Make A SquareProblem code: MKSQR |
All submissions for this problem are available.
Statement
You are give a set of 2-d vectors (x,y) [ -10^8 ? x,y ? 10^8, x ? y ] of size n (1 ? n ? 50000 ). Lets denote the ith vector as vi.
You are to determine if the following system of equations has a solution :
a1*v1 + a2*v2 + a3*v3 + ... ai*v1 + ... an*vn = (k,k) for some arbitrary k.
All ai's are non-negative integers [ 0 ? ai ? 10^16 ] and
ALL ai's CANNOT BE ZERO ;).
In other words, you need to find some linear combination of these vectors with positive coefficient such that you end up with a vector(a,b) with a=b.
Input
First line of the input contains an integer t ( 1 ? t ? 100 ) which denotes the number of test cases to follow.
For each test case, the first line contains n ( number of vectors in the set) . n lines follow, each containing a pair of space separated integers a and b which denote the vector(a,b).
Output
Output should contain exactly t lines, with "YES" or "NO" ( without the quotes - see the sample test case for more details ).
Sample Input
2 3 0 1 -1 0 1 0 4 1 2 10 -6 -5 -1 1 -1
Sample Output
YES YES
Explanation
Test case 1 : a1 = 0 , a2 = 1, a3 = 1.
Test case 2 : a1 = 2 , a2 = 0 , a3 = 1, a4 = 3.
| Author: | anshuman_singh |
| Date Added: | 10-09-2010 |
| Time Limit: | 1 sec |
| Source Limit: | 50000 Bytes |
| Languages: | ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, F#, FORT, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TEXT, WSPC |
Comments
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HELP
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If you are still having problems, see a sample solution here.
use scanf(),printf() instead
use scanf(),printf() instead of cin,cout.
Judge ..... i will like to
Judge ..... i will like to mention that there is a problem in the input test cases..
i submitted my solution and got it accepted
but my solution gives different answer for a test case, than the accepted solution of another user..
1
3
0 0
0 0
0 0
i think the answer is "YES"..