cloudy_happy

HPU暑期积分赛4

E题：

Description

这个世界并不一定抽象。

在某个大陆的某端，有一个异或王国，该国会评判一个人是否会使用异或（即位运算中的异或 XOR，对于两个数的二进制位，1 XOR 1 = 0, 0 XOR 0 = 0, 1 XOR 0 = 1,0 XOR 1 = 1）的能力，从而评判他是否是该国的人。

Philo为了避免风险，只能强行去完成国王的异或测试。

异或测试：一共有n个士兵棋子排成一列，他们的顺序不允许被打乱。每个棋子都有一个能力值a_iai，你可以任意选取任意一段连续区间，从左到右依次进行异或和。要求获得最大的异或值。

请你输出能得到的最大的值。

Input

输入一个正整数n,(0 < n \leq 100)(0

Output

一个正整数;

Sample Input 1

5
1 2 1 1 2

Sample Output 1

Sample Input 2

3
1 2 7

Sample Output 2

思路：

刚看这个题O（100*100），这么简单吗？还没多少人写，不敢相信，看了几遍确认没毛病于是暴力签到，美滋滋

代码：

#include
using namespace std;
int a[110];
int dp[110];
int main()
{
	int n,ans = 0;
	scanf("%d",&n);
	for (int i = 1;i <= n;i ++)
	{
		scanf("%d",&a[i]);
		ans = max(ans,a[i]);
	}
	for (int i = 1;i <= n;i ++)
	{
		int cnt = a[i];
		for (int j = i + 1;j <= n;j ++)
		{
			cnt = cnt ^ a[j];
			ans = max(ans,cnt);
		}
	}
	printf("%d\n",ans);		
	return 0;
}

J题:

装箱问题

Description

有一个箱子容量为 V （正整数， 0≤V≤20000 ），同时有 n 个物品（ 0

要求 n 个物品中，任取若干个装入箱内，使箱子的剩余空间为最小。

Input

1 个整数，表示箱子容量

1 个整数，表示有 n 个物品

接下来 n 行，分别表示这 n 个物品的各自体积

Output

1个整数，表示箱子剩余空间。

Sample Input 1

Sample Output 1

Source

丁金峰

思路：

一道简单的01背包签到题

代码：

#include
#define ll long long
#define mem(a) memset(a,0,sizeof(a))
using namespace std;
int a[50];
int dp[20010];
int main()
{
	int v,n;
	scanf("%d %d",&v,&n);
	for (int i = 1;i <= n;i ++)
	{
		scanf("%d",&a[i]);
	}
	for (int i = 1;i <= n;i ++)
		for (int j = v;j >= a[i];j --)
			dp[j] = max(dp[j],dp[j - a[i]] + a[i]);
	printf("%d\n",v - dp[v]);
	return 0;
}

K题：

方框

Description

用'*'打印出一个nxn的字符图形（1<=n<=100）.

Input

多组输入。每行输入一个n，输入EOF结束文件.

Output

输出一个满足题意的图形.

Sample Input 1

Sample Output 1

*
**
**
*****
*   *
* * *
*   *
*****
******
*    *
* ** *
* ** *
*    *
******
**********
*        *
* ****** *
* *    * *
* * ** * *
* * ** * *
* *    * *
* ****** *
*        *
**********
***********
*         *
* ******* *
* *     * *
* * *** * *
* * * * * *
* * *** * *
* *     * *
* ******* *
*         *
***********

思路：

题目描述有点不详细，意思就是打一个多重回形，想了好久还是不太会，最后想到一种先按行打，最后把多的去掉的方法，时间不太够了，赛后同桌说可以存起来直接输出就好了，一语惊醒，唉，智商太低，自己还菜（大哭）

代码：

#include
using namespace std;
char maze[110][110];
int main()
{
	int n;
	while (~scanf("%d",&n))
	{
		int p = n,r = 1;
		memset(maze,' ',sizeof(maze));
		while (n >= 1)
		{
			for (int i = r;i <= n;i ++)
			{
				maze[r][i] = '*';
				maze[n][i] = '*';
				maze[i][r] = '*';
				maze[i][n] = '*';
			}
			n -= 2;
			r += 2;
		}
		for (int i = 1;i <= p;i ++)
		{
			for (int j = 1;j <= p;j ++)
				printf("%c",maze[i][j]);
			putchar('\n');
		}
	}
	return 0;
}

