2015 Multi-University Training Contest 6 solutions BY ZJU（部分解题报告）

 

官方解题报告：http://bestcoder.hdu.edu.cn/blog/2015-multi-university-training-contest-6-solutions-by-zju/

 

 

表示很难看。。。。orz

 

1003题      链接：http://acm.hdu.edu.cn/showproblem.php?pid=5355

 

Cake

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 1138    Accepted Submission(s): 152
Special Judge

Problem Description

 

There are   m  soda and today is their birthday. The   1 -st soda has prepared   n  cakes with size   1,2,…,n . Now   1 -st soda wants to divide the cakes into   m  parts so that the total size of each part is equal.  

Note that you cannot divide a whole cake into small pieces that is each cake must be complete in the   m  parts. Each cake must belong to exact one of   m  parts.

 

 

Input

 

There are multiple test cases. The first line of input contains an integer   T , indicating the number of test cases. For each test case:

The first contains two integers   n  and   m   (1≤n≤105,2≤m≤10) , the number of cakes and the number of soda.
It is guaranteed that the total number of soda in the input doesn’t exceed 1000000. The number of test cases in the input doesn’t exceed 1000.

 

 

Output

 

For each test case, output "YES" (without the quotes) if it is possible, otherwise output "NO" in the first line.

If it is possible, then output   m  lines denoting the   m  parts. The first number   si  of   i -th line is the number of cakes in   i -th part. Then   si  numbers follow denoting the size of cakes in   i -th part. If there are multiple solutions, print any of them.

 

 

Sample Input

 

   
   
   
   

    
    
    
    4
1 2
5 3
5 2
9 3
   
   
   
   

 

 

Sample Output

 

   
   
   
   

    
    
    
    NO
YES
1 5
2 1 4
2 2 3
NO
YES
3 1 5 9
3 2 6 7
3 3 4 8
   
   
   
   

 

 

Source

 

2015 Multi-University Training Contest 6

 

 

题意：n块蛋糕（大小1--n）分给m个人，要求每个人得到蛋糕大小总和相等

 

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <vector>
#include <math.h>
#include <bitset>
#include <algorithm>
#include <climits>
using namespace std;

#define ls 2*i
#define rs 2*i+1
#define UP(i,x,y) for(i=x;i<=y;i++)
#define DOWN(i,x,y) for(i=x;i>=y;i--)
#define MEM(a,x) memset(a,x,sizeof(a))
#define W(a) while(a)
#define gcd(a,b) __gcd(a,b)
#define LL long long
#define N 100005
#define INF 0x3f3f3f3f
#define EXP 1e-8
#define rank rank1
const int mod = 1000000007;

int t,n,m;
int a[N];
int ans[15][N],tem[N],path[N],len[N];
LL sum;

int main()
{
    int i,j,k;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d%d",&n,&m);
        sum = (n+1)*n/2;
        if(sum%m)
        {
            printf("NO\n");
            continue;
        }
        sum/=m;
        MEM(tem,0);
        MEM(len,0);
        for(i = n;i>=1;i--)
        {
            for(j = 0;j<m;j++)
            {
                if(tem[j]+i<=sum)
                {
                    tem[j]+=i;
                    path[i]=j;
                    break;
                }
            }
        }
        for(i = 0;i<m;i++)
        {
            if(tem[i]!=sum)
            break;
        }
        if(i!=m)
        {
            printf("NO\n");
            continue;
        }
        for(i = 1;i<=n;i++)
        {
            k = path[i];
            ans[k][len[k]++] = i;
        }
        printf("YES\n");
        for(i = 0;i<m;i++)
        {
            printf("%d %d",len[i],ans[i][0]);
            for(j = 1;j<len[i];j++)
            {
                printf(" %d",ans[i][j]);
            }
            printf("\n");
        }
    }

    return 0;
}

 

1006题          链接：http://acm.hdu.edu.cn/showproblem.php?pid=5358

 

First One

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 757    Accepted Submission(s): 230

Problem Description

 

soda has an integer array   a1,a2,…,an . Let   S(i,j)  be the sum of   ai,ai+1,…,aj . Now soda wants to know the value below:

∑i=1n∑j=in(⌊log2S(i,j)⌋+1)×(i+j)

Note: In this problem, you can consider   log20  as 0.

