3119: Book
http://www.lydsy.com/JudgeOnline/problem.php?id=3119
| RunID | User | Problem | Result | Memory | Time | Language | Code_Length | Submit_Time |
| 393153 | Liu_Ts | 3119 | Accepted | 904 kb | 328 ms | C++ | 504 B | 2013-04-18 07:59:10 |
题意
要求构造一个序列，
满足，长度为N，和为M，第一个数是X，
从第二项开始一定比前一项大A或比前一项小B；
保证有解。
题解
如果在第i个位置上+A，他会对所有i以后（N-i+1）个数造成影响，
即对和造成的影响是+(N-i+1）*A
那么设+A操作总共对x个数造成影响，-B操作总共对y个数造成影响。
列得：
xA-yB=M-N*X;
x+y=n*(n-1)/2;
可以把x、y解出来。
问题就变成了用1..n-1之间的数去凑x或者y。
就从n-1开始，不断减小x就可以了。
#include<cstdio>
#include<cstring>
using namespace std;
long long N,M,n,m,x,y,X,A,B;
bool f[100011];
int main()
{
scanf("%lld%lld%lld%lld%lld",&N,&X,&A,&B,&M);
m=M-N*X;n=N*(N-1)/2;
x=(m+B*n)/(A+B);y=n-x;
int now=N-1;
while(x)
{
if (x-now>=0)
f[now]=1,x-=now;
now--;
}
printf("%lld",X);
for(int i=N-1;i>=1;i--)
{
if(f[i]) X+=A;else X-=B;
printf(" %lld",X);
}
puts("");
}
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