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# 1857. Largest Color Value in a Directed Graph

<https://leetcode.com/problems/largest-color-value-in-a-directed-graph>

## Description

There is a **directed graph** of `n` colored nodes and `m` edges. The nodes are numbered from `0` to `n - 1`.

You are given a string `colors` where `colors[i]` is a lowercase English letter representing the **color** of the `ith` node in this graph (**0-indexed**). You are also given a 2D array `edges` where `edges[j] = [aj, bj]` indicates that there is a **directed edge** from node `aj` to node `bj`.

A valid **path** in the graph is a sequence of nodes `x1 -> x2 -> x3 -> ... -> xk` such that there is a directed edge from `xi` to `xi+1` for every `1 <= i < k`. The **color value** of the path is the number of nodes that are colored the **most frequently** occurring color along that path.

Return *the **largest color value** of any valid path in the given graph, or* `-1` *if the graph contains a cycle*.

**Example 1:**

![](https://assets.leetcode.com/uploads/2021/04/21/leet1.png)

```

**Input:** colors = "abaca", edges = [[0,1],[0,2],[2,3],[3,4]]
**Output:** 3
**Explanation:** The path 0 -> 2 -> 3 -> 4 contains 3 nodes that are colored "a" (red in the above image).
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2021/04/21/leet2.png)

```

**Input:** colors = "a", edges = [[0,0]]
**Output:** -1
**Explanation:** There is a cycle from 0 to 0.
```

**Constraints:**

* `n == colors.length`
* `m == edges.length`
* `1 <= n <= 105`
* `0 <= m <= 105`
* `colors` consists of lowercase English letters.
* `0 <= aj, bj < n`

## ac

```java
```