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2017百度之星 资格赛

2024-11-19 09:12:39   203人阅读

1001

度度熊保护村庄

Accepts: 26
Submissions: 703
Time Limit: 2000/1000 MS (Java/Others)
Memory Limit: 32768/32768 K (Java/Others)
Problem Description

哗啦啦村袭击了喵哈哈村！

度度熊为了拯救喵哈哈村，带着自己的伙伴去救援喵哈哈村去了！度度熊与伙伴们很快的就过来占据了喵哈哈村的各个军事要地，牢牢的守住了喵哈哈村。

但是度度熊发现，这是一场旷日持久的战斗，所以度度熊决定要以逸待劳，保存尽量多的体力，去迎战哗啦啦村的战士。

于是度度熊决定派尽量多的人去休息，但是同时也不能松懈对喵哈哈村的保护。

换句话而言，度度熊希望尽量多的人休息，而且存在一个包围圈由剩下的人组成，且能够恰好的包围住喵哈哈村的所有住房（包括边界）。

请问最多能让多少个人休息呢？

Input

本题包含若干组测试数据。

第一行一个整数n，表示喵哈哈村的住房数量。

接下来n行，每行两个整数(x1[i],y1[i])，表示喵哈哈村的住房坐标。

第n+1行一个整数m，表示度度熊的士兵数量。

接下来m行，每行两个整数(x2[i],y2[i])，表示度度熊伙伴的坐标。

满足:

1<=n,m<=500

-10000<=x1[i],x2[i],y1[i],y2[i]<=10000

Output

请输出最多的人员休息的数目。

如果无法保护整个村庄的话，输出"ToT"

Sample Input
2
1 1
2 2
4
0 0
0 4
4 2
4 0
1
1 1
2
0 0
0 1
Sample Output
1
ToT
思路很混乱，没搞出来，不会做哎

1002

度度熊的王国战略

度度熊国王率领着喵哈哈族的勇士，准备进攻哗啦啦族。

哗啦啦族是一个强悍的民族，里面有充满智慧的谋士，拥有无穷力量的战士。

所以这一场战争，将会十分艰难。

为了更好的进攻哗啦啦族，度度熊决定首先应该从内部瓦解哗啦啦族。

第一步就是应该使得哗啦啦族内部不能同心齐力，需要内部有间隙。

哗啦啦族一共有n个将领，他们一共有m个强关系，摧毁每一个强关系都需要一定的代价。

现在度度熊命令你需要摧毁一些强关系，使得内部的将领，不能通过这些强关系，连成一个完整的连通块，以保证战争的顺利进行。

请问最少应该付出多少的代价。

Input

本题包含若干组测试数据。

第一行两个整数n，m，表示有n个将领，m个关系。

接下来m行，每行三个整数u,v,w。表示u将领和v将领之间存在一个强关系，摧毁这个强关系需要代价w

数据范围：

2<=n<=3000

1<=m<=100000

1<=u,v<=n

1<=w<=1000

Output

对于每组测试数据，输出最小需要的代价。

Sample Input
2 1
1 2 1
3 3
1 2 5
1 2 4
2 3 3
Sample Output
1
3

并查集 然后更新最小值，注意重边相加和自环
#include <iostream> 
#include <algorithm> 
#include <cstring> 
#include <cstdio>
#include <vector> 
#include <queue> 
#include <cstdlib> 
#include <iomanip>
#include <cmath> 
#include <ctime> 
#include <map> 
#include <set> 
using namespace std; 
#define lowbit(x) (x&(-x)) 
#define max(x,y) (x>y?x:y) 
#define min(x,y) (x<y?x:y) 
#define MAX 100000000000000000 
#define MOD 1000000007
#define pi acos(-1.0) 
#define ei exp(1) 
#define PI 3.141592653589793238462
#define ios() ios::sync_with_stdio(false)
#define INF 0x3f3f3f3f 
#define mem(a) (memset(a,0,sizeof(a))) 
typedef long long ll;
int f[3006],n,m;
int g[3006][3006];
int a,b,c,k;
set<int>s[30006];
set<int>::iterator it;
int val[3000];
int find(int x)
{
    return f[x]==x?x:find(f[x]);
}
void init(int x,int y)
{
    int u=find(x);
    int v=find(y);
    if(u!=v)
    {
        if(u<v) f[v]=u;
        else f[u]=v;;
    }
}
int main()
{
    while(scanf("%d%d",&n,&m)!=EOF)
    {
        ll ans=0;
        memset(g,0,sizeof(g));
        memset(val,0,sizeof(val));
        k=0;
        for(int i=0;i<=n;i++)
            f[i]=i;
        for(int i=0;i<m;i++)
        {
            scanf("%d%d%d",&a,&b,&c);
            init(a,b);
            g[a][b]+=c;
            g[b][a]+=c;
        }
        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<i;j++)
            {
                val[i]+=g[i][j];
                val[j]+=g[i][j];
            }
        }
        for(int i=1;i<=n;i++)
        {
            if(val[i]==0) continue;
            s[find(i)].insert(val[i]);
        }
        for(int i=1;i<=n;i++)
        {
            if(s[i].size()==0) continue;
            it=s[i].begin();
            ans+=*it;
            s[i].clear();
        }
        printf("%I64d\n",ans);
    }
    return 0;
}

