Numbers
HDU 6168 Numbers 2017ACM暑期多校联合训练 - Team 9 1008
Problem Description
zk has n numbers a1,a2,…,an. For each (i,j) satisfying 1≤i<j≤n, zk generates a new number (ai+aj). These new numbers could make up a new sequence b1，b2,…,bn(n−1)/2.
LsF wants to make some trouble. While zk is sleeping, Lsf mixed up sequence a and b with random order so that zk can’t figure out which numbers were in a or b. “I’m angry!”, says zk.
Can you help zk find out which n numbers were originally in a?
Input
Multiple test cases(not exceed 10).
For each test case:
∙The first line is an integer m(0≤m≤125250), indicating the total length of a and b. It’s guaranteed m can be formed as n(n+1)/2.
∙The second line contains m numbers, indicating the mixed sequence of a and b.
Each ai is in [1,10^9]
Output
For each test case, output two lines.
The first line is an integer n, indicating the length of sequence a;
The second line should contain n space-seprated integers a1,a2,…,an(a1≤a2≤…≤an). These are numbers in sequence a.
It’s guaranteed that there is only one solution for each case.
Sample Input
6
2 2 2 4 4 4
21
1 2 3 3 4 4 5 5 5 6 6 6 7 7 7 8 8 9 9 10 11
Sample Output
3
2 2 2
6
1 2 3 4 5 6
题意：
已知数组a由n个元素组成，数组b由数组a里面的任意两个元素相加组成，则数组b里面的元素个数为n(n-1)/2.
现在a数组和b数组混合在一起一共有m个元素，求解a数组里面的元素个数，并将这些元素打印出来。
模拟，混合数组里面的两个最小的元素一定是a数组里面的值，这样每次将找到的值与a数组中已有的值相加得到的值从混合数组里面删去，这样混合数组中现存的第一个值肯定就是要加入到a数组里面的，接着重复进行上面的过程，直到找齐a数组里面的元素。
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e4;
typedef long long ll;
ll a[maxn];
int main()
{
ll num, m;
while(~scanf("%lld", &m))
{
map <ll, ll> as;
ll min1=1000000009,min2=1000000000;
ll n=(sqrt(8*m+1)-1)/2;
for(ll i=0; i<m; i++)
{
scanf("%lld",&num);
if(num<min2)
{
min1=min2;
min2=num;
}
else if(num<min1)
{
min1=num;
}
as[num]++;
}
as[min1] --;
as[min2] --;
a[0] = min2;
a[1] = min1;
ll ans = 1;
while(ans != n - 1)
{
for(ll i = 0; i < ans; ++ i)///前ans个元素于第ans个元素想加，再在map中减去
{
as[a[i] + a[ans]] --;
}
map<ll, ll>::iterator it = as.begin();
while(it!= as.end())
{
if(it -> second == ll(0))///如果该元素个数为零，将该元素删除
{
as.erase(it ++);
}
else
{
break;
}
}
a[++ ans] = as.begin() -> first;///a数组元素加一
as[a[ans]] --;
}
printf("%lld
",n);
printf("%lld",a[0]);
for(int i=1; i<n; i++)
printf("% lld",a[i]);
printf("
");
}
return 0;
}