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| 1 | /* | |
| 2 | Longest Non-Decreasing Subsequence | |
| 3 | Vremenska slozenost: O(N*logN) | |
| 4 | Memorija: O(N) | |
| 5 | */ | |
| 6 | ||
| 7 | #include <bits/stdc++.h> | |
| 8 | using namespace std; | |
| 9 | ||
| 10 | const int N=1e5+10; | |
| 11 | ||
| 12 | struct Node | |
| 13 | {
| |
| 14 | int parent; | |
| 15 | Node() | |
| 16 | {
| |
| 17 | parent=-1; | |
| 18 | } | |
| 19 | } g[N]; //graf (stablo) koji sluzi za rekonstrukciju LISa | |
| 20 | ||
| 21 | int n, a[N], dp[N], lis; // dp[i] <==> idx najmanjeg broja kom je LIS duzine i | |
| 22 | vector<int> sol; //rekonstruisan LIS | |
| 23 | ||
| 24 | int bs (int x, int bound) //hocu broj X da stavim na postojeci LIS duzine RET | |
| 25 | {
| |
| 26 | - | int l=0, r=bound, mid, ret=0; |
| 26 | + | int l=1, r=bound, mid, ret=0; |
| 27 | while (l<=r) | |
| 28 | {
| |
| 29 | mid=l+(r-l)/2; | |
| 30 | if (dp[mid]==-1 || a[dp[mid]]>x) r=mid-1; | |
| 31 | else | |
| 32 | {
| |
| 33 | ret=mid; | |
| 34 | l=mid+1; | |
| 35 | } | |
| 36 | } | |
| 37 | return ret+1; //novi LIS ce biti duzine RET+1 | |
| 38 | } | |
| 39 | ||
| 40 | void dfs (int v) | |
| 41 | {
| |
| 42 | sol.push_back(v); | |
| 43 | if (g[v].parent==-1) return; | |
| 44 | dfs (g[v].parent); | |
| 45 | } | |
| 46 | ||
| 47 | void reconstruct () | |
| 48 | {
| |
| 49 | dfs (dp[lis]); | |
| 50 | reverse (sol.begin(), sol.end()); //tehnicki suvisno | |
| 51 | } | |
| 52 | ||
| 53 | int main() | |
| 54 | {
| |
| 55 | scanf ("%d", &n);
| |
| 56 | memset (dp, -1, sizeof dp); | |
| 57 | ||
| 58 | for (int i=1;i<=n;i++) | |
| 59 | {
| |
| 60 | scanf ("%d", &a[i]);
| |
| 61 | ||
| 62 | int idx=bs(a[i], i-1); | |
| 63 | lis=max(lis, idx); | |
| 64 | ||
| 65 | if (dp[idx]==-1 || a[dp[idx]]>a[i]) | |
| 66 | {
| |
| 67 | dp[idx]=i; | |
| 68 | if (idx>1) g[i].parent=dp[idx-1]; //koja pozicija je u LISu pre i | |
| 69 | } | |
| 70 | } | |
| 71 | ||
| 72 | reconstruct(); | |
| 73 | ||
| 74 | printf ("%d\n", lis);
| |
| 75 | for (int i=0;i<lis;i++) printf ("%d ", a[sol[i]]);
| |
| 76 | ||
| 77 | return 0; | |
| 78 | } |