P3617 Resistor Network

What is a resistor? Everyone should know. What is a circuit? You probably know as well. However, in this problem, the definition of a circuit is a bit different: Every circuit has a positive terminal on the left and a negative terminal on the right. Specifically, circuits are defined as follows: - A single $1\Omega$ resistor (together with its two endpoints) is a circuit. (Although a wire can be regarded as a $0\Omega$ resistor, a wire alone is not a circuit.) - If $A$ and $B$ are both circuits, let $1,2,3$ be three nodes from left to right. Connect the positive and negative terminals of $A$ to $1$ and $2$, respectively, and those of $B$ to $2$ and $3$, respectively. Then the part from $1$ to $3$ is a circuit, with $1$ as the positive terminal and $3$ as the negative terminal. - If $A$ and $B$ are both circuits, let $1,2,3,2',3',1'$ be six nodes, where $1$ is to the left of $2$ and $3$, $2$ is to the left of $2'$, $3$ is to the left of $3'$, and $2'$ and $3'$ are to the left of $1'$. There are wires between $1$ and $2$, between $1$ and $3$, between $2'$ and $1'$, and between $3'$ and $1'$. Connect the positive and negative terminals of $A$ to $2$ and $2'$, respectively, and those of $B$ to $3$ and $3'$, respectively. Then the part from $1$ to $1'$ is a circuit, with $1$ as the positive terminal and $1'$ as the negative terminal. Now you are given a circuit. Find the resistance between its positive and negative terminals.

Cjwssb recently encountered a tough problem in physics. He does not know how to compute the equivalent resistance of a circuit. He turned to you for help. This circuit satisfies the following constraints: 1. The circuit consists only of wires and resistors of $1\Omega$. 2. The circuit is connected from left to right, that is, for every resistor or wire with endpoints $x,y$, it holds that $x

The first line contains two positive integers $n,m$, the numbers of nodes and resistors. Nodes are numbered from left to right, so a smaller index is to the left of a larger index. Each of the next $m$ lines contains three integers $a_i,b_i,c_i$, meaning there is a resistor between nodes $a_i$ and $b_i$ with resistance $c_i$, where $c_i$ is either $0$ or $1$, and for every $i$ it is guaranteed that $a_i

Output a real number, the total resistance, rounded to three decimal places.

[Sample Explanation] Draw the diagram and the answer is obvious. [Constraints] | Score | $n$ | $m$ | |:-:|:-:|:-:| | $20\%$ | $n\le 5$ | $m\le 5$ | | $50\%$ | $n\le 100$ | $m\le 120$ | | $70\%$ | $n\le 1000$ | $m\le 1200$ | | $100\%$ | $n\le 10^5$ | $m\le 1.2\times 10^6$ | P.S. The testdata are randomly generated under a fixed $n$, and the answer is guaranteed not to exceed 10 000. By: saffah. Translated by ChatGPT 5