1003

度度熊与邪恶大魔王

度度熊为了拯救可爱的公主，于是与邪恶大魔王战斗起来。

邪恶大魔王的麾下有n个怪兽，每个怪兽有a[i]的生命值，以及b[i]的防御力。

度度熊一共拥有m种攻击方式，第i种攻击方式，需要消耗k[i]的晶石，造成p[i]点伤害。

当然，如果度度熊使用第i个技能打在第j个怪兽上面的话，会使得第j个怪兽的生命值减少p[i]-b[j]，当然如果伤害小于防御，那么攻击就不会奏效。

如果怪兽的生命值降为0或以下，那么怪兽就会被消灭。

当然每个技能都可以使用无限次。

请问度度熊最少携带多少晶石，就可以消灭所有的怪兽。

Input

本题包含若干组测试数据。

第一行两个整数n，m,表示有n个怪兽，m种技能。

接下来n行，每行两个整数，a[i],b[i]，分别表示怪兽的生命值和防御力。

再接下来m行，每行两个整数k[i]和p[i]，分别表示技能的消耗晶石数目和技能的伤害值。

数据范围:

1<=n<=100000

1<=m<=1000

1<=a[i]<=1000

0<=b[i]<=10

0<=k[i]<=100000

0<=p[i]<=1000

Output

对于每组测试数据，输出最小的晶石消耗数量，如果不能击败所有的怪兽，输出-1

Sample Input
1 2
3 5
7 10
6 8
1 2
3 5
10 7
8 6
Sample Output
6
18

完全背包问题，每个血量都不超过1000，可以将，每个技能的所能造成的伤害作为变量，晶石消耗量作为权值构建背包，最后，根据怪的生命和防御力作为条件查询就行了
#include <iostream> 
#include <algorithm> 
#include <cstring> 
#include <cstdio>
#include <vector> 
#include <queue> 
#include <cstdlib> 
#include <iomanip>
#include <cmath> 
#include <ctime> 
#include <map> 
#include <set> 
using namespace std; 
#define lowbit(x) (x&(-x)) 
#define max(x,y) (x>y?x:y) 
#define min(x,y) (x<y?x:y) 
#define MAX 100000000000000000 
#define MOD 1000000007
#define pi acos(-1.0) 
#define ei exp(1) 
#define PI 3.141592653589793238462
#define ios() ios::sync_with_stdio(false)
#define INF 0x3f3f3f3f 
#define mem(a) (memset(a,0,sizeof(a)))
typedef long long ll;
struct Node
{
    int x;
    int y;
}node[100005];
int dp[1005][12],n,m;
int k[1005],p[1005];
int main()
{
    while(scanf("%d%d",&n,&m)!=EOF)
    {
        int ans=-1;
        ll sum=0;
        for(int i=0;i<n;i++)
        {
            scanf("%d%d",&node[i].x,&node[i].y);
            ans=max(ans,node[i].y);
        }
        bool flag=false;
        for(int i=0;i<m;i++)
        {
            scanf("%d%d",&k[i],&p[i]);
            if(p[i]>ans) flag=true;
        }
        if(!flag){printf("-1\n");continue;}
        for(int i=0;i<=10;i++)
        {
            for(int j=0;j<=1000;j++)
            {
                dp[j][i]=INF;
            }
            dp[0][i]=0;
        }
        for(int i=0;i<m;i++)
        {
            for(int j=0;j<p[i];j++)
            {
                int x=p[i]-j;
                for(int t=1;t<x;t++)
                    dp[t][j]=min(dp[t][j],k[i]);
                for(int t=x;t<=1000;t++)
                    dp[t][j]=min(dp[t][j],dp[t-x][j]+k[i]);
            }
        }
        for(int i=0;i<n;i++)
        {
            sum+=dp[node[i].x][node[i].y];
        }
        printf("%lld\n",sum);
    }
    return 0;
}