 

 

Input

 

There are multiple test cases. The first line of input contains an integer   T , indicating the number of test cases. For each test case:

The first line contains an integer   n   (1≤n≤105) , the number of integers in the array.
The next line contains   n  integers   a1,a2,…,an   (0≤ai≤105) .

 

 

Output

 

For each test case, output the value.

 

 

Sample Input

 

   
   
   
   

    
    
    
    1
2
1 1
   
   
   
   

 

 

Sample Output

 

   
   
   
   

    
    
    
    12
   
   
   
   

 

 

Source

 

2015 Multi-University Training Contest 6

 

 

题意：求

 

思路：利用S(i,j)单调性，     log2(S(i,j))+1= k =2^(k-1)<= S(i,j)<2^k

考虑枚举log(sum(i,j)+1的值，记为k，然后统计(i+j)的和即可。

对于每一个k，找到所有满足2^(k-1)<=sum(i,j)<=2^k-1的（i+j），

 

k<=2*log2(10^5)<34

 

转载请注明出处：寻找&星空の孩子 

 

 

 

#include<stdio.h>
#include<math.h>
#include<algorithm>
#define LL long long
using namespace std;
LL num[100005];
LL sum[100005];
int main()
{
    int T;
    scanf("%d",&T);
    while(T--)
    {
        LL n;
        scanf("%lld",&n);
        num[0]=sum[0]=0;
        for(int i=1; i<=n; i++)
        {
            scanf("%lld",&num[i]);
            sum[i]=sum[i-1]+num[i];
        }
        LL ans=0;
        for(LL k=1; k<=34; k++)
        {
            LL l=1,r=0;//注意r的初始值在l的左边；因为存在1个值的情况!
            LL KL=1LL<<(k-1);
            if(k==1) KL--;
            LL KR=1LL<<(k);
            for(LL i=1; i<=n; i++)
            {
                l=max(i,l);//区间左边界
                while(l<=n&&sum[l]-sum[i-1]<KL) l++;//确定左边界
                r=max(l-1,r);//区间右边界,注意r在l前的时候从l-1开始
                while(r+1<=n&&sum[r+1]-sum[i-1]>=KL&&sum[r+1]-sum[i-1]<KR) r++;//确定区间右边界
                if(r<l) continue;
                ans+=k*((i+l)+(i+r))*(r-l+1)/2;
            }
        }
        printf("%lld\n",ans);
    }
    return 0;
}

 

 

 

 

1008题         链接：http://acm.hdu.edu.cn/showproblem.php?pid=5360

 

Hiking

Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 544    Accepted Submission(s): 290
Special Judge

Problem Description

 

There are   n  soda conveniently labeled by   1,2,…,n . beta, their best friends, wants to invite some soda to go hiking. The   i -th soda will go hiking if the total number of soda that go hiking except him is no less than   li  and no larger than   ri . beta will follow the rules below to invite soda one by one:
1. he selects a soda not invited before;
2. he tells soda the number of soda who agree to go hiking by now;
3. soda will agree or disagree according to the number he hears.

Note: beta will always tell the truth and soda will agree if and only if the number he hears is no less than   li  and no larger than   ri , otherwise he will disagree. Once soda agrees to go hiking he will not regret even if the final total number fails to meet some soda's will.

Help beta design an invitation order that the number of soda who agree to go hiking is maximum.

 

 

Input

 

There are multiple test cases. The first line of input contains an integer   T , indicating the number of test cases. For each test case:

The first contains an integer   n   (1≤n≤105) , the number of soda. The second line constains   n  integers   l1,l2,…,ln . The third line constains   n  integers   r1,r2,…,rn .   (0≤li≤ri≤n)
It is guaranteed that the total number of soda in the input doesn't exceed 1000000. The number of test cases in the input doesn't exceed 600.

 

 

Output

 

For each test case, output the maximum number of soda. Then in the second line output a permutation of   1,2,…,n  denoting the invitation order. If there are multiple solutions, print any of them.

