HDU3038 How Many Answers Are Wrong【带权并查集 区间统计】

How Many Answers Are Wrong

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 15928    Accepted Submission(s): 5590

 

Problem Description

TT and FF are ... friends. Uh... very very good friends -________-b

FF is a bad boy, he is always wooing TT to play the following game with him. This is a very humdrum game. To begin with, TT should write down a sequence of integers-_-!!(bored).

Then, FF can choose a continuous subsequence from it(for example the subsequence from the third to the fifth integer inclusively). After that, FF will ask TT what the sum of the subsequence he chose is. The next, TT will answer FF's question. Then, FF can redo this process. In the end, FF must work out the entire sequence of integers.

Boring~~Boring~~a very very boring game!!! TT doesn't want to play with FF at all. To punish FF, she often tells FF the wrong answers on purpose.

The bad boy is not a fool man. FF detects some answers are incompatible. Of course, these contradictions make it difficult to calculate the sequence.

However, TT is a nice and lovely girl. She doesn't have the heart to be hard on FF. To save time, she guarantees that the answers are all right if there is no logical mistakes indeed.

What's more, if FF finds an answer to be wrong, he will ignore it when judging next answers.

But there will be so many questions that poor FF can't make sure whether the current answer is right or wrong in a moment. So he decides to write a program to help him with this matter. The program will receive a series of questions from FF together with the answers FF has received from TT. The aim of this program is to find how many answers are wrong. Only by ignoring the wrong answers can FF work out the entire sequence of integers. Poor FF has no time to do this job. And now he is asking for your help~(Why asking trouble for himself~~Bad boy)

Input

Line 1: Two integers, N and M (1 <= N <= 200000, 1 <= M <= 40000). Means TT wrote N integers and FF asked her M questions.

Line 2..M+1: Line i+1 contains three integer: Ai, Bi and Si. Means TT answered FF that the sum from Ai to Bi is Si. It's guaranteed that 0 < Ai <= Bi <= N.

You can assume that any sum of subsequence is fit in 32-bit integer.

Output

A single line with a integer denotes how many answers are wrong.

Sample Input

10 5
1 10 100
7 10 28
1 3 32
4 6 41
6 6 1

Sample Output

1

Source

2009 Multi-University Training Contest 13 - Host by HIT

问题链接：HDU3038 How Many Answers Are Wrong

问题描述：多组数据。TT 写一串数字，对 FF 不可见。FF 选择一个区间（会重复操作）， TT 把这个区间的和告诉 FF，然而，一些和是不正确的，所以，有一些答案是矛盾的，根据这些矛盾求出答案错误的个数。注意两点：1、TT 给的一个和是正确的，如果它与之前给的和不矛盾。2、FF 发现一个与之前矛盾的和之后，该和不再参与之后的分析，直接被抛弃了。

解题思路：https://blog.csdn.net/wlx65003/article/details/74926616

AC的C++代码:

#include
#include

using namespace std;

const int N=200005;
int w[N],pre[N];//w[i]表示结点i到其父节点的距离
int res; 

void init(int n)
{
	for(int i=0;i<=n;i++){
		pre[i]=i;//初始化每个节点的父节点为自己 
		w[i]=0;//自己到自己的距离为0 
	} 
}

int find(int x)
{
	if(x!=pre[x]){
		int r=pre[x];
		pre[x]=find(r);
		w[x]+=w[r]; 
	} 
	return pre[x];
}


void join(int x,int y,int c)
{
	int fx=find(x);
	int fy=find(y);
	if(fx!=fy){
		pre[fy]=fx;
		w[fy]=w[x]-w[y]+c;
	}
	else{
		if(w[y]-w[x]!=c) res++;
	}
}

int main()
{
	int n,m,a,b,c;
	while(~scanf("%d%d",&n,&m)){
		init(n);
		res=0;
		while(m--){
			scanf("%d%d%d",&a,&b,&c);
			join(a-1,b,c); 
		}
		printf("%d\n",res);
	}
	return 0;
}