1004

度度熊的午饭时光

Accepts: 609
Submissions: 7650
Time Limit: 2000/1000 MS (Java/Others)
Memory Limit: 32768/32768 K (Java/Others)
Problem Description

度度熊最期待每天的午饭时光，因为早饭菜品清淡，晚饭减肥不敢吃太多（胖纸的忧伤T.T）。

百度食堂的午餐超级丰富，祖国各大菜系应有尽有，度度熊在每个窗口都有爱吃的菜品，而且他还为喜爱的菜品打了分，吃货的情怀呀(>.<)。

但是，好吃的饭菜总是很贵，每天的午饭预算有限，请帮度度熊算一算，怎样打饭才能买到的最好吃的饭菜?(不超过预算、不重样、午餐等分最高的情况下，选择菜品序号加和最小，加和相等时字典序最小的组合)

Input

第一行一个整数T，表示T组数据。 每组测试数据将以如下格式从标准输入读入：

B

N

score_1 cost_1

score_2 cost_2

:

score_N cost_N

第一行，正整数B（0 <= B <= 1000），代表午餐的预算。

第二行，正整数N (0 <= N <= 100)，代表午餐可选的菜品数量

从第三行到第 (N + 2) 行，每行两个正整数，以空格分隔，score_i表示菜品的得分，cost_i表示菜品的价格(0 <= score_i, cost_i <= 100)。

Output

对于每组数据，输出两行： 第一行输出："Case #i:"。i代表第i组测试数据。 第二行输出菜品的总得分和总花费，以空格分隔。 第三行输出所选菜品的序号，菜品序号从1开始，以空格分隔。

Sample Input
2
29
6
9 10
3 4
6 5
7 20
10 9
15 11
0
2
2 23
10 12
Sample Output
Case #1:
34 29
2 3 5 6
Case #2:
0 0

重点在于路径标记，和字典序最小，除去这些，就只是一个很简单的01背包问题
#include <iostream> 
#include <algorithm> 
#include <cstring> 
#include <cstdio>
#include <vector> 
#include <queue> 
#include <cstdlib> 
#include <iomanip>
#include <cmath> 
#include <ctime> 
#include <map> 
#include <set> 
using namespace std; 
#define lowbit(x) (x&(-x)) 
#define max(x,y) (x>y?x:y) 
#define min(x,y) (x<y?x:y) 
#define MAX 100000000000000000 
#define MOD 1000000007
#define pi acos(-1.0) 
#define ei exp(1) 
#define PI 3.141592653589793238462
#define ios() ios::sync_with_stdio(false)
#define INF 0x3f3f3f3f 
#define mem(a) (memset(a,0,sizeof(a)))
typedef long long ll;
int dp[1005],ans,t;
int path[105][1005];
int vis[1005][105];
struct Node
{
    int score;
    int cost;
}node[105];
int N,n,cast;
int top,mark;
int main()
{
    scanf("%d",&t);
    cast=0;
    while(t--)
    {
        scanf("%d%d",&N,&n);
        ans=0;
        int pos=INF,cnt,sum,inf=0;
        memset(dp,0,sizeof(dp));
        memset(path,0,sizeof(path));
        memset(vis,0,sizeof(vis));
        for(int i=1;i<=n;i++)
        {
            scanf("%d%d",&node[i].score,&node[i].cost);
        }
        printf("Case #%d:\n", ++cast);
        for(int i=1;i<=n;i++)
        {
            for(int j=N;j>=node[i].cost;j--)
            {
                if(dp[j]<dp[j-node[i].cost]+node[i].score)
                {
                    dp[j]=dp[j-node[i].cost]+node[i].score;
                    path[i][j]=1;
                }
            }
        }
        for(int i=0;i<=N;i++)
        {
            ans=max(dp[i],ans);
        }
        top=1;mark=1;
        for(int k=N;k>=0;k--)
        {
            if(dp[k]==ans)
            {
                cnt=0;sum=0;
                for(int i=n,j=k;i>=1 && j>=0;i--)
                {
                    if(path[i][j])
                    {
                        vis[top][++cnt]=i;
                        sum+=i;
                        j-=node[i].cost;
                    }
                }
                vis[top][0]=cnt;
                sort(vis[top]+1,vis[top]+1+cnt);
                if(pos>sum)
                {
                    pos=sum;
                    mark=top;
                }
                else if(pos==sum)
                {
                    for(int s=1;s<=vis[top][0] && s<=vis[mark][0];s++)
                    {
                        if(vis[mark][s]==vis[top][s]) continue;
                        else if(vis[mark][s]<vis[top][s]) break;
                        else {mark=top;break;}
                    }
                }
                top++;
            }
        }
        for(int i=1;i<=vis[mark][0];i++)
            inf+=node[vis[mark][i]].cost;
        printf("%d %d\n",ans,inf);
        if(vis[mark][0]==0) continue;
        else
        {
            for(int i=1;i<=vis[mark][0];i++)
            {
                if(i!=1) printf(" ");
                printf("%d",vis[mark][i]);
            }
            printf("\n");
        }
    }
    return 0;
}

