最长不下降子序列 O(nlogn) || 记忆化搜索

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

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

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

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

用二分查找法

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

 int dfs (int id , int dep )
 {
     if (dp[id] != ) return dp[id] ;
     if (id == n - ) return dp[id] ;
     bool flag =  ;
     for (int i = id +  ; i < n ; i ++) {
         if (a[i] > a[id]) {
             g[dep].push_back (dfs ( i , dep + ) ) ;
             flag =  ;
         }
     }
     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 ,  , sizeof(dp)) ;
         for (int i =  ; i < n ; i ++) scanf ("%d" , &a[i]) ;
         for (int i =  ; i < n ; i ++) dp[i] =  ;
         for (int i = n -  ; i >=  ; i --) { dfs (i , ) ;  }
         int len = -inf ;
         for (int i =  ; i < n ; i ++) len = std::max (len , dp[i]) ;
         printf ("%d\n" , len ) ;
     }
     return  ;
 }

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