Sum of these two numbers is 190 + 25 = 215, which will be represented by 2->1->5->null. . Find the 0-based index of the first. Level up your coding skills and quickly land a job. Static data structure: Static data structure has a fixed. Every cell of the maze contains these numbers 1, 2 or 3. Write a function that takes an array as an argument and returns the length of the longest bitonic subsequence. Find Complete Code at GeeksforGeeks Article: video is contributed by Anant PatniPlease Like,. The questions will be featured from a pool of public problems from the GFG Practice Portal. Find the maximum sum among such. The task is to check if the linked list has a loop. j], find the two smallest numbers and add them, you will get score for that subarray. If the sum obtained by applying Kadane’s algorithm is greater than the overall maximum sum, update the overall maximum sum. For the given query of: Type 1: given l and r (they are positions), and task is to print the Largest sum Contiguous Subarray. If we calculate A 3, then the number of triangles in Undirected Graph is equal to trace (A 3) / 6. Jones and published in 1963. A leaf node is also considered as SumTree. Find if there is any subarray with a sum equal to zero. It may be assumed that size of array is more than m*k. Example 1: Input: N = 7 a [] = {2,6,1,9,4,5,3} Output:Given an array arr[] of size N and an integer K. An efficient solution is based on Largest rectangular sub-matrix whose sum is 0 which reduces the time complexity to O (n^3). So in the result vector, we will add arr [currIndex]. Given a linked list of N nodes. Following is an example of SumTree. The maximum sum path may or may not go through the root. Maximum path sum in a triangle. Follow the steps below to solve the given problem: We will calculate the total sum of the given array. To solve the problem, we will do the post-order traversal. n-1] containing n positive integers, a subsequence of arr [] is called Bitonic if it is first increasing, then decreasing. Note:The cells are named with an integer. Solve company interview questions and improve your coding intellect. Next largest is ‘y’ but that occurs 0 times in k so we will skip it. . MIN_VALUE. Problem Submissions Comments. Steps to implement-. A negative cycle is one in which the overall sum of the cycle comes negative. Analysis of Graph Coloring Using Greedy Algorithm: The above algorithm doesn’t always use minimum number of colors. Example 2: Input: N = 3, S = 29 Output: -1 Explanation: There is no such three digit number whose sum is 29. NOTE: The adjacency list denotes the edges of the graph where edges [i] stores. Back to Explore Page. Find the length of each subarray. Nodes are labeled from 0 to n-1, the task is to check if it contains a negative weight cycle or not. Third line for each testcase contains two cell numbers whose nearest meeting cell needs to be found. Given adjacency list adj as input parameters . GfG Weekly + You = Perfect Sunday Evenings! Given a number N, the task is to find the largest prime factor of that number. The sum is 110 and no two elements are adjacent. Algorithm to Find Negative Cycle in a Directed Weighted Graph Using Bellman-Ford: Initialize distance array dist [] for each vertex ‘v‘ as dist [v] = INFINITY. Given an N-Ary tree, find and return the node for which sum of data of all children and the node itself is maximum. This gives sum = 13. Given an array A[] of size N, return length of the longest subarray of non- negative integers. Example 1: Input: 1 / \ 2 3 / \ / \ 4 5 6 7 Output: 28 Explanation Level up your coding skills and quickly land a job. The space complexity is also O(V + E) since we need to store the adjacency list and the visited array. 1). It is done when a certain node creates an imbalance in the heap due to some operations on that node. 2. Remove all nodes which don't lie in any path with sum>= k; Maximum spiral sum in Binary Tree; Sum of nodes at k-th level in a tree represented as string; Sum of all the numbers that are formed from root to leaf paths; Merge Two Binary Trees by doing Node Sum (Recursive and Iterative) Find root of the tree where children id sum for every node. Welcome to our daily problem solving session where Siddharth will be tackling the Problem of The Day. Hence, maximum circular subarray sum is 22. Clearing the DSA round for the Interviews, as these are the questions generally asked in the companies like Amazon, Microsoft, Google, etc. If there is no cycle in the graph then return -1. Your task is to complete the function LargestSubset. Time complexity: O(N 2) Auxiliary Space: O(1) Efficient Approach: The idea is to use the Kadane’s Algorithm to find the maximum subarray sum and store the starting and ending index of the subarray having maximum. If the stack is not empty, compare top most element