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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