最长不下降子序列 O(nlogn) || 记忆化搜索

#include<stdio.h>
int a[1000] , temp[1000] ;
int n , top ;

int binary_search (int x) {
    int fir = 0 ;
    int last = top ;
    int mid ;
    while (fir <= last ) {
        mid = (fir + last) / 2 ;
        if ( x <= temp[mid] ) {
            last = mid - 1;
        }
        else {
            if (x <= temp[mid + 1] )
                return mid + 1 ;
            else
                fir = mid + 1 ;
        }
    }
}

int main () {
  //  freopen ("a.txt" ,"r" , stdin) ;
    while ( scanf ("%d" , &n ) != EOF ) {
        for (int i = 0 ; i < n ; i++ ) {
            scanf ("%d" , &a[i]) ;
        }

        top = 0 ;//目前最长不下降子序列的长度
        temp[top] = a[0] ;////temp[i]为长度为i的上升子序列末尾元素的最小值
        for (int i = 1 ; i < n ; i++ ) {
            if ( a[i] >= temp[top] ) {
                temp[++top] = a[i] ;
            }
            else {
                if ( a[i] < temp[0] ) {
                    temp[0] = a[i] ;
                }
                else {
                    temp[binary_search(a[i])] = a[i] ;
                }
            }
        }
        printf ("%d
" , top + 1) ;
    }
    return 0 ;
}

#include<stdio.h>
#include<string.h>
#include<vector>
#include<algorithm>
const int inf = 0x3f3f3f3f ;
std::vector <int> g[1000 + 10] ;
int a[1111] ;
int dp[1111] ;
int n ;

int dfs (int id , int dep )
{
    if (dp[id] != 1) return dp[id] ;
    if (id == n - 1) return dp[id] ;
    bool flag = 0 ;
    for (int i = id + 1 ; i < n ; i ++) {
        if (a[i] > a[id]) {
            g[dep].push_back (dfs ( i , dep + 1) ) ;
            flag = 1 ;
        }
    }
    if (flag) {
        int t = max_element (g[dep].begin () , g[dep].end () ) - g[dep].begin () ;
        dp[id] += g[dep][t] ;
        g[dep].clear () ;
    }
    return dp[id] ;
}

int main ()
{
   // freopen ("a.txt" , "r" , stdin ) ;
    while ( ~scanf ("%d" , &n) ) {
        memset (dp , 0 , sizeof(dp)) ;
        for (int i = 0 ; i < n ; i ++) scanf ("%d" , &a[i]) ;
        for (int i = 0 ; i < n ; i ++) dp[i] = 1 ;
        for (int i = n - 2 ; i >= 0 ; i --) { dfs (i , 0) ;  }
        int len = -inf ;
        for (int i = 0 ; i < n ; i ++) len = std::max (len , dp[i]) ;
        printf ("%d
" , len ) ;
    }
    return 0 ;
}