title: Longest Palindrome Subsequence Space
signature: pub fn longest_palindrome_subsequence_space(s: String) -> i32 {
test_code: use std::collections::HashMap;
  use std::collections::HashSet;
  use std::cmp::*;
  use std::collections::*;
  use std::fmt::*; 
  
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  pub fn validate_solution(actual: i32, expected: i32)->bool{
  return actual==expected
  }
  pub fn driver(s: String, expected: i32)->String{
      if validate_solution(PLACEHOLDER_FN_NAME(s), expected) {
        return "PASSED".to_string();
      };
      return "FAILED".to_string();
  
  }
  
  fn main() {
      println!("TEST-0...{}", driver(
        " E".to_string(), 
        1
      ));
      
      println!("TEST-1...{}", driver(
        "0845591950".to_string(), 
        7
      ));
      
      println!("TEST-2...{}", driver(
        "00101011".to_string(), 
        5
      ));
      
      println!("TEST-3...{}", driver(
        "pLSvlwrACvFaoT".to_string(), 
        3
      ));
      
      println!("TEST-4...{}", driver(
        "7246".to_string(), 
        1
      ));
      
      println!("TEST-5...{}", driver(
        "1010101100000".to_string(), 
        8
      ));
      
      println!("TEST-6...{}", driver(
        "obPkcLSFp".to_string(), 
        1
      ));
      
      println!("TEST-7...{}", driver(
        "914757557818".to_string(), 
        7
      ));
      
      println!("TEST-8...{}", driver(
        "1".to_string(), 
        1
      ));
      
      println!("TEST-9...{}", driver(
        "PKvUWIQ".to_string(), 
        1
      ));
      
  }
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 ];
  }