LeetCode 2065: Maximum Path Quality of a Graph Solution
Master LeetCode problem 2065 (Maximum Path Quality of a Graph), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.
2065. Maximum Path Quality of a Graph
Problem Explanation
Explanation
To solve this problem, we can use a dynamic programming approach. We will iterate through all possible paths starting and ending at node 0 within the given time constraint. At each step, we will calculate the maximum quality of the path by considering the values of the nodes visited so far.
We will maintain a 3D dp array where dp[i][j][k] represents the maximum quality of a path starting at node 0, ending at node i, and taking exactly j seconds to travel, with k representing the bitmask of nodes visited in the path.
Finally, we will iterate through all possible paths within the time constraint and return the maximum quality found.
Time Complexity
The time complexity of this approach is O(n * maxTime * 2^n), where n is the number of nodes and maxTime is the maximum time constraint.
Space Complexity
The space complexity is O(n * maxTime * 2^n) for the dp array.
Solution Code
class Solution {
public int maximumPathQuality(int[] values, int[][] edges, int maxTime) {
int n = values.length;
int[][][] dp = new int[n][maxTime + 1][1 << n];
for (int t = 1; t <= maxTime; t++) {
for (int[] edge : edges) {
int u = edge[0], v = edge[1], time = edge[2];
for (int mask = 0; mask < (1 << n); mask++) {
dp[v][t][mask | (1 << v)] = Math.max(dp[v][t][mask | (1 << v)], dp[u][t - time][mask] + values[v]);
dp[u][t][mask | (1 << u)] = Math.max(dp[u][t][mask | (1 << u)], dp[v][t - time][mask] + values[u]);
}
}
}
int maxQuality = 0;
for (int t = 1; t <= maxTime; t++) {
for (int i = 0; i < n; i++) {
maxQuality = Math.max(maxQuality, dp[i][t][(1 << n) - 1]);
}
}
return maxQuality;
}
}Try It Yourself
Loading code editor...
Related LeetCode Problems
Frequently Asked Questions
How to solve LeetCode 2065 (Maximum Path Quality of a Graph)?
This page provides optimized solutions for LeetCode problem 2065 (Maximum Path Quality of a Graph) in Java, C++, and Python, along with a detailed explanation and an interactive code editor to test your code.
What is the time complexity of LeetCode 2065 (Maximum Path Quality of a Graph)?
The time complexity for LeetCode 2065 (Maximum Path Quality of a Graph) varies by solution. Check the detailed explanation section for specific complexities in Java, C++, and Python implementations.
Can I run code for LeetCode 2065 on DevExCode?
Yes, DevExCode provides an interactive code editor where you can write, test, and run your code for LeetCode 2065 in Java, C++, or Python.