of stack with next. The task is to check if the given linked list is palindrome or not. Input: a [] = {10, -10, 20, -40} k = 6 Output: -10 Explanation: The 6th largest sum among sum of all contiguous subarrays is -10. Here adj [i] contains vectors of size 2, where the first integer in that. Approach: The given problem can be solved by finding all the paths from a given source to a destination and using a Priority Queue to find the K th largest weight. Follow the below steps to Implement the idea: Initialize the variables max_so_far = INT_MIN and max_ending_here = 0. Traverse through all pairs again and search for X – (current pair sum) in the hash table. Input: list= [12 4 -5 7 -9] Output: 5. . Then the next search space possible will be in the. However, the longest path problem has a linear time solution for directed acyclic graphs. ; Create a variable curr_sum and increase the value of curr_sum by arr[i] while traversing the array from index 0 till the value of curr_sum is less than halfSum; When. Prefix Sum 136. Example 1: Input: N = 5 Output: 120 Explanation : 5! = 1*2*3*4*5 = 120 Example 2: Input: N = 10 Output: 3628800 Explanation :For m = 1, the number is 168 + 3 = 171, the sum of whose digits is 9. - GitHub - iamujj15/Leetcode-GFG-Solutions: This Repository contains my solution for the problems I p. Given an array a [] of size N, and Q queries of two types 1 and 2. Print the shortest path between them. Your task is to complete the function maxSubMatrixSumQueries () which takes the 2D array of integers mat, n, m, queries and q as input parameters and returns an array of integers denoting the maximum sum for each query. . 3] contains equal number of 0's and 1's. Find the maximum for each and every contiguous subarray of size K. Linear data structure: Data structure in which data elements are arranged sequentially or linearly, where each element is attached to its previous and next adjacent elements, is called a linear data structure. Course Description. You need to find the the length of the largest cycle in the maze. Daily video editorials. But in the case of the number of elements being large, the array in which we store the contiguous. 6% Submissions: 239K+ Points: 1. Explore Page. Given two strings denoting non-negative numbers X and Y. Example 1: Input: Output: 1 Explanation: 3 -> 3 is a cycle. Example 1: Input: E = [[0,1,9]] S = 0 Output: 0 9 Explanation : Shortest distance of all nodes from source is printed. Sum of array elements possible by appending arr [i] / K to the end of the array K times for array elements divisible by K. 594 views 1 month ago GFG POTD series. The task is to find the sum of weights of the edges of the Minimum Spanning Tree. (Order of array remains unchanged). To compute sum of current window, remove first element of previous window and add. at any step, the sum of the square of digits obtained is a single-digit number except 1 or 7. Queries to check if the path between two nodes in a tree is a palindrome. Example 1: Input: 1 / 2 3 / / 4 5 6 7 Output: 28 ExplanationLn 1, Col 1. Rather than going into much theory, let us see the process of arriving at lucky numbers,Take the set of integers1, 2, 3, 4, 5, 6. second = Integer. The idea is to. You are given an array arr [] of size n. Therefore, we can choose all the positive elements from the array, and each time we can make. Find the 0-based index of the first row that has the maximum number of 1's. Thus, the explicit formula is . Relax all the edges (u,v,weight) N-1 times as per the below condition: dist [v] = minimum (dist [v], distance. If total array size is not multiple of k, then we can take partial last array. A sequence, sorted in increasing order is. Nodes are labeled from 0 to n-1, the task is to check if it contains a negative weight cycle or not. This is the highest possible sum of a. Given an array. Pre-requisite: BS-18. If maxm < 0, then print the value of maxm. Minimize sum of product of same-indexed elements of two arrays by reversing a subarray of one of the two arrays. World Cup Hack-A-Thon; GFG Weekly Coding Contest; Job-A-Thon: Hiring. Find the length of the longest sub-sequence such that elements in the subsequence are consecutive integers, the consecutive numbers can be in any order. Longest path is from 5 to 7 of length 5. Example 2: The above graph has two cycles of length 4 and 3, the product of cycle lengths is 12. Auxiliary Space: O (V+E) If you like GeeksforGeeks and would like to contribute, you can also write an article using write. the used approach of using sum at each node until the node is again repeated in the cycle. Follow the steps below to solve the problem: Initialize a variable, say maxm, to store the largest element of the given array. Given a 2D array, find the maximum sum submatrix in it. Beginner's DSA Sheet; Love Babbar Sheet; Top 50 Array Problems; Top 50 String Problems; Top 50 DP Problems; Top 50 Graph Problems; Top 50 Tree Problems; Contests. After partitioning, each subarray has their values changed to become the maximum value of that subarray. Also, the number of colors used sometime depend on the order in which vertices are processed. Given a Directed Graph with V vertices (Numbered from 0 to V-1) and E edges, check whether it contains any cycle or not. The solution is based on the fact that “ If a graph has no odd length cycle then it must be Bipartite, i. 2) Initialize a count variable to 0. This is the best place to expand your knowledge and get prepared for your next interview. Given a binary tree, find the largest value in each level. Menu. The sum of nodes considering 2 as the root of subtree is 2 = 2. max and update the first max to the current element. In case of multiple subarrays, return the subarray indexes which come first on moving from left to right. Find the contiguous sub-array(containing at least one number) which has the maximum sum and return its sum. Return -1 if there are no cycles. Print a given matrix in spiral form using the simulation approach: To solve the problem follow the below idea: Draw the path that the spiral makes. Convert all even weight edges into two. This is O (N) runtime: each edge (of which there's at most N) is followed at most 3 times in the graph, and the cache is updated exactly once for each node in the graph. In case you need more clarity about a question, you may use the expected output button to see output for your given input. This is the best place to expand your knowledge and get prepared for your next interview. The value of currsum exceeds the desired sum by currsum – sum. Maximize array product by changing any array element arr [i] to (-1)*arr [i] - 1 any number of times. second and repeat step 1 until currIndex is not -1 or it does not. e entry/exit points are unidirectional doors like valves). Minimum and maximum node that lies in the path connecting two nodes in a Binary Tree. Global data. Example 1: Input: N = 8 K = 3 A [] = {8 5 9 10 5 6 19 8} Output: 38 Explanation: Possible increasing subsequence of length 3 with maximum possible sum is 9 10 19. Let the set be E. Back to Explore Page. Whether you're preparing for your first job interview or aiming to upskill in this ever-evolving tech landscape, GeeksforGeeks Courses are your key to success. I used a dfs on graph approach in. The element at front of the Qi is the largest and element at rear/back of Qi is the smallest of current window. If no cycle exists, return -1. The task is to find the sum of weights of the edges of the Minimum Spanning Tree. ; Increase the. The two sub-arrays are [1, 2, 5] [2, 3]. Example 2: Input: n = 7 A [] = {1, 2, 0, 3, 2, 4, 5} Output: 5 Explanation: The largest element of given array is 5. Method 1: We can go through the brute force by checking every possible path but that is much time taking so we should try to. Auxiliary Space: O(n), where N represents the size of the given array. Given a boolean 2D array of n x m dimensions where each row is sorted. Let A [] [] be the adjacency matrix representation of the graph. @Mingle_Tech @Code_Star #mingletech #Mingle_TechThank you for watching this video 💛geeks for geeks, Missing Number in matrix, Absolute List Sorting, Bal. From the map, find the number of subarrays previously found having sum equal to currsum-sum. Example 1: Input: n = 3, edges. Recommended: Please solve it on “ PRACTICE ” first, before moving on to the solution. More than 100 million people use GitHub to discover, fork, and contribute to over 330 million projects. Given the graph consist of pair and weight attached to it. Design 123. Type 2: given type, index, and value, update aindex = value. Inputs are same. org. Given a binary tree with a value associated. But since both elements are adjacent, it is not a valid pair. In the worst case, the randomized function may always pick a corner element. The task is to find the largest sum of a cycle in the maze(Sum of a cycle is the sum of the cell indexes of all cells present in that cycle). Example 2: Input: nums = [1] Output: 1 Explanation: The subarray [1] has the largest sum 1. We fix the left and right columns one by one and find the largest sub-array with 0 sum contiguous rows for every left and right column pair. NOTE: If there is a tie, then compare with segment's length and return segment which has maximum length. Input: N = 4 Arr[] = {-1,-2,-3,-4} Output: -1 Explanation: Max subarray sum is -1 of element (-1) Your Task: You don't need to read input or print anything. Maximum subsequence sum such that no three are consecutive in O (1) space. Given adjacency list adj as input parameters . Menu. Jobs. We one by one remove every edge from the graph, then we find