However, the longest path problem has a linear time solution for directed acyclic graphs. Sum of two large numbers | Practice | GeeksforGeeks. a strictly increasing subsequence. Naive Approach: Run two loops to generate all subarrays and then choose all subarrays of size k and find maximum and minimum values. , it can be colored with two colors “. Problem Statement. Example 1: Input: 1 / 4 4 / 6. Solution. 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. If all the elements are. Example 1: Input: N = 3 K = 2 Arr = {3,2,1} Output: 5 Explanation: The different subarray sums we c. DFS for a connected graph produces a tree. Note that in graph on right side, vertices 3 and 4 are swapped. Explore; Problems;. Now the problem reduces to finding the largest subarray having a sum greater than zero. Input: arr [] = {1, 4, 2, 10, 2, 3, 1, 0, 20} k = 4, sum = 18 Output: YES Subarray = {4, 2. If max_ending_here < 0 then update max_ending_here = 0. 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. . Otherwise, push all the element of the array in a linear data structure like vector and if. Example 2: Input: N = 3, S = 29 Output: -1 Explanation: There is no such three digit number whose sum is 29. All DSA Problems; Problem of the Day; GFG SDE Sheet; Curated DSA Lists. cpp. You are given an array Arr of size N. In the end, the min heap contains the K largest elements of the array. Also, the number of colors used sometime depend on the order in which vertices are processed. Time Complexity: O(N·M) Auxiliary Space: O(N*M) Efficient Approach: The above approach can be optimized based on the observation that the maximum prefix sum is equal to the sum of the maximum prefix sum of arrays A[] and B[]. We initialize distances to all vertices as minus infinite and distance to source as 0, then we find a topological sorting of the graph. If the stack is not empty, compare top most element of stack with next. Approach: The is to do a Breadth First Traversal (BFS) for a graph. Platform to practice programming problems. For example, the number 190 will be represented by the linked list, 1->9->0->null, similarly 25 by 2->5->null. Solved 3 Linked list problems using Recursion and two-pointers approach:. Find Complete Code at GeeksforGeeks Article: Like, Comment and Share the Video among you. Excluding all those subarrays from the current subarray, gives new subarrays having the desired sum. Next largest is ‘y’ but that occurs 0 times in k so we will skip it. + 3 more. ; Now create a max/min variable (let’s say m) with value. For subsets found to be not containing K consecutive array elements, calculate their sum. Given a binary tree with a value associated. So the first unit fraction becomes 1/3, then recur for (6/14 – 1/3) i. Output: 11. The two sub-arrays are [1, 2, 5] [2, 3]. Your task is to complete the function FindWays () which takes matrix as input parameter and returns a list containg total number of ways to reach at (n, n) modulo 109 + 7 and maximum number of Adventure. Maximum sub-array is defined in terms of the sum of the elements in the sub-array. Practice. Output. Note: The cells are named with an integer value from 0 to N-1. The element at front of the Qi is the largest and element at rear/back of Qi is the smallest of current window. Recommended: Please solve it on “ PRACTICE ” first, before moving on to the solution. Find three element from different three arrays such that a + b + c =. Given an array of positive integers. Example. Else remove the top element of the stack. Start with the largest character ‘z’. If there is no cycle in the graph then return -1. Example 1: Input: X = "25", Y = "23" Output: 48 Explanation: The sum of 25 and 23 is 48. The idea is to find the sum of string traversed until now. Calculate sum of nodes left subtree and right subtree. D. Given a maze with N cells. I used a dfs on graph approach in. Given a binary tree. After that we will initialize our two subarray from (N – 2K) and (N – K) indices, where. If. Minimize sum of product of same-indexed elements of two arrays by reversing a subarray of one of the two arrays. Company Tags. Given two strings denoting non-negative numbers X and Y. Given an undirected and connected graph and a number n, count total number of cycles of length n in the graph. If not possible returns -1. Input : 331 Output : 313 Input : 3444 Output : Palindrome cannot be formed. Given an array of integers. Find the maximum subset-sum of elements that you can make from the given array such that for every two consecutive elements in the array, at least one of the elements is present in our subset. Find the largest sum of a cycle in the maze; Determine whether a universal sink exists in a directed graph; Roots of a tree which give minimum height; Two Clique Problem (Check if Graph can be divided in two Cliques) Hypercube Graph; A Peterson Graph Problem; Channel Assignment Problem; Number of sink nodes in a graphGiven a weighted, undirected and connected graph of V vertices and E edