Even Cycle Edge Addition

You are given an integer

n

representing the number of nodes in an undirected graph (initially containing no edges) and a list of queries edges, where edges[i] = [u, v, w]. For each query, you attempt to add an edge between nodes

u

and

v

with weight

w

(where

w

is either 0 or 1). However, an edge is only successfully added if, after its addition, every cycle in the resulting graph has an even sum of weights. If adding the edge would create any cycle with an odd sum of weights, the edge is discarded. Process all edges in the given order and return the total number of edges successfully added to the graph. Constraints:

1 \le n \le 10^5

1 \le edges.length \le 10^5

0 \le u_i, v_i < n

w_i \in \{0, 1\}

JavaDSUXOR Sum

Read

Dynamic Cycle Parity Maintenance

You are given

n

nodes labeled from

0

n-1

and a sequence of undirected edges. Each edge is given as a triplet

[u_i, v_i, w_i]

, where

u_i

and

v_i

are nodes and

w_i \in \{0, 1\}

is the weight. Initially, the graph has no edges. You must process the edges in the given order. An edge is added to the graph if and only if its addition does not create any cycle whose sum of edge weights is odd. Return the total number of edges successfully added to the graph. Constraints:

1 \le n \le 10^5

1 \le \text{edges.length} \le 10^5

0 \le u_i, v_i < n

w_i \in \{0, 1\}

JavaDSU

Read

Even Cycle Edge Addition

You are given an integer

n

u

and

v

with weight

w

(where

w

1 \le n \le 10^5

1 \le edges.length \le 10^5

0 \le u_i, v_i < n

w_i \in \{0, 1\}

JavaDSUXOR Sum

Read

Dynamic Cycle Parity Maintenance

You are given

n

nodes labeled from

0

n-1

and a sequence of undirected edges. Each edge is given as a triplet

[u_i, v_i, w_i]

, where

u_i

and

v_i

are nodes and

w_i \in \{0, 1\}

1 \le n \le 10^5

1 \le \text{edges.length} \le 10^5

0 \le u_i, v_i < n

w_i \in \{0, 1\}

JavaDSU

Read