the shortest path between two corner vertices of it. The currently found number can not occur again so it is. To add x to sum, -x can be subtracted from it because sum- (-x) = sum + x. Example 2: Input: N. Solved the problem of finding the starting point of a cycle in Linked list; Day 78. There is a cycle in a graph only if there is a back edge present in the graph. Example 1: Input: 1 / \ 2 3 / \ / \ 4 5 6 7 Output: 28 Explanation Your task is to complete the function isNegativeWeightCycle () which takes n and edges as input paramater and returns 1 if graph contains negative weight cycle otherwise returns 0. Approach: The given problem can be solved using. Time Complexity of the above solution is O (n2). Solved the problem Split Array Largest Sum using Binary Search; Binary-Search Repo: Day 83. Example 1: Input: n = 3, edges. Given a matrix of size NxM and a list of queries containing (a,b) pairs. The Karger’s algorithm would produce this Min-Cut if and only if none of the edges in set {e 1, e 2, e 3, . Naive Approach: The naive approach is to generate all the possible subarray and print that subarray which has maximum sum. , 4/42. Largest sum of digits in all Divisors. Maximize product of array by replacing array elements with its sum or product with element from another array. Following are some standard algorithms that are Greedy algorithms: 1) Kruskal’s Minimum Spanning Tree (MST): In Kruskal’s algorithm, we create an MST by picking edges one by one. If there is a prefix with a sum equal to ( x – s), then the subarray with the given sum is found. tli : Row number of top left of. Explanation: The odd Numbers in the range are -9, -7, -5, -3, -1, 1, 3, 5, 7, 9 and the 8th Largest odd number is -5. Input : s = 20, d = 3 Output : 299. Inputs to queries are left top and right bottom indexes of submatrix whose sum is to find out. So, this DSA sheet by Love Babbar contains 450 coding questions which will help in: Understanding each and every concept of DSA. 4) Return result. So the first position of the kth sequence will be occupied by the number present at index = k / (n-1)! (according to 1-based indexing). Examples: Input : 12345 Output : 15 Input : 45632 Output :20. You don't need to read input or print. K is the size of subarrays and M is the count of subarray. The task is to find the sum of weights of the edges of the Minimum Spanning Tree. We can easily solve this problem in linear time using Kadane’s algorithm. Sliding Window 100. Count of largest sized groups while grouping according to product of digits; Find the subsequence with given sum in a superincreasing sequence; Find the size of largest group where groups are according to the xor of digits; Maximum number of times Array can be reduced in half when its all elements are evenThe task is to complete the function isPalindrome() which takes head as reference as the only parameter and returns true or false if linked list is palindrome or not respectively. Let e = uv be an edge of G and consider the graph H = G – uv. nirazv April 20, 2021, 8:32am 8. Given an array Arr[] of N integers. first = Integer. Constraints: * 1 <= nums. Step 2: Pick edge 8-2. Each cell may have multiple entry points but not more than one exit (ie. The idea is to. If there are more than or equal to 3 positive elements or more than or equal to 3 negative elements, then the condition arr[i]+arr[j]+arr[k] = an element of the array cannot be true. This is the best place to expand your knowledge and get prepared for your next interview. The task is to find subtree with maximum sum in the tree and return its sum. This is not true, The graph may have no hamiltonian cycle and in the same time have a circuit with a weight larger then n, consider just the case of a graph with tree vertices, say 1,2,3. Recommended: Please solve it on “ PRACTICE ” first, before moving on to the solution. Given two numbers 'N' and 'S' , find the largest number that can be formed with 'N' digits and whose sum of digits should be equals to 'S'. Longest subarray of only 0's or 1's with atmost K flips. Hence this is the valid answer. To find the largest subarray having a sum greater than zero, we check the value of. For each element in the array: Push the element onto the max heap. Given a singly linked list of size N of integers. Shortest path length between two given nodes such that adjacent nodes are at bit difference 2. No cycle is formed, include it. If you are a frequent user of our Practice Portal, you may have already solved the featured Problem of the Day in the past. Efficient Approach: The idea is to consider the odd elements as 1 and even elements as -1 and return the length of the longest sub-array with the sum equal to 0. With over 1500+ candidates placed in 200+ companies in the last 1 year, Job-A-Thon brings you yet another chance to get placed in top companies. For each connected component, the array is analyzed and the maximum contiguous subarray sum is computed based on Kadane’s Algorithm as explained in this article. This is the best place to expand your knowledge and get prepared for your next interview. For example, we have. Input: L = -3, R = 3, K = 1. For a better experience, watch the video at 1. The task is to find the sum of weights of the edges of the Minimum Spanning Tree. Send feedback. Example 1: Input: n = 6 arr[] = {0,0,5,5,0,0} Output: 6. 4. . And we have to count all such cycles that exist. Find the maximum possible sum from one leaf node to another. K is the size of subarrays and M is the count of subarray. Practice. Examples: {-10, 2, -1, 5}, {-2, 4, -1, 4, -1}. Find the maximum of the sums of all such subsequences. A back edge is an edge that is from a node to itself (selfloop) or one. Solved 3 problems using two-pointers approach: Find triplets with 0 sum Level up your coding skills and quickly land a job. ; Now create a max/min variable (let’s say m) with value. For an undirected graph, we can either use BFS or DFS to detect the above two. If a pair is found with the required sum, then make sure that all elements are distinct array elements and an element is not considered more than once. It takes O (log N) to balance the tree. Since there are total n elements, maximum sum is n for both arrays. If any of the subarray with size K has the sum equal to the given sum then print YES otherwise print NO. Geekbits count & redemption. Contests. Back to Explore Page. We fix the left and right columns one by one and find the largest sub-array with 0 sum contiguous rows. A global variable is set that is compared at each iteration with the local sum values to obtain the final result. Below are the steps: Create a prefix sum array (say pref []) from the given array arr []. Note: The cells are named with an integer value from 0 to N-1. For example, consider the following two graphs. Graph 134. All the above paths are of length 3, which is the shortest distance between 0 and 5. Example 1: Input: N = 7 A = {1, 101, 2, 3, 100, 4, 5} Output: {1, 2, 3, 100} Explaination: This subsequence has the highest sum of 106. We are given a directed graph. A-143, 9th Floor, Sovereign Corporate Tower, Sector-136, Noida, Uttar Pradesh - 201305Approach: The given problem can be solved by finding the last element which is greater than its next element, and swapping it with the next smaller element in the array. Example 1: Input: N = 3. Practice. Example 2: Input: 10 / 20 30 / 10 10 Output: 0 Explanation: The given tree is not a sum tree. Maximum sum path in a matrix from top-left to bottom-right. We can solve this problem similar to two pointers method. P: If ‘a’ is the initial term and ‘d’ is a common difference. Assume that every graph with no odd cycles and at most q edges is bipartite and let G be a graph with q + 1 edges and with no odd cycles. Sum of upper triangle and lower triangle. If an a. Approach: The problem can be solved using the following mathematical idea:. Easy 224K 27. An empty linked list is considered as c. Medium Accuracy: 32. Program to find sum of elements in a given 2D array. To get alternating subsequences with maximum length and the largest sum, we will be traversing the whole list (length of list)-1 times for comparing signs. Follow the steps below to solve the problem: Store all the edges corresponding to all the unique weight in a map M. If the size of the max heap exceeds K, pop (remove) the smallest element from the min heap. By induction, H has a bipartition (X, Y). I used a dfs on graph approach in. Solve. Recommended: Please solve it on “ PRACTICE ” first, before moving on to the solution. Find Complete Code at GeeksforGeeks Article: Like, Comment and Share the Video among you. low = 1 high = min (N, M) Next Search Space: In each iteration find the mid of the search space and then Finally, check that all subarrays of that size have the sum less than K. e. 5xMethods And Algorithms Used1. Explanation: This diagram clearly shows no cycle. Solve company interview questions and improve your coding intellectBack to Explore Page. We also add end to previous sum. Example 1: Input: N = 2, S = 9 Output: 90 Explaination: It is the biggest num. Inversion Count: For an array, inversion count indicates how far (or close) the array is from being sorted. The task is to check if there exists any subarray with K elements whose sum is equal to the given sum. Let the number be 12345. In the above step, the row sum from starting to ending column can be calculated in constant time by creating an auxiliary matrix of size N*M containing the prefix sum of each row. Method 1 There can be two cases for the maximum sum: Case 1: The elements that contribute to the maximum sum are arranged such