I 题：

Add one minus one

Description

给出n个数，每次可以选择两个数进行操作（即：一个数+1，另一个数-1；注意二者的值都变化；例：选择4与2进行操作，可以是4-1=3与2+1=3）。
问经过数次操作，最多能够得到多少个相同的数。
在保证得到的相同的数的数目最多的情况下，新生成的n个数中最大值与最小值的差最小为多少？

Input

输入包含一个整数T（1<=T<=100），代表T组测试数据。
每组测试数据，输入一个整数n（1<=n<=1000）。
接下来输入一个整数序列a[0],a[1],a[2]...a[n-1]，其中0

Output

对于每组测试样例，输出包含两部分：
第一行输出一个整数x，代表经过数次操作，最多能够得到的相同的数的数目。
第二行输出一个整数y，代表在保证得到的相同的数的数目最多的情况下，新生成的n个数中最大值与最小值的差最小为多少

Sample Input 1

Sample Output 1

思路：

对于这n个数，我们不管他们都是多少，加起来之后把sum / n看成他们的标准来看，如果sum % n == 0,那么很显然，这n个数经过有限次变换可以变成sum / n,且差值为0，如果sum / n != 0,那么我们最多变成n - 1个相同的，但这n - 1 个数我们可以变成 sum / n 或者 n - sum % n,所以只需要比较一下哪个差值最小即好

代码：

#include
using namespace std;
int main()
{
	int t;
	scanf("%d",&t);
	while (t --)
	{
		int n,x,sum = 0;
		scanf("%d",&n);
		for (int i = 0;i < n;i ++)
		{
			scanf("%d",&x);
			sum += x;
		}
		printf("%d\n",(sum % n) ? n - 1 : n);
		printf("%d\n",min(n - sum % n,sum % n));
	}
	return 0;
}

K题：

A Winged Steed

Description

有nn种千里马，每一种都有若干匹，第ii种马的颜值a_iai,价格d_idi.现有mm个牧马人要去挑选千里马，每一位牧马人对马的颜值都有要求：{所选马的颜值总和} \geqslant A_i⩾Ai.现在让你来为牧马人做满足要求的最低预算.

Input

单组测试数据，第一行两个整数n,mn,m,( 1 \leq n,m \leq 1e4)(1≤n,m≤1e4).
接下来nn行，每行两个整数a_1,d_1,a_2,d_2,...a_n,d_na1,d1,a2,d2,...an,dn.
最后一行mm个整数A_1,A_2,...A_mA1,A2,...Am，( 1 \leq a_i,d_i,A_i \leq 1e4)(1≤ai,di,Ai≤1e4).

Output

输出mm个整数占一行，用空格隔开，表示每一位牧马人的最低花费.

Sample Input 1

Sample Output 1

3 3

思路：

这题跟百度之星度度熊和大魔王那题基本一样，把Ai看成m个背包，对于每个背包都是完全背包的写法，但有一点就是背包是有一个最大容量的，而这道题只要花费最少，背包容量是不用管的，起初倒也想到了一个捷径就是把m给扩到1e5，如果di的数据小的话，我最后再把dp逆序处理一下就能过了，可惜学长也很聪明，di偏偏至少1e5+，所以投机取巧不可取，看了大牛的代码，原来只需要一个if

代码：

#include
#define inf 0x3f3f3f3f
using namespace std;
const int maxn = (int)1e4 + 10;
int a[maxn],d[maxn],p[maxn];
int dp[maxn];
int main()
{
	int n,m,r = 0;
	scanf("%d %d",&n,&m);
	for (int i = 1;i <= n;i ++)
		scanf("%d %d",&a[i],&d[i]);
	for (int i = 1;i <= m;i ++)
	{
		scanf("%d",&p[i]);
		r = max(r,p[i]);
	}
	for (int i = 1;i <= r;i ++)
	{
		dp[i] = inf;
		for (int j = 1;j <= n;j ++)
			if (i < a[j])
				dp[i] = min(dp[i],d[j]);  //dp[i]表示某人要求颜值最少为i的最少花费 
			else
				dp[i] = min(dp[i],dp[i - a[j]] + d[j]);
	}
	printf("%d",dp[p[1]]);
	for (int i = 2;i <= m;i ++)
		printf(" %d",dp[p[i]]);
	putchar('\n');
	return 0;
}

