Uva 839 - Not so Mobile

  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 is W_l×D_l = W_r×D_r where D_l is the left distance, D_r is the right distance, W_l is the left weight and W_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 both W_l and W_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 

1

0 2 0 4
0 3 0 1
1 1 1 1
2 4 4 2
1 6 3 2

 

Sample Output 

YES

 

 

---

Jose Paulo Leal, ACM-UP'2001

 

#include<stdio.h>
#include<malloc.h>
#include<string.h>
/*
typedef struct BiTree{
    int weight, value;
    struct BiTree *lch, *rch;
}BiTree, BiNTree;
*/

int Traverse(int& balance)
{
    int wl, dl, wr, dr;
    scanf("%d%d%d%d", &wl, &dl, &wr, &dr);
/*    BiNTree left, right;

    Tree->lch = (BiNTree)malloc(sizeof(BiTree));
    Tree->lch->weight = dl;
    Tree->lch->lch = Tree->lch->rch = NULL;
    if(wl == 0)
        Tree->lch->value = Traverse(Tree->lch, balance);
    else Tree->lch->value = wl;
    
    Tree->rch = (BiNTree)malloc(sizeof(BiTree));
    Tree->rch->weight = dr;
    Tree->rch->lch = Tree->rch->rch = NULL;
    if(wr == 0)
        Tree->rch->value = Traverse(Tree->rch, balance);
    else Tree->rch->value = wr;
*/    
    if(wl == 0) wl = Traverse(balance);
    if(wr == 0) wr = Traverse(balance);
    if(wl*dl != wr*dr) balance = 0;
    return wl+wr;
}

int main()
{

    int T, n, i, j, balance;
/*    BiNTree Tree = NULL; */
    scanf("%d", &T);
    while(T--)
    {
/*        Tree = (BiNTree)malloc(sizeof(BiTree));
        Tree->weight = Tree->value = NULL;
        Tree->lch = Tree->rch = NULL;
*/
        balance = 1;
        Traverse(balance);
        if(balance) printf("YES\n");
        else printf("NO\n");
        if(T != 0) printf("\n");
        
    }
    return 0;
} 

解题思路：

题目的意思是：类似于杠杆原理你要保持平衡那么左边的重量乘以距离 == 右边的重量乘以右边的距离，只不过这里的意思是说如果mobile的左边或右边的重量变为零了，那么它下面坑定还有另外一辆mobile，此时的重量替代为下面这辆mobile的左边和右边重量的相加，

赤裸裸的水题啊，害的我要看题目两边，而且代码中可以看到，被坑加忽悠了！！！