that no wrapping is there. Replace each element of an array with 1 if it is greater than or equal to X, else replace it with -1. This is the highest possible sum. Note: The cells are named with an integer value from 0 to N-1. Calendar representation of data. For example in the given tree, maxSum Node = 4 with maximum sum of 28. First of all consider every ‘0’ in the matrix as ‘-1’. The function “largestSum” takes array “arr” and it size is “n”. Return -1 if it is not possible. You are required to return the head of the linked list 2->1->5->null. The practice system tells you exactly the test case where your code failed. Find the length of the longest sub-sequence such that elements in the subsequence are consecutive integers, the consecutive numbers can be in any order. Follow the steps to solve the problem: Use a DFS traversal starting from the root. Therefore, sum is = 2 + 3 + 1 + 5 = 11. Platform to practice programming problems. Level up your coding skills and quickly land a job. The idea is similar to linear time solution for shortest path in a directed acyclic graph. The idea is to find all subarrays and then find those subarrays whose any of the subarrays does not have a sum equal to zero. Note: edges [i] is defined as u, v and weight. Initialize a Max-Heap using a priority queue, say. Find the value of the maximum (say M1) and the second maximum (say M2) node’s. In this video, I have solved the "Largest Sum Cycle" problem from GFG Practice - Problem Of The Day. Declare a variable count with value 0 to store the final answer. , it can be colored with two colors “. Example 1: Input: N = 8 K = 3 A [] = {8 5 9 10 5 6 19 8} Output: 38 Explanation: Possible increasing subsequence of length 3 with maximum possible sum is 9 10 19. The solution is based on the fact that “ If a graph has no odd length cycle then it must be Bipartite, i. We initialize distances to all vertices as minus infinite and distance to source as 0, then we find a topological sorting of the graph. Explanation: The subarray having maximum sum with distinct element is {2, 3, 1, 5}. The time complexity of the given BFS algorithm is O(V + E), where V is the number of vertices and E is the number of edges in the graph. MIN_VALUE. Maximum sum path in a matrix from top-left to bottom-right. So the first unit fraction becomes 1/3, then recur for (6/14 – 1/3) i. Find the length of the longest subarray with atmost K occurrences of the integer X. org or mail your article to review-team@geeksforgeeks. The problem is to find the shortest distances between every pair of vertices in a given edge-weighted directed graph. Note: edges [i] is defined as u, v and weight. If the sum of all elements is greater than S and its size is greater than K, then update answer with minimum of answer and length of the subarray. If the array consists of only positive numbers the problem can be efficiently solved using only the sliding window technique as discussed here. Can you solve this real interview question? Binary Tree Maximum Path Sum - Level up your coding skills and quickly land a job. ; Sort the array in descending order. Whenever we reach a node at the kth level, we add its value to a sum. We can find the largest and second-largest in O (n) time by traversing the array once. Expected Time Complexity: O (n*m) Expected Auxiliary Space: O (n*m) Constraints: 1 ≤ n, m ≤ 500. The basic idea behind cycle sort is to divide the input array into cycles, where each cycle consists of elements that belong to the same. 1. Return the largest sum of the given array after partitioning. Cycles of length n in an undirected and connected graph. Input : arr [] = [4, 3, 1, 5, 6] Output : 11 Subarrays with. The output for the above will be. 1) If current has no right child a) Increment count and check if count is equal to K. Step 1-> 12345 % 10 which is equal-too 5 + ( send 12345/10 to next step ) Step 2-> 1234 % 10. 89% Submissions: 109K+ Points: 4. The solution is based on Maximum sum rectangle in a 2D matrix. Note: The above code assumes that there is at least one positive element in the array. Solve Problem. Input: nums = {2, 8, 5, 4} Output: 1 Explanation: swap 8 with 4. Every node has been assigned a given value. Geek lost the password of his super locker. Given an array of 0s and 1s. You are given an array Edge [] of N integers, where Edge [i] The task is to find the largest sum of a cycle in the maze (Sum of a cycle is the sum of the cell indexes of all cells present in that cycle). Example 1: Input: N = 5 Arr[]. The idea is to convert given problem to a simpler problem where we have to just check if there is cycle of odd length or not. The maximum among all the nodes is the maximum path sum of the tree. A brute force approach is to store all the contiguous sums in another array and sort it and print the k-th largest.