Introduction

In this blog post, we will explore how to solve the LeetCode problem "1857" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

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:
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:
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

Explanation

Here's a breakdown of the solution:

• Topological Sort & Dynamic Programming: Detect cycles using topological sort (Kahn's algorithm). If a cycle exists, return -1. Otherwise, use dynamic programming to compute the maximum color value for each node, considering all incoming paths.
• Color Counts: Maintain a matrix counts where counts[i][c] stores the maximum number of times color c appears on any path ending at node i.

• Iterative Calculation: Start with nodes with no incoming edges and iteratively update the counts matrix for their neighbors based on the maximum color values of the current node.

• Runtime Complexity: O(n + m), where n is the number of nodes and m is the number of edges.

• Storage Complexity: O(n + m + n*26), where n is the number of nodes, m is the number of edges, and the n*26 comes from the counts array.

Code

    from collections import deque

def largestPathValue(colors: str, edges: list[list[int]]) -> int:
    n = len(colors)
    graph = [[] for _ in range(n)]
    in_degree = [0] * n

    for u, v in edges:
        graph[u].append(v)
        in_degree[v] += 1

    counts = [[0] * 26 for _ in range(n)]
    queue = deque()

    for i in range(n):
        if in_degree[i] == 0:
            queue.append(i)
            counts[i][ord(colors[i]) - ord('a')] = 1

    visited_count = 0
    max_color_value = 0

    while queue:
        u = queue.popleft()
        visited_count += 1
        max_color_value = max(max_color_value, max(counts[u]))

        for v in graph[u]:
            for i in range(26):
                counts[v][i] = max(counts[v][i], counts[u][i] + (1 if ord(colors[v]) - ord('a') == i else 0))
            in_degree[v] -= 1
            if in_degree[v] == 0:
                queue.append(v)

    if visited_count != n:
        return -1
    else:
        return max_color_value