poj 2356 Find a multiple (剩余类,抽屉原理)


Find a multiple

Time Limit: 1000MS   Memory Limit: 65536K
Total Submissions: 6965   Accepted: 3052   Special Judge

Description

The input contains N natural (i.e. positive integer) numbers ( N <= 10000 ). Each of that numbers is not greater than 15000. This numbers are not necessarily different (so it may happen that two or more of them will be equal). Your task is to choose a few of given numbers ( 1 <= few <= N ) so that the sum of chosen numbers is multiple for N (i.e. N * k = (sum of chosen numbers) for some natural number k).

Input

The first line of the input contains the single number N. Each of next N lines contains one number from the given set.

Output

In case your program decides that the target set of numbers can not be found it should print to the output the single number 0. Otherwise it should print the number of the chosen numbers in the first line followed by the chosen numbers themselves (on a separate line each) in arbitrary order.

If there are more than one set of numbers with required properties you should print to the output only one (preferably your favorite) of them.

Sample Input

5
1
2
3
4
1

Sample Output

2
2
3

Source

Ural Collegiate Programming Contest 1999

和上一道题类似。

由抽屉原理可知,一定不存在无解的情况。

然后这道题。。。wa了多次。。

原因是读错题。。

输出的是原始的a[i],不是i。。。

样例恰好a[2]=2,a[3] =3

真是sad....

 1 /*************************************************************************
 2     > File Name: code/poj/2356.cpp
 3     > Author: 111qqz
 4     > Email: [email protected]
 5     > Created Time: 2015年08月21日 星期五 13时43分41秒
 6  ************************************************************************/
 7
 8 #include<iostream>
 9 #include<iomanip>
10 #include<cstdio>
11 #include<algorithm>
12 #include<cmath>
13 #include<cstring>
14 #include<string>
15 #include<map>
16 #include<set>
17 #include<queue>
18 #include<vector>
19 #include<stack>
20 #define y0 abc111qqz
21 #define y1 hust111qqz
22 #define yn hez111qqz
23 #define j1 cute111qqz
24 #define tm crazy111qqz
25 #define lr dying111qqz
26 using namespace std;
27 #define REP(i, n) for (int i=0;i<int(n);++i)
28 typedef long long LL;
29 typedef unsigned long long ULL;
30 const int inf = 0x3f3f3f3f;
31 const int N=2E4+7;
32 int a[N];
33 int sum[N];
34 int n;
35 int p[N];
36 int main()
37 {
38     scanf("%d",&n);
39     sum[0]= 0;
40     for ( int i = 1  ; i <= n ; i++){
41     scanf("%d",&a[i]);
42     a[i] = a[i];
43     sum[i] = (sum[i-1] + a[i])%n;
44     }
45     memset(p,0,sizeof(p));
46     for ( int i = 1 ; i <= n ; i++){
47     if (sum[i]==0){
48         printf("%d\n",i);
49         for ( int j = 1 ; j <= i ; j++){
50         printf("%d\n",a[j]);
51         }
52         break;
53     }
54     if (p[sum[i]]){
55        // cout<<"111qqz"<<endl;
56         printf("%d\n",i-p[sum[i]]);
57         for ( int j = p[sum[i]]+1 ; j <= i ; j++){
58         printf("%d\n",a[j]);
59         }
60         break;
61     }
62         p[sum[i]] =  i;
63
64     }
65
66     return 0;
67 }

时间: 2024-10-10 10:08:20

poj 2356 Find a multiple (剩余类,抽屉原理)的相关文章

POJ 2356 Find a multiple (dp + 鸽笼原理)

OJ题目:click here~~ 题目分析:n个数,从中取若干个数,和为n的倍数.给出一种取法. 因为只要给出其中一种方案就行,鸽笼原理可以求出取出的数为连续的方案. 关于鸽笼原理,点这里~ 直接贴过来: 有n+1件或n+1件以上的物品要放到n个抽屉中,那么至少有一个抽屉里有两个或两个以上物品. 如果你知道这个结论: a1,a2,a3...am是正整数序列,至少存在整数k和r,1<=k<r<=m,使得ak+a(k+1)+...+a(r)是m的倍数. 证明比较简单: Sk表示前k个数之和

poj 2356 Find a multiple 鸽巢原理的简单应用

题目要求任选几个自然数,使得他们的和是n的倍数. 由鸽巢原理如果我们只选连续的数,一定能得到解. 首先预处理前缀和模n下的sum,如果发现sum[i]==sum[j] 那么(sum[j]-sum[i])%n一定为0,直接输出i+1~j就够了. 为什么一定会有解,因为sum从1~n有n个数,而模n下的数只有0~n-1,把n个数放入0~n-1个数里,怎么也会有重复,所以这种构造方法一定没问题. 其实可以O(n)实现,嫌麻烦,就二重循环无脑了. #include <iostream> #includ

POJ 2356 Find a multiple 鸽巢原理

题目来源:POJ 2356 Find a multiple 题意:n个数 选出任意个数 使得这些数的和是n的倍数 思路:肯定有解 并且解是连续的一段数 证明: 假设有m个数 a1,a2,a3...am    s1 s2 s3...sm为前缀和 s1 = a1 s2 = a1+a2 s3 = a1+a2+a3... sm = a1+a2+a3+...+am 1.如果某个前缀和si%m == 0 那么得到解 2.设x1=s1%m x2 = s2%m x3 = s3%m xm = sm%m 因为1不成

poj 2356 Find a multiple (鸽巢原理妙用)

题目链接:http://poj.org/problem?id=2356 Description The input contains N natural (i.e. positive integer) numbers ( N <= 10000 ). Each of that numbers is not greater than 15000. This numbers are not necessarily different (so it may happen that two or more

POJ 2356. Find a multiple 抽屉/鸽巢原理

Find a multiple Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 7192   Accepted: 3138   Special Judge Description The input contains N natural (i.e. positive integer) numbers ( N <= 10000 ). Each of that numbers is not greater than 15000

POJ 2356 Find a multiple 抽屉原理

从POJ 2356来体会抽屉原理的妙用= =! 题意: 给你一个n,然后给你n个数,让你输出一个数或者多个数,让这些数的和能够组成n: 先输出一个数,代表有多少个数的和,然后再输出这些数: 题解: 首先利用前缀和先预处理一下,然后如果sum[i]==0的话,很显然就直接输出i,然后接下来从第一位一直输出到第i位就行了 然后接下来直接用一个mod数组表示上一个答案为这个mod的时候的编号是多少 就是mod[sum[i]%n]=i; 然后判断一下if(mod[sum[i]%n]!=0)然后就直接从m

poj 2356 Find a multiple(鸽巢原理)

Description The input contains N natural (i.e. positive integer) numbers ( N <= 10000 ). Each of that numbers is not greater than 15000. This numbers are not necessarily different (so it may happen that two or more of them will be equal). Your task i

poj 2356 Find a multiple【鸽巢原理 模板应用】

Find a multiple Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 6651   Accepted: 2910   Special Judge Description The input contains N natural (i.e. positive integer) numbers ( N <= 10000 ). Each of that numbers is not greater than 15000

[POJ 2356] Find a multiple

Find a multiple Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 6535   Accepted: 2849   Special Judge Description The input contains N natural (i.e. positive integer) numbers ( N <= 10000 ). Each of that numbers is not greater than 15000