 

 

Sample Input

 

   
   
   
   

    
    
    
    4
8
4 1 3 2 2 1 0 3
5 3 6 4 2 1 7 6
8
3 3 2 0 5 0 3 6
4 5 2 7 7 6 7 6
8
2 2 3 3 3 0 0 2
7 4 3 6 3 2 2 5
8
5 6 5 3 3 1 2 4
6 7 7 6 5 4 3 5
   
   
   
   

 

 

Sample Output

 

   
   
   
   

    
    
    
    7
1 7 6 5 2 4 3 8
8
4 6 3 1 2 5 8 7
7
3 6 7 1 5 2 8 4
0
1 2 3 4 5 6 7 8
   
   
   
   

 

 

Source

 

2015 Multi-University Training Contest 6

 

 

题意：问邀请的顺序，使得最终去的人最多，每个人有一个区间[l,r]的人数要求

 

分析：用优先队列维护，按照r从小到大；不是很难注意细节。

 

#include<stdio.h>
#include<queue>
#include<algorithm>
#include<string.h>
using namespace std;
const int N = 100005;
struct nnn
{
    int l,r,id;
}node[N];
struct NNNN
{
    int r,id;
    friend bool operator<(NNNN aa,NNNN bb)
    {
        return aa.r>bb.r;
    }
};

priority_queue<NNNN>q;
bool cmp1(nnn aa, nnn bb)
{
    return aa.l<bb.l;
}
int id[N];
bool vist[N];
int main()
{
    int T,n,ans;
    NNNN now;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d",&n);
        ans=0;

        /*for(int i=1; i<=n; i++)
            printf("%d ",i);
            printf("=id\n\n");*/
        for(int i=0; i<n; i++)
        {
            scanf("%d",&node[i].l);
            node[i].id=i+1;
        }
        for(int i=0; i<n; i++)
            scanf("%d",&node[i].r);
        sort(node,node+n,cmp1);
        memset(vist,0,sizeof(vist));
        int i=0;
        while(i<n)
        {
            bool ff=0;
            while(i<n&&ans>=node[i].l&&ans<=node[i].r)
            {
                now.r=node[i].r;
                now.id=node[i].id;
                q.push(now);
                //printf("in = %d\n",now.id);
                i++;
                ff=1;
            }
            if(ff)i--;
            while(!q.empty())
            {
                now=q.top(); q.pop();
                if(now.r<ans)continue;
                //printf("out = %d\n",now.id);
                ans++;
                id[ans]=now.id;
                vist[now.id]=1;
                if(node[i+1].l<=ans)
                    break;
            }
            i++;
        }
        while(!q.empty())
        {
            now=q.top(); q.pop();
            if(now.r<ans)continue;
            //printf("out = %d\n",now.id);
            ans++;
            id[ans]=now.id;
            vist[now.id]=1;
        }

        bool fff=0;
        printf("%d\n",ans);
        for( i=1; i<=ans; i++)
        if(i>1)
            printf(" %d",id[i]);
        else if(i==1)
            printf("%d",id[i]);
        if(ans)fff=1;
        for( i=1; i<=n; i++)
            if(vist[i]==0&&fff)
                printf(" %d",i);
            else if(vist[i]==0)
                printf("%d",i),fff=1;
        printf("\n");
    }
}

 

1011题      链接：http://acm.hdu.edu.cn/showproblem.php?pid=5363

 

Key Set

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 420    Accepted Submission(s): 275

Problem Description

 

soda has a set   S  with   n  integers   {1,2,…,n} . A set is called key set if the sum of integers in the set is an even number. He wants to know how many nonempty subsets of   S  are key set.

 

 

Input

 

There are multiple test cases. The first line of input contains an integer   T   (1≤T≤105) , indicating the number of test cases. For each test case:

The first line contains an integer   n   (1≤n≤109) , the number of integers in the set.

 

 

Output

 

For each test case, output the number of key sets modulo 1000000007.

 

 

Sample Input

 

   
   
   
   

    
    
    
    4
1
2
3
4
   
   
   
   

 

 

Sample Output

 

   
   
   
   

    
    
    
    0
1
3
7
   
   
   
   

 

 

Source

 

2015 Multi-University Training Contest 6

 

#include<stdio.h>
#define LL long long
#define mod 1000000007
LL ppow(LL a,LL b)
{
    LL c=1;
    while(b)
    {
        if(b&1) c=c*a%mod;
        b>>=1;
        a=a*a%mod;
    }
    return c;
}
int main()
{
    int T;
    LL n;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%lld",&n);
        printf("%lld\n",ppow(2,n-1)-1);
    }
    return 0;
}