HDU5542-The Battle of Chibi

The Battle of Chibi

                                                                             Time Limit: 6000/4000 MS (Java/Others)    Memory Limit: 65535/65535 K (Java/Others)
                                                                                                        Total Submission(s): 1573    Accepted Submission(s): 553

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≤103)  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.

   
    
  

 

Source

The 2015 China Collegiate Programming Contest

 

Recommend

wange2014

 

题意：给出n个数，问长度为k的子序列有多少

解题思路：dp+树状数组维护

#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>
#include <cmath>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <vector>
#include <bitset>

using namespace std;

#define LL long long
const int INF = 0x3f3f3f3f3f;
const int mod = 1000000007;

int n, k, m;
int a[1005],b[1005];
int x[1005][1005];
int dp[1005][1005];

int lowbit(int x)
{
	return x&-x;
}

int getsum(int xx, int kk)
{
	int sum = 0;
	while (xx>0)
	{
		sum += x[xx][kk];
		xx -= lowbit(xx);
		sum %= mod;
	}
	return sum;
}

void add(int xx, int kk, int val)
{
	while (xx <= m)
	{
		x[xx][kk] += val;
		x[xx][kk] %= mod;
		xx += lowbit(xx);
	}
}

int main()
{
	int t, cas = 0;
	scanf("%d", &t);
	while (t--)
	{
		scanf("%d%d", &n, &k);
		printf("Case #%d: ", ++cas);
		for (int i = 1; i <= n; i++) scanf("%d", &a[i]), b[i] = a[i];
		sort(a + 1, a + 1 + n);
		m = unique(a + 1, a + 1 + n) - a;
		for (int i = 1; i <= n; i++)
			b[i] = lower_bound(a + 1, a + 1 + m, b[i]) - a;
		memset(x, 0, sizeof x);
		memset(dp, 0, sizeof dp);
		for (int i = 1; i <= n; i++)
		{
			dp[i][1] = 1;
			add(b[i], 1, 1);
			for (int j = 2; j <= k; j++)
			{
				dp[i][j] += getsum(b[i] - 1, j - 1);
				add(b[i], j, dp[i][j]);
			}
		}
		int sum = 0;
		for (int i = 1; i <= n; i++)
			sum += dp[i][k], sum %= mod;
		printf("%d\n", sum);
	}
	return 0;
}