|
| 1 | +// Dynamic programming solution |
| 2 | +#include <bits/stdc++.h> |
| 3 | +#include <ext/rope> |
| 4 | +using namespace std; |
| 5 | +using namespace __gnu_cxx; |
| 6 | + |
| 7 | +using ld = long double; |
| 8 | +using llint = long long; |
| 9 | +using ullint = unsigned long long; |
| 10 | +using pii = pair <int,int>; |
| 11 | +using pcc = pair <char,char>; |
| 12 | +using pss = pair <string,string>; |
| 13 | +using vi = vector <int>; |
| 14 | +using vb = vector <bool>; |
| 15 | +using vii = vi::iterator; |
| 16 | + |
| 17 | +#define INF (1<<30) |
| 18 | +#define MOD 1000000007 |
| 19 | +#define mp make_pair |
| 20 | +#define mt make_tuple |
| 21 | +#define all(c) c.begin(), c.end() |
| 22 | +#define ms(name,val) memset(name, val, sizeof name) |
| 23 | +#define np nullptr |
| 24 | + |
| 25 | + |
| 26 | +int n; |
| 27 | +string s; |
| 28 | +vector <vi> DP; |
| 29 | + |
| 30 | +void printLPS() |
| 31 | +{ |
| 32 | + string seq; |
| 33 | + int i = 0, j = n-1; |
| 34 | + |
| 35 | + while (i <= j) |
| 36 | + { |
| 37 | + if (s[i] == s[j]) |
| 38 | + { |
| 39 | + seq += s[j]; |
| 40 | + ++i, --j; |
| 41 | + } |
| 42 | + else |
| 43 | + { |
| 44 | + if (DP[i][j-1] > DP[i+1][j]) |
| 45 | + --j; |
| 46 | + else |
| 47 | + ++i; |
| 48 | + } |
| 49 | + } |
| 50 | + |
| 51 | + int m = seq.size(); |
| 52 | + |
| 53 | + if (DP[0][n-1] & 1) |
| 54 | + { |
| 55 | + if (m == 1) |
| 56 | + cout << seq << '\n'; |
| 57 | + else |
| 58 | + { |
| 59 | + string add = string(1, seq[m-1]); |
| 60 | + seq.pop_back(); |
| 61 | + string rseq = seq; |
| 62 | + reverse(all(rseq)); |
| 63 | + cout << seq << add << rseq << '\n'; |
| 64 | + } |
| 65 | + } |
| 66 | + else |
| 67 | + { |
| 68 | + string rseq = seq; |
| 69 | + reverse(all(rseq)); |
| 70 | + cout << seq << rseq << '\n'; |
| 71 | + } |
| 72 | +} |
| 73 | + |
| 74 | +int findLPS() |
| 75 | +{ |
| 76 | + n = s.size(); |
| 77 | + DP.resize(n); |
| 78 | + |
| 79 | + for (int t1 = 0; t1 < n; ++t1) |
| 80 | + { |
| 81 | + DP[t1].resize(n); |
| 82 | + DP[t1][t1] = 1; |
| 83 | + } |
| 84 | + |
| 85 | + for (int topCol = 1; topCol < n; ++topCol) |
| 86 | + { |
| 87 | + for (int i = 0, j = topCol; j < n; ++i, ++j) |
| 88 | + { |
| 89 | + if (s[i] == s[j]) |
| 90 | + { |
| 91 | + DP[i][j] = 2; // maximal if len of sequence is 2 |
| 92 | + if (j > i+1) DP[i][j] += DP[i+1][j-1]; |
| 93 | + } |
| 94 | + else DP[i][j] = max(DP[i][j-1], DP[i+1][j]); |
| 95 | + // maximum by: |
| 96 | + // 1) ignoring letter s[i] |
| 97 | + // 2) ignoring letter s[j] |
| 98 | + } |
| 99 | + } |
| 100 | + |
| 101 | + return DP[0][n-1]; |
| 102 | +} |
| 103 | + |
| 104 | +int main() |
| 105 | +{ |
| 106 | + ios_base::sync_with_stdio(0); |
| 107 | + //cin.tie(0); |
| 108 | + |
| 109 | + cin >> s; |
| 110 | + cout << findLPS() << '\n'; |
| 111 | + printLPS(); |
| 112 | + |
| 113 | + |
| 114 | + |
| 115 | + return 0; |
| 116 | +} |
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