Problem H
Special Subsequences
Input File: ph.in
Time Limit: 5 seconds
Given a sequence of n integers x1,x2, …, xn and an integer k, 1≦k≦n,
we want to know if there exists a consecutive subsequence xi ,xi+1, …, xj for
some i and j, 1≦i≦j≦n, such that the sum
Is divisible by k or not.
For example, let n = 7 and k = 6. In the sequence of 7 integers.
2,5,1,-4,5,9,3
The sum of the following consecutive subsequences can be divisible by k = 6.
1. i = 2, j = 3: 5+1 = 6,
2. i = 1, j = 6: 2+5+1-4+5+9 = 18,
3. i = 6, j = 7: 9+3 = 12,
We are going to write a very efficient program to solve the problem with
large numver of integers in a short span of time. It is required to print only
one particular solution, not all solutions. The solution we want to print is the
first such subsequence. The first solution is the one with the smallest value
of i. In the above example, the answer we want is i = 1 and j = 6. If there
are more than one solution with the same value of i, we want the one with
smallest valu of j.
An instance of the problem consists of
1. the number of integers n,
2. the sequence of integer xi , 1 ≦i≦n, and
3. the divisor k.
These data are stored in +2 lines in the input file.
1. The first line is the integer n.
2. The following is lines are the n integers xi , 1≦i≦n. Each line
contains at most 20 integers.
3. The last line is the integer k.
In this problem, we assume that 1≦ n ≦100000, and -230 ≦ xi ≦ 230.
Note that the test data file may contain more than one instances. The last
instance is followed by a line containing a single 0.
在此將題目修改 1 ≦ k ≦ 2147483647, 並且將所有數字排在同一行並不會切割
The outputs for each test case are the two integers i and j which are the indexes of
the consecutive subsequence whose sum is divisible by k. Print exactly one space
between i and j. If there are no solution print “no solutions.”
7 2 5 1 -4 5 9 3 6 10 11 -3 1 13 -5 6 1 -8 -4 5 10 0
1 6 5 9
公開 測資點#0 (100%): 5.0s , <10M