uva839

  Not so Mobile 

Before being an ubiquous communications gadget, a mobile was just a structure made of strings and wires suspending colourfull things. This kind of mobile is usually found hanging over cradles of small babies.

The figure illustrates a simple mobile. It is just a wire, suspended by a string, with an object on each side. It can also be seen as a kind of lever with the fulcrum on the point where the string ties the wire. From the lever principle we know that to balance a simple mobile the product of the weight of the objects by their distance to the fulcrum must be equal. That isW_l×D_l =W_r×D_r whereD_l is the left distance,D_r is the right distance,W_l is the left weight andW_r is the right weight.

In a more complex mobile the object may be replaced by a sub-mobile, as shown in the next figure. In this case it is not so straightforward to check if the mobile is balanced so we need you to write a program that, given a description of a mobile as input, checks whether the mobile is in equilibrium or not.

Input 

The input begins with a single positive integer on a line by itself indicating the number of the cases following, each of them as described below. This line is followed by a blank line, and there is also a blank line between two consecutive inputs.

The input is composed of several lines, each containing 4 integers separated by a single space. The 4 integers represent the distances of each object to the fulcrum and their weights, in the format:W_l D_l W_r D_r

If W_l or W_r is zero then there is a sub-mobile hanging from that end and the following lines define the the sub-mobile. In this case we compute the weight of the sub-mobile as the sum of weights of all its objects, disregarding the weight of the wires and strings. If bothW_l andW_r are zero then the following lines define two sub-mobiles: first the left then the right one.

Output 

For each test case, the output must follow the description below. The outputs of two consecutive cases will be separated by a blank line.

Write `YES' if the mobile is in equilibrium, write `NO' otherwise.

Sample Input 

10 2 0 40 3 0 11 1 1 12 4 4 21 6 3 2

Sample Output 

YES

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Jose Paulo Leal, ACM-UP'2001

#include<stdio.h>  #include<string.h>  int ok;int run_tree(int W1,int D1,int W2,int D2){int w1,w2,d1,d2;if(W1==0){scanf("%d%d%d%d",&w1,&d1,&w2,&d2);W1=run_tree(w1,d1,w2,d2);}if(W2==0){scanf("%d%d%d%d",&w1,&d1,&w2,&d2);W2=run_tree(w1,d1,w2,d2);}if(ok&&W1*D1!=W2*D2)ok=0;return W1+W2;}main(){int n,w1,w2,d1,d2;freopen("D:\\bbbb.txt","r",stdin);scanf("%d",&n);while(n--){scanf("%d%d%d%d",&w1,&d1,&w2,&d2);ok=1;run_tree(w1,d1,w2,d2);printf(ok?"YES\n":"NO\n");if(n!=0)  printf("\n");}return 0;}