POJ 1182: "Food Chain"

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POJ 1182: Food Chain

Problem Statement

动物王国中有三类动物A,B,C，这三类动物的食物链构成了有趣的环形。A吃B， B吃C，C吃A。 
现有N个动物，以1－N编号。每个动物都是A,B,C中的一种，但是我们并不知道它到底是哪一种。 
有人用两种说法对这N个动物所构成的食物链关系进行描述： 
第一种说法是"1 X Y"，表示X和Y是同类。 
第二种说法是"2 X Y"，表示X吃Y。 
此人对N个动物，用上述两种说法，一句接一句地说出K句话，这K句话有的是真的，有的是假的。当一句话满足下列三条之一时，这句话就是假话，否则就是真话。 
1） 当前的话与前面的某些真的话冲突，就是假话； 
2） 当前的话中X或Y比N大，就是假话； 
3） 当前的话表示X吃X，就是假话。 
你的任务是根据给定的N（1 <= N <= 50,000）和K句话（0 <= K <= 100,000），输出假话的总数。 

Interpretation

There are 3 types of animals - A, B, and C. A eats B, B eats C, and C eats A. A person tells you K statements about N animals. There are 2 types of facts, in this format:
  • 1 X Y - Animal X and Animal Y are the same type
  • 2 X Y - Animal X EATS Animal Y
You are to count how many lies there are. A statement is a lie when it meets at least one of these criteria:
  • X or Y is bigger than N (there is no such animal)
  • X is said to eat itself
  • It contradicts with a previous statement that's not a lie

Specifications

Data Structures and How

This problem utilizes a union-find data structure. However, this union-find data structure has to be altered to consider in another array, keeping track of the relationship between the node and its root. There are only three possible relationships between two nodes, X and Y: same, X eats Y, or Y eats X. For this reason the relationships are identified with the numbers 0, 1, and 2. 
This "relationship factor" has a few special properties. When the relationship between X and Y is R1 and the relationship between Y and Z is R2, then the relationship between X and Z is the sum of R1 and R2 mod 3.
If X and Y is in the same tree and we don't know the relationship of X and Y but we do know their relationship with their root, then the relationship of X and Y is the difference of the relationship of X and the relationship of Y (in respect of the root) mod 3.
These are very useful towards our program.

Why?

The disjoint set is used to store relationships between nodes that are verified to be true.

Things to Watch Out

  • In the Union-Find Set (and any other tree), each node has only one parent, not a set of parents, unlike a directed graph.
  • POJ ignores "ios_base::sync_with_stdio(false)".

Code
#include <cstdio>
#define MAXN 50005
using namespace std;

int N, rela[MAXN];

class DSSet
{
private:
    int rt[MAXN];
public:
    DSSet()
    {
        for(int i=0; i<N; i++) { rt[i] = i; rela[i] = 0; }
    }
    int root(int n)
    {
        if(rt[n] == n) return n;
        int p = rt[n];
        rt[n] = root(p);
        rela[n] = (rela[n] + rela[p]) % 3;
        return rt[n];
    }
    void merge(int m, int n, int com)
    {
        int rm = root(m), rn = root(n);
        rt[rn] = rm;
        rela[rn] = (rela[m] - rela[n] + com + 2) % 3;
    }
};

int main()
{
    int K, ans = 0; scanf("%d %d", &N, &K);
    DSSet S;
    for(int i=0; i<K; i++)
    {
        int com, x, y; scanf("%d %d %d", &com, &x, &y);
        if(x > N || y > N || (x == y && com == 2)) ans++; // definite LIE - prelimanaries
        else if(S.root(x) == S.root(y))
        {
            if(com == 1 && rela[x] != rela[y]) { ans++; continue; } // definite LIE
            if(com == 2 && (rela[x] + 1)%3 != rela[y]) { ans++; continue; } // definite LIE
        }
        else S.merge(x, y, com);
    }
    printf("%d\n", ans);
}

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