CF597C Subsequences 树状数组 + 动态规划

设$f(i, j)$表示以$i$结尾的，长为$j$的上升子序列的数量

转移时用树状数组维护即可

复杂度为$O(kn \log n)$

 

注：特判0

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
namespace remoon {
    #define ri register int
    #define ll long long
    #define tpr template <typename ra>
    #define rep(iu, st, ed) for(ri iu = st; iu <= ed; iu ++)
    #define drep(iu, ed, st) for(ri iu = ed; iu >= st; iu --)    
    #define gc getchar
    inline int read() {
        int p = 0, w = 1; char c = gc();
        while(c > '9' || c < '0') { if(c == '-') w = -1; c = gc(); }
        while(c >= '0' && c <= '9') p = p * 10 + c - '0', c = gc();
        return p * w;
    }
    int wr[50], rw;
    #define pc(iw) putchar(iw)
    tpr inline void write(ra o, char c = '\n') {
        if(!o) pc('0');
        if(o < 0) o = -o, pc('-');
        while(o) wr[++ rw] = o % 10, o /= 10;
        while(rw) pc(wr[rw --] + '0');
        pc(c);
    }
}
using namespace std;
using namespace remoon;

#define sid 100050

int n, k, a[sid];
ll t[sid][12];

inline void upd(int o, ll v, int k) {
    for(ri i = o; i <= n + 1; i += i & (-i))
        t[i][k] += v;
}

inline ll qry(int o, int k) {
    ll ret = 0;
    for(ri i = o; i; i -= i & (-i))
        ret += t[i][k];
    return ret;
}

inline void DP() {
    ll ans = 0;
    if(k == 0) ans = 1;
    rep(i, 1, n) {
        upd(a[i], 1, 1);
        rep(j, 2, k + 1) {
            ll S = qry(a[i] - 1, j - 1);
            if(j == k + 1) { ans += S; break; } 
            upd(a[i], S, j);
        }
    }
    write(ans);
}

int main() {
    n = read(); k = read();
    rep(i, 1, n) a[i] = read() + 1;
    DP();
    return 0;
}