A题：

Ball

Description

给a个黑球和b个白球，这些球除了颜色外没有别的不同，现随机的摸c个球，问至少有一个黑球的概率是多少？

Input

第一行,一个整数T表示测试组数( 0 < T \leq 1000 接下来T行，每行有三个用空格隔开的整数a,b,ca,b,c . (0 < a + b < 1e9, 0 < c <= b0

Output

对每个测试数据，请在一行中输出一个整数表示答案.(答案是一个p/q的形式且是模MOD下的意义，所以对于p/q就是 p * inv（q）. MOD = 1e9 + 7MOD=1e9+7)

Sample Input 1

1
3 2 1

Sample Output 1

200000002

Source

lzs

思路：

首先确定这道题的概率表示是1 - C(b,c) / C(a + b,c)，即1 - p / q 的形式，然后就是求q的逆元，这里可以用费马小定理求逆元

但要注意一点就是a + b的数据量在1e9，暴力求a + b的阶乘肯定是不可能的，我们只能靠线下打表才能过，线下打表大致就是分块把时间复杂度从1e9缩到最大为块的大小（我的是1e5）然后就还把公式搞成好几个阶乘什么的我就不写了，全在代码里了

代码：

#include
#define ll long long
using namespace std;/*  */
const ll mod = (int)1e9 + 7;
const int maxn = (int)1e4 + 50;
const int MAXN = (int)1e5;
//打表结果
ll f[maxn] = {1,457992974,107146451,373281933,559805077,154425679,679209364,526226141,644158465,730342129,641102369,99410016,363599536,361684231,539157852,448516387,309854856,95657988,663484182,311407840,578095319,229611066,765808214,142477924,585806050,119948046,579773866,816761238,861745250,639926530,5832229,630915411,242744764,932799119,899032987,929795683,150478174,609593566,627860803,358784546,259081142,57134788,544918953,8837465,907400235,59433257,421968194,500425006,278955367,248057675,974067448,293296655,996965954,212873022,473966292,261465122,479920311,214054614,752161465,719792849,316220877,224748329,1575312,652382508,620898940,663134272,405577532,116225742,956413299,257438891,690120224,437383740,24521750,596209708,576078970,304661605,929871923,412584039,14422365,604303898,251368199,808427728,582439362,55596303,220087090,704262886,98361446,295620142,763414075,927340096,980250487,248981102,618104354,839684660,398723029,386267146,764421236,558837848,476998749,345911460,682498929,58865407,152611299,37365474,345470378,681184885,403024660,947000742,140864216,22803916,134623568,733842728,373126171,337899910,461157687,427907847,363224613,642502601,526497651,759652538,95936601,173914411,19447777,382610562,584319463,140928835,569582206,226022701,9045328,784835785,933097914,76048860,959173997,780658683,559096347,391177708,12442609,40743573,508362944,781264818,167332441,33592533,75538458,714210512,275742306,739650465,137855279,889166166,60332461,798657991,598816162,464484063,31223863,344176836,767213175,292015879,564190300,296547306,222078457,977909564,336060741,474159159,632048012,952625711,895642779,810640932,171183381,305391286,851161246,209567103,248744620,551739578,635103992,526685249,605016577,892704918,853414712,566161015,546047842,894851390,626497524,433082692,867430659,512332467,904851726,118508240,475501650,815664143,298693437,652967545,288843364,865229790,52298443,803384326,743602491,406755567,479708090,643624459,125625755,316969704,491101308,708750650,662967999,571611259,385457627,668723114,482257159,899820643,393222011,401679067,245341950,587770205,474567292,725000295,196002818,560364972,754437203,498728445,542706821,970854495,565768255,246407879,524308015,724201825,545648343,913230882,58680787,702934318,792180189,131514392,246899319,192185054,99934426,98200674,788944266,756627904,676012445,734897886,610686655,130907341,968999,379198792,595032530,642903797,244819707,7998896,511710008,696896528,902492598,3525929,586350670,296000745,979137619,86414019,980655027,328019447,474700377,306429182,30153596,966484628,638587686,610696318,420932107,477267870,353049206,497857012,281562548,500956856,921459833,157600969,881746146,924389072,850268753,87892573,711117420,526658674,919203761,262557378,831442297,122316469,19426633,190298375,910061172,214146479,862345480