# Disjoint Set Union on trees | Set 1

Given a tree and weights of nodes. Weights are non-negative integers. Task is to find maximum size of a subtree of a given tree such that all nodes are even in weights.

Prerequisite : Disjoint Set Union

Examples :

```Input : Number of nodes = 7
Weights of nodes = 1 2 6 4 2 0 3
Edges = (1, 2), (1, 3), (2, 4),
(2, 5), (4, 6), (6, 7)
Output : Maximum size of the subtree
with even weighted nodes = 4
Explanation :
Subtree of nodes {2, 4, 5, 6} gives the maximum size.

Input : Number of nodes = 6
Weights of nodes = 2 4 0 2 2 6
Edges = (1, 2), (2, 3), (3, 4),
(4, 5), (1, 6)
Output : Maximum size of the subtree
with even weighted nodes = 6
Explanation :
The given tree gives the maximum size.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach :We can find solution by simply running DFS on tree. DFS solution gives us answer in O(n). But, how can we use DSU for this problem? We first iterate through all edges. If both nodes are even in weights, we make union of them. Set of nodes with maximum size is the answer. If we use union-find with path compression then time complexity is O(n).

Below is the implementation of above approach :

 `// CPP code to find maximum subtree such ` `// that all nodes are even in weight ` `#include ` ` `  `using` `namespace` `std; ` ` `  `#define N 100010 ` ` `  `// Structure for Edge ` `struct` `Edge  ` `{ ` `    ``int` `u, v; ` `}; ` ` `  `/* ` `    ``'id': stores parent of a node. ` `    ``'sz': stores size of a DSU tree. ` `*/` `int` `id[N], sz[N]; ` ` `  `// Function to assign root ` `int` `Root(``int` `idx) ` `{ ` `    ``int` `i = idx; ` `     `  `    ``while``(i != id[i])  ` `        ``id[i] = id[id[i]], i = id[i]; ` `     `  `    ``return` `i; ` `} ` ` `  `// Function to find Union ` `void` `Union(``int` `a, ``int` `b) ` `{ ` `    ``int` `i = Root(a), j = Root(b); ` `     `  `    ``if` `(i != j) ` `    ``{ ` `        ``if``(sz[i] >= sz[j]) ` `        ``{ ` `            ``id[j] = i, sz[i] += sz[j]; ` `            ``sz[j] = 0; ` `        ``} ` `        ``else` `        ``{ ` `            ``id[i] = j, sz[j] += sz[i]; ` `            ``sz[i] = 0; ` `        ``} ` `    ``} ` `} ` ` `  `// Utility function for Union ` `void` `UnionUtil(``struct` `Edge e[], ``int` `W[], ``int` `q) ` `{ ` ` `  `    ``for``(``int` `i = 0; i < q; i++) ` `    ``{ ` `        ``// Edge between 'u' and 'v' ` `        ``int` `u, v; ` `        ``u = e[i].u, v = e[i].v; ` ` `  `        ``// 0-indexed nodes ` `        ``u--, v--; ` ` `  `        ``// If weights of both 'u' and 'v'  ` `        ``// are even then we make union of them. ` `        ``if``(W[u] % 2 == 0 && W[v] % 2 == 0)  ` `                    ``Union(u,v); ` `    ``} ` `} ` ` `  `// Function to find maximum ` `// size of DSU tree ` `int` `findMax(``int` `n, ``int` `W[]) ` `{ ` `    ``int` `maxi = 0; ` `    ``for``(``int` `i = 1; i <= n; i++)  ` `        ``if``(W[i] % 2 == 0)  ` `            ``maxi = max(maxi, sz[i]);    ` `             `  `    ``return` `maxi; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``/* ` `        ``Nodes are 0-indexed in this code ` `        ``So we have to make necessary changes ` `        ``while taking inputs ` `    ``*/` ` `  `    ``// Weights of nodes ` `    ``int` `W[] = {1, 2, 6, 4, 2, 0, 3}; ` ` `  `    ``// Number of nodes in a tree ` `    ``int` `n = ``sizeof``(W) / ``sizeof``(W[0]); ` ` `  `    ``// Initializing every node as ` `    ``// a tree with single node. ` `    ``for``(``int` `i = 0; i < n; i++)  ` `            ``id[i] = i, sz[i] = 1; ` ` `  `    ``Edge e[] = {{1, 2}, {1, 3}, {2, 4},  ` `                ``{2, 5}, {4, 6}, {6, 7}}; ` ` `  `    ``int` `q = ``sizeof``(e) / ``sizeof``(e[0]); ` ` `  `    ``UnionUtil(e, W, q); ` ` `  `    ``// Find maximum size of DSU tree. ` `    ``int` `maxi = findMax(n, W); ` ` `  `    ``printf``(``"Maximum size of the subtree with "``);  ` `    ``printf``(``"even weighted nodes = %d\n"``, maxi); ` `     `  `    ``return` `0; ` `} `

Output:

```Maximum size of the subtree with even weighted nodes = 4
```

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