101264: [AtCoder]ABC126 E - 1 or 2
Description
Score : $500$ points
Problem Statement
There are $N$ cards placed face down in a row. On each card, an integer $1$ or $2$ is written.
Let $A_i$ be the integer written on the $i$-th card.
Your objective is to guess $A_1, A_2, ..., A_N$ correctly.
You know the following facts:
- For each $i = 1, 2, ..., M$, the value $A_{X_i} + A_{Y_i} + Z_i$ is an even number.
You are a magician and can use the following magic any number of times:
Magic: Choose one card and know the integer $A_i$ written on it. The cost of using this magic is $1$.
What is the minimum cost required to determine all of $A_1, A_2, ..., A_N$?
It is guaranteed that there is no contradiction in given input.
Constraints
- All values in input are integers.
- $2 \leq N \leq 10^5$
- $1 \leq M \leq 10^5$
- $1 \leq X_i < Y_i \leq N$
- $1 \leq Z_i \leq 100$
- The pairs $(X_i, Y_i)$ are distinct.
- There is no contradiction in input. (That is, there exist integers $A_1, A_2, ..., A_N$ that satisfy the conditions.)
Input
Input is given from Standard Input in the following format:
$N$ $M$ $X_1$ $Y_1$ $Z_1$ $X_2$ $Y_2$ $Z_2$ $\vdots$ $X_M$ $Y_M$ $Z_M$
Output
Print the minimum total cost required to determine all of $A_1, A_2, ..., A_N$.
Sample Input 1
3 1 1 2 1
Sample Output 1
2
You can determine all of $A_1, A_2, A_3$ by using the magic for the first and third cards.
Sample Input 2
6 5 1 2 1 2 3 2 1 3 3 4 5 4 5 6 5
Sample Output 2
2
Sample Input 3
100000 1 1 100000 100
Sample Output 3
99999