codeforces-597C-Subsequences【树状数组】

597C-Subsequences

                time limit per test1 second memory limit per test256 megabytes

For the given sequence with n different elements find the number of increasing subsequences with k + 1 elements. It is guaranteed that the answer is not greater than 8·1018.

Input
First line contain two integer values n and k (1 ≤ n ≤ 105, 0 ≤ k ≤ 10) — the length of sequence and the number of elements in increasing subsequences.

Next n lines contains one integer ai (1 ≤ ai ≤ n) each — elements of sequence. All values ai are different.

Output
Print one integer — the answer to the problem.

input
5 2
1
2
3
5
4
output
7

题目链接：cf-597C

题目大意：从1~n有n个数组，给出这n个数字的排列次序，问求长度为k+1的最长上升子序列有多少个。

题目思路：这道题类似于2015-CCPC的一道题目。HDU-5542题解

以下是代码：

#include <vector>
#include <map>
#include <set>
#include <algorithm>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <string>
#include <cstring>
using namespace std;
#define ll long long
#define lowbit(x) ((x) & -(x))
ll num[100010];
ll dp[200010][12];
ll b[100010];
int n,m;
ll sum(ll x,ll y)   //计算y长度的子序列，前x项有多少种情况的和
{
    ll ret = 0;
    while(x > 0)
    {
        ret = (ret + dp[x][y]);
        x -= lowbit(x);
    }
    return ret;
}
void add(ll x,ll y,ll d)  //更新x及以上长度，能取到的y的值为d
{
    while(x <= n)
    {
        dp[x][y] = (dp[x][y] + d);
        x += lowbit(x);
    }
}
int main(){
    while(scanf("%d%d",&n,&m) != EOF)
    {
        m += 1;
        memset(dp,0,sizeof(dp));
        for (int i = 1; i <= n; i++)
        {
            scanf("%lld",&num[i]);
        }
        for (int i = 1; i <= n; i++)
        {
            for (int j = 1; j <= min(i+1,m); j++)
            {
                if (j == 1) add(num[i],1,1);
                else
                {
                    ll temp = sum(num[i] - 1,j - 1);
                    add(num[i],j,temp);
                }
            }
        }
        printf("%lld\n",sum(n,m));
    }
    return 0;
}