s\n",driver(
          "1", 
          1L
      )))
  
      cat(sprintf("TEST-9...%s\n",driver(
          "PKvUWIQ", 
          1L
      )))
  
  }
  
  main()
source_py: def longest_palindrome_subsequence_space(s):
      n = len(s)
      a = ([0] * n)
      for i in range((n - 1), (- 1), (- 1)):
          back_up = 0
          for j in range(i, n):
              if (j == i):
                  a[j] = 1
              elif (s[i] == s[j]):
                  temp = a[j]
                  a[j] = (back_up + 2)
                  back_up = temp
              else:
                  back_up = a[j]
                  a[j] = max(a[(j - 1)], a[j])
      return a[(n - 1)]
source_cpp: int longest_palindrome_subsequence_space(string & s) {
    int n = s . length ( );
    int a [ n ];
    for ( int i = n - 1;
    i >= 0;
    i -- ) {
      int back_up = 0;
      for ( int j = i;
      j < n;
      j ++ ) {
        if ( j == i ) a [ j ] = 1;
        else if ( s [ i ] == s [ j ] ) {
          int temp = a [ j ];
          a [ j ] = back_up + 2;
          back_up = temp;
        }
        else {
          back_up = a [ j ];
          a [ j ] = max ( a [ j - 1 ], a [ j ] );
        }
      }
    }
    return a [ n - 1 ];
  }