,560607302,293462255,370787091,542955556,768910131,850500036,31318378,181909169,500033013,496532173,916364742,582702682,778006566,168757859,361307467,76479948,219226870,477639087,126712923,930180103,732041432,941723214,130794194,28581913,85186984,268124147,88516556,685075984,488636005,53790970,30473806,672818243,906976408,581968000,78103048,842267748,348586163,947532066,464777188,451116854,878381584,333707614,448457825,650009312,53500714,886294336,648763344,868829344,570443478,613566917,73995168,695702195,776902855,853242582,107560517,485348706,31109298,229827108,590398688,827117592,771153434,492711911,111567856,296974594,269232911,463847391,546178363,649090736,276477167,204857297,72518508,760019200,656049509,942731826,505080571,544075857,422316785,185735387,876081033,550588097,264638935,632593345,941126423,706629399,642498983,898187927,769005417,854821744,205765722,297803207,468116664,596729075,409898960,466541843,190009221,798967520,644759890,743420839,206187615,198998756,359622660,526623452,836550874,952046139,202071291,82926604,130808582,924044367,848688381,23777891,59761470,924258126,204012302,450837733,960862718,723816384,547639586,535478979,87226689,53975412,320608814,517436639,173809161,63932312,478679185,156530778,571781438,807928028,681452055,305569485,278224088,545662462,710807771,29493652,581977264,721996174,820229375,49456224,979809664,480391065,222176885,526281212,927482461,151117811,44756165,299085602,643484121,522961673,277106101,374481484,814440466,489252071,587318335,589831644,15753781,323604647,21771073,153393495,433729686,268164416,359932651,48301315,364347439,90383486,945599636,172827403,695951947,800588969,106892865,757146415,213590923,169338716,599312274,192601723,455503344,398699886,668865790,675113999,708394300,139831846,983975503,135840345,334346960,475501867,167226923,530389102,852493922,499294891,922898261,415376,619965361,114785958,146628257,576550918,635060378,294587621,55789549,714006296,103228118,457685563,221896631,875018827,971180026,254653019,274155554,813805606,9027036,172340144,518728060,498342367,676243000,258170000,496205651,43217172,714008239,67347853,912590546,909565792,54071151,16783532,557470122,495844744,95325827,402811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02,790523771,794859549,916291845,318580210,60217575,874580373,668677123,65591903,513047302,910026008,178909003,613496200,881482632,916304134,747296925,42587322,548026212,957757479,437155518,812279408,918951065,792299597,899946391,321697039,36670825,857922528,43744543,84428155,957469762,79147005,929269243,270142104,321900901,944491355,775543604,427709220,528255018,674721611,381350331,629894526,169838765,889482960,512634493,817479361,262044551,445396258,339271869,970053019,186968777,870125056,687740343,320428001,303338827,901511835,924265341,9058966,327625657,860842034,789825490,851258730,296589615,904066718,121000338,520374634,217147361,653145383,171989322,87654126,867046994,457294725,490484575,988922932,967284733,599140106,644960213,679659893,838526218,580938783,63126637,694075816,819577801,603739686,492741665,543574940,812501999,971085075,510950308,671517513,370290353,18797131,916660987,216549068,152233223,858814345,343799473,477335006,246311854,335102896,271361010,164992964,852694071,554291156,165393390,338262892,21985433,8195350,302780015,160150497,483975089,361084936,682610501,509406823,680128316,803513526,114644779,573964644,321935156,685723887,473979326,677822059,53102426,163052139,917041303,617666448,95249276,954826526,207172258,782192657