1005

 

寻找母串

Accepts: 143
Submissions: 1366
Time Limit: 2000/1000 MS (Java/Others)
Memory Limit: 32768/32768 K (Java/Others)
Problem Description

对于一个串S，当它同时满足如下条件时，它就是一个01偏串： 1、只由0和1两种符组成； 2、在S的每一个前缀中，0的个数不超过1的个数； 3、S中0的个数和1的个数相等。

现在给定01偏串S，请计算一下S在所有长度为n的01偏串中作为子串出现的次数的总和。 由于结果比较大，结果对1e9+7取余后输出。

样例解释： 在第二个样例中，长度为4的偏串共两个1010，1100。10在1010中出现了两次，在1100中出现了1次。所以答案是3。

Input

第一行给出一个整数T(1<=T<=40),表示测试数据的数目。 每一组测试包含一个整数n和字符串S，中间用空格分开。(1<=|S|<=100000，1<=n<=1000000000)

输入保证S是一个01偏串。

Output

对于每一组数据，输出一个整数占一行，表示答案。

Sample Input
2
2 10
4 10
Sample Output
1
3


解题思路：

打表找规律：s串与内容没有关系，只与s串的长度有关系 接下来只以10101010101010为例
模式串：                 字串：                               匹配条件：
10                      10                                  10              1        total        1
1010                    10                                  1010            2        
                                                            1100            1        total        3
101010                  10                                  101010          3
                                                            101100          2
                                                            110100          2
                                                            110010          2
                                                            111000          1        total         10
10101010                10                                  10101010        4
                                                            10101100        3
                                                                             10110100        3
                                                            11010100        3
                                                            10110010        3
                                                            11001010        3
                                                            11010010        3
                                                            11011000        2
                                                            11001100        2
                                                            10111000        2
                                                            11101000        2
                                                            11100100        2
                                                            11100010        2
                                                            11110000        1         total        35

