The Battle of Chibi HDU

Problem Description
Cao Cao made up a big army and was going to invade the whole South China. Yu Zhou was worried about it. He thought the only way to beat Cao Cao is to have a spy in Cao Cao’s army. But all generals and soldiers of Cao Cao were loyal, it’s impossible to convince any of them to betray Cao Cao.

So there is only one way left for Yu Zhou, send someone to fake surrender Cao Cao. Gai Huang was selected for this important mission. However, Cao Cao was not easy to believe others, so Gai Huang must leak some important information to Cao Cao before surrendering.

Yu Zhou discussed with Gai Huang and worked out N information to be leaked, in happening order. Each of the information was estimated to has ai value in Cao Cao’s opinion.

Actually, if you leak information with strict increasing value could accelerate making Cao Cao believe you. So Gai Huang decided to leak exact M information with strict increasing value in happening order. In other words, Gai Huang will not change the order of the N information and just select M of them. Find out how many ways Gai Huang could do this.

Input
The first line of the input gives the number of test cases, T(1≤100). T test cases follow.

Each test case begins with two numbers N(1≤N≤10^3) and M(1≤M≤N), indicating the number of information and number of information Gai Huang will select. Then N numbers in a line, the ith number ai(1≤ai≤109) indicates the value in Cao Cao’s opinion of the ith information in happening order.

Output
For each test case, output one line containing Case #x: y, where x is the test case number (starting from 1) and y is the ways Gai Huang can select the information.

The result is too large, and you need to output the result mod by 1000000007(109+7).

Sample Input
2
3 2
1 2 3
3 2
3 2 1

Sample Output
Case #1: 3
Case #2: 0
Hint
In the first cases, Gai Huang need to leak 2 information out of 3. He could leak any 2 information as all the information value are in increasing order.
In the second cases, Gai Huang has no choice as selecting any 2 information is not in increasing order.

大致题意：告诉你n个数，问你有多少个长度为m的递增子序列。

思路：和 CodeForces - 597 C. Subsequences这题差不多，只不过需要先将这n个数离散化一下，然后再用m个树状数组去优化dp

代码如下

#include<cstring> #include<cstdio> #include<iostream>   #include <algorithm>  #define ll long long int   using namespace std;const int N=1e3+5; const int mod=1e9+7;ll dp[N][N];int n,m;int f;struct node{    int value;    int ii;}num[N];int cmp(node a,node b){    return a.value<b.value;}int lowbit(int x){    return x&-x;}int sum(int x){    int s=0;    while(x>0)    {        ll ss=s+dp[x][f];        while(ss>mod) ss-=mod;//取模这样写会快一点        s=ss;//      s=(s+dp[x][f])%mod;        x=x-lowbit(x);    }    return s;}void add(int x,int date){    while(x<=n)    {        ll ss=dp[x][f]+date;        while(ss>mod) ss-=mod;        dp[x][f]=ss;//      dp[x][f]=(dp[x][f]+date)%mod;        x=x+lowbit(x);    }}int main()  {    int mark[N];    int T;    scanf("%d",&T);    for(int cas=1;cas<=T;cas++)    {        memset(dp,0,sizeof(dp));        scanf("%d%d",&n,&m);        for(int i=1;i<=n;i++)        {            scanf("%d",&num[i].value);            num[i].ii=i;        }        sort(num+1,num+1+n,cmp);//离散化         int k=-1,t=0;        for(int i=1;i<=n;i++)        {            if(num[i].value!=k)            {                ++t;                k=num[i].value;            }            mark[num[i].ii]=t;        }        for(int i=1;i<=n;i++)        {            int minn=min(i,m);//一个优化，能剪枝掉很多没用的情况            for(int j=1;j<=minn;j++)            {                int ans;                f=j;                f--;                if(f==0)                    ans=1;                else                     ans=sum(mark[i]-1);                f++;                add(mark[i],ans);            }        }        f=m;        printf("Case #%d: %d\n",cas,sum(t));    }    return 0;  }