,877643222,623151847,492897596,527572212,532702135,829422649,745391035,768941501,478657069,56081734,429707160,841072969,344857140,198803488,741626808,19820900,779734593,309906471,877891340,642939667,305583444,224546239,53635336,744645153,496442755,960584207,348421260,787464577,116164597,867195255,73903881,197001309,226879956,562908177,536841269,363551706,709515651,368324673,30514807,412622873,630057303,389088357,875410153,792914276,131384366,99359978,386541987,653102924,307321014,994065976,953786104,730583919,627500870,292151509,377329025,573443769,613973085,816691591,599685896,974508445,708543683,966533706,845486631,333457751,301196854,264848873,894553004,759137421,309986645,574480664,371930700,364502974,416322416,775556523,859917803,281761694,767790141,879674443,389995666,20211256,766570439,325014894,379943099,957347508,676511002,792894374,888140011,755146193,824619763,437157360,802932692,946198358,619700091,625494526,373451745,948994836,487012980,596952378,639054294,83118246,752243809,52836141,756614559,114955307,847645126,710424773,925139828,886787632,23001875,268761837,557583419,234337026,860551136,894939441,823495900,818476649,95460945,987535081,578471809,459628134,12029751,348246100,676216445,751971766,576368335,520389069,78835193,52979524,960033065,494290402,120815665,610541980,961431677,592296500,73146164,300019098,119895268,230976447,630786699,98016105,612866870,593422313,291993453,92077788,954958912,23895805,585347275,571536697,206526983,486828649,707764537,441442575,245423562,628018983,847549272,119263545,954421367,724553294,384826244,201882845,374116154,97348051,247001105,782816485,241289571,527174998,550507082,993282622,249360270,420567331,378750527,539300380,976517503,681566251,646654592,555103342,958797332,911520292,946033733,788599446,883122906,886354425,616017573,716431887,216046746,788872381,999340546,283129306,575014853,682599498,85104325,392505761,219092361,312720425,205951465,127398072,877002932,231120229,676290554,383521365,989326738,299086439,765080455,622618140,3258987,599755664,95568681,78742678,894658473,433576760,434360362,474857680,330810163,944598142,780882948,597789250,163787210,311490118,385914044,510148825,74434897,326957567,723091468,433350723,822439091,908200376,35784547,525561111,118654619,128900492,696559662,751235252,973737505,240437894,598245292,168759145,895487487,907890920,139066955,606924610,915276325,353658242,547380283,61705100,869544707,762816834,306032293,778368564,59434732,933768689,590393084,523894858,267469129,926316480,698611116};
ll quick(ll a,ll b)//快速幂 
{
	ll ans = 1;
	a = a % mod;
	while (b)
	{
		if (b & 1)
			ans = ans * a % mod;
		a = a * a % mod;
		b >>= 1;
	}
	return ans;
}
ll inv(ll x)//费马小定理求逆元 
{
	return quick(x,mod - 2);
}ll solve(ll a) //分块后的阶乘 
{
	ll p = a / MAXN;
	ll l = p * MAXN + 1;
	ll ans = f[p];
	for (int i = l;i <= a;i ++)
		ans = ans * i % mod;
	return ans;
}
/*-------线下打表--------*/ 
//void init()
//{
//	int pos = 0;
//	ll ans = 1;
//	for (int i = 2;i <= (int)1e9;i ++)
//	{
//		ans = ans * i % mod;
//		if (i % 100000 == 0)
//			f[pos ++] = ans;
//	}
//	for (int i = 0;i < pos;i ++)
//		printf("%lld,",f[i]);
//}
/*-------线下打表--------*/ 
int main()
{
	int t;
	ll a,b,c;
	scanf("%d",&t);
	while (t --)
	{
		scanf("%lld %lld %lld",&a,&b,&c);
		ll ans = (solve(a + b - c) % mod * (solve(b) % mod)) % mod
		          * inv(solve(a + b) % mod * (solve(b - c) % mod) % mod) % mod;
		ans = (1 - ans) + mod;
		printf("%lld\n",ans);
	}
	return 0;	
}

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