即组合数C（n*2-1，n）n=（n-strlen（s））/2+1；
=f[n]*(n+1)/2;
f[n]=2*(2*n-1)*f[n-1]/(i+1);
所以打表可得
#include <iostream> 
#include <algorithm> 
#include <cstring> 
#include <cstdio>
#include <vector> 
#include <queue> 
#include <cstdlib> 
#include <iomanip>
#include <cmath> 
#include <ctime> 
#include <map> 
#include <set> 
using namespace std; 
#define lowbit(x) (x&(-x)) 
#define max(x,y) (x>y?x:y) 
#define min(x,y) (x<y?x:y) 
#define MAX 100000000000000000 
#define MOD 1000000007
#define pi acos(-1.0) 
#define ei exp(1) 
#define PI 3.141592653589793238462
#define ios() ios::sync_with_stdio(false)
#define INF 0x3f3f3f3f 
#define mem(a) (memset(a,0,sizeof(a)))
typedef long long ll;
char s[1000009];
ll n,t;
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    613098019,82701766,247051132,940988662,699855854,653160599,253589170,454574426,648632475,561229480,439013878,780463812,751080642,475363127,872955171,221419431,660718935,616253276,620991239,322955474,95900697,736953117,435364733,400032675,143150458,892976596,778936048,870114869,693427846,916920202,531290913,159313409,854027823,956895320,431001333,958032952,435621676,147281691,782644049,363417645,788629073,318986652,45280716,627497306,862125833,55176692,769605990,50913091,759547794,415399356,91873313,435971457,972361711,886131838,698360174,778537252,867612407,363143588,210628827,227452019,167347791,136481555,794414626,886837851,833212071,867100102,962413595,506550918,150461107,97396199,322574611,286566460,418048639,126619502,49890932,424873463,577636888,598651314,214771282,633007716,67600639,872694032,899190404,807799524,536389663,783650145,198103723,406176925,596091368,865801146,255660985,950263612,204698161,570789483,35674858,355559169,627978911,108585701,612463851,227550456,44549978,430769857,197325621,365494994,215296621,794175066,165486775,239680547,990696203,54536891,267132823,879937767,468746039,925979058,896931201,784849771,365504305,221529004,715124186,598394296,273404498,942530408,892470275,339529469,637182412,714030555,4591038,747727171,993858038,98351859,587568276,635308938,66381702,523069101,611647432,93089964,621299142,87170109,91184576,582205309,384761096,623784317,274148172,565367846,707139350,413965784,111585803,462251445,228866268,199084146,547319848,912054783,776081313,50512733,398666776,860515976,132645483,784732014,283636962,567053755,762371460,902545259,6795752,933181225,79095380,382697365,79944172,18195218,904541583,983398375,352534501,206544638,590062152,870793758,26235371,885333891,755593357,797697319,233605783,916638079,592465092,389607454,700420311,196459900,86420454,160839557,696575,569324134,807071644,759233878,743587997,984681992,941063338,324982757,676014860,600520498,188292161,129801562,413126752,313832643,937070759,97526604,541466777,603982189,77969188,347408805,311339522,716968535,967397279,253173933,37355703,352327793,883519616,967973262,117140785,240224335,807324871,845415681,840729498,935684923,155577573,734434833,191517923,654123163,637896624,852058670,173168370,730184794,50915735,324841114,628137110,205149114,182695122,548334792,230832142,246897375,673812822,774458235,12653594,589139188,823592104,141584849,661263989,634220976,838048410,865644208,959538649,496526723,706515642,30364288,288996675,618298630,512675413,255909709,961226649,196140093,464842799,73771491,907822468,820941783,633421126,938423057,725611016,889132555,244245553,600535214,454683334,918501588,156397960,727549083,462344797,552581171,951585647,331017637,713844297,201014346,220893764,942832265,205089583,855055766,558242708,467800323,544040124,5018684,600324086,275710404,942082597,882387855,283394592,984698042,699687145,218659340,671476043,786242938,615660310,451633451,264041371,62057607,615318684,358229710,600528374,737949511,309417464,928413938,485704507,508289212,335423875,674380863,518017044,336119074,617416674,485819110,941096637,929311054,597002446,973475334,265580872,563517784,251569149,148530184,95396816,883600979,282561244,840871566,519908445,640741041,421822961,632376045,139437876,790411904,591820303,741935921,948651905,366299783,716525381,15431695,15465625,971346451,168728596,608506519,27394837,851151360,602776233,970664278,322046939,511916124,340275737,1956214,363111458,481072216,658163046,518552634,132664065,981823198,216243081,159795020,767941105,457986980,858463537,976190745,171187323,572871813