title: Longest Palindrome Subsequence Space
signature: int longestPalindromeSubsequenceSpace(string s) {
test_code: #include <algorithm>
  #include <assert.h>
  #include <cstdlib>
  #include <iostream>
  #include <map>
  #include <set>
  #include <string>
  #include <tuple> 
  #include <unordered_map>
  #include <vector>
  #include <math.h>
  #include <cmath>
  #include <bits/stdc++.h>
  #include <numeric>
  #include <functional>
  
  using namespace std;
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  bool validateSolution(int actual, int expected){
      return actual == expected;
  }
  
  string driver(string s, int expected){
      try
      {
          if (validateSolution(PLACEHOLDER_FN_NAME(s), expected)){
              return "PASSED";
          }
          return "FAILED";
      }
      catch (const std::overflow_error& exception_obj)
      {
          return typeid(exception_obj).name();
      }
      catch (const std::runtime_error& exception_obj)
      {
          return typeid(exception_obj).name();
      }
      catch (const std::exception& exception_obj)
      {
          return typeid(exception_obj).name();
      }
      catch (...)
      {
          return "UNK_ERROR";
      }
  }
  
  int main() {
      string result = "";
  
      result = driver(" E", 1); 
      cout << "TEST-" << 0 << "..."
           <<  result
           << "\n";
  
      result = driver("0845591950", 7); 
      cout << "TEST-" << 1 << "..."
           <<  result
           << "\n";
  
      result = driver("00101011", 5); 
      cout << "TEST-" << 2 << "..."
           <<  result
           << "\n";
  
      result = driver("pLSvlwrACvFaoT", 3); 
      cout << "TEST-" << 3 << "..."
           <<  result
           << "\n";
  
      result = driver("7246", 1); 
      cout << "TEST-" << 4 << "..."
           <<  result
           << "\n";
  
      result = driver("1010101100000", 8); 
      cout << "TEST-" << 5 << "..."
           <<  result
           << "\n";
  
      result = driver("obPkcLSFp", 1); 
      cout << "TEST-" << 6 << "..."
           <<  result
           << "\n";
  
      result = driver("914757557818", 7); 
      cout << "TEST-" << 7 << "..."
           <<  result
           << "\n";
  
      result = driver("1", 1); 
      cout << "TEST-" << 8 << "..."
           <<  result
           << "\n";
  
      result = driver("PKvUWIQ", 1); 
      cout << "TEST-" << 9 << "..."
           <<  result
           << "\n";
  
      return 0;
  }
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 ];
  }