,647899578,408338249,44147207,156374207,940179853,58043446,28385650,424517633,511617049,926045094,319879729,514748429,614317869,421026423,671332980,6835612,938930076,458303594,925057217,380172144,417162197,8078854,424003560,2008065,807569105,429700641,464740805,457368858,589073747,394260986,391506131,929826825,432872648,690774587,357406694,692130031,273616783,445027156,511488576,31976171,170358186,20482390,918198464,271438684,749710986,389073776,939445726,23455846,956187346,748137028,734748051,303817400,94204386,126522637,81942995,832809073,197225686,406203721,149560387,711052519,501674175,547993890,871374386,551852029,842913905,11301805,658024191,322045818,938590456,235068927,986201888,729075821,230293940,88489051,430417352,457640653,512463037,164939381,78855727,918299124,19019884,318003658,964003586,887976673,465062825,998287188,345218097,418436509,423868376,737852682,222443100,431664080,191790675,179137865,240191988,426955600,372855698,834981397,769820197,12457840,592849249,301573725,529831284,455945822,908361093,348036200,725019234,272002918,302014486,868309988,267131588,110362906,658933926,714755636,575129133,572255614,242451399,460854477,379734453,261883330,173252303,205271891,875823576,295295415,344691305,88281196,291229175,339458347,199662270,135955543,945346312,464533492,871840955,247580453,899980261,309580183,86978522,845735069,219736536,817617603,405963484,880265007,291366034,314006019,86753505,849126155,994666022,724217006,569965800,190010599,920028225,755930223,376881817,18255664,401402435,819561952,810240409,896675374,5648890,14322856,899043492,141273287,496383310,791004873,659659128,952106154,219105831,176538445,879815182,445593480,150528189,94493662,797589952,732282876,567925839,796782054,629643845,130694449,475573885,497611040,499200426,183468775,892394136,17028961,825354772,382036602,10367014,453970224,702396666,603040526,616353655,902691380,983386965,692566149,247825935,66330622,225112465,895795849,52320773,155947313,718224149,164300545,677709978,266340441,218514417,204476400,286595553,643512303,598766962,788301683,892598856,520036990,859133788,979526775,296869156,670015326,164319827,647208607,679949247,172064170,865163183,337039103,105046080,579964945,123270759,385113924,576031432,771688525,704910535,414466742,609386035,928631412,485368568,479480031,505949447,116422341,568991478,93574014,961174363,735174682,235632013,19234330,650946685,144392601,510837538,567469814,856042956,806198989,116886696,207340279,223268817,253945420,584643811,616483622,711150993,357748602,626063923,607222114,600586776,28542569,796083795,549421818,591429425,607254162,355391295,492527448,847958740,287070353,814226472,643144229,698819990,177700395,611101671,490661583,275559707,950224920,844587825,53229930,339523379,979109376,126378471,444745387,726629825,351823753,475484131,518938465,963071536,84665553,643867081,825793617,408943841,879707301,471828659,223598556,384354814,153231894,188992442,483627866,255018189,675911377,500327547,638084035,486199656,903986764,949245648,862319148,790947898,142578126};
//f[n]=2*(2*n-1)/(n+1)*f[n-1];
ll quick_pow(ll x,ll y)
{
    ll ans=1;
    while(y)
    {
        if(y&1) ans=ans*x%MOD;
        y>>=1;
        x=x*x%MOD;
    }
    return ans;
}
/*int main()
{
    ll ans=1;
    int tot=0;
    for(int i=2;i<=500000000;i++)
    {
        ans=(ans*2*(i*2-1)%MOD*quick_pow(i+1,MOD-2)%MOD)%MOD;
        if(i%100000==0)
        {
            printf("%lld,",ans);
            tot++;
        }
    }
    printf("\n***************************************\n%d\n",tot);
    return 0;
}*/
int main ()
{
    scanf("%d",&t);
    while(t--)
    {
        ll ans;
        scanf("%d %s",&n,&s);
        int len=strlen(s);
        if(len>n || n&1) {printf("0\n");continue;}
        int pos=(n-len)/2+1;
        int k=pos/100000;
        ans=vis[k];
        for(int i=k*100000+1;i<=pos;i++)
        {
            ans=(ans*2*(i*2-1)%MOD*quick_pow(i+1,MOD-2)%MOD)%MOD;
        }
        ans=(ans*(pos+1)%MOD*quick_pow(2,MOD-2)%MOD)%MOD;
        printf("%I64d\n",ans);
    }
    return 0;
}
/*
101010 3
101100 2
110100 2
110010 2
111000 1
total 10
int n=(n-m)/2+1;
C(2*n-1,n);
 */
/*
2
2 10
4 10
 */
/*
1
3
 */
/*
5
1000000000 10
1000000000 1010
1000000000 1100
1000000000 111000
1000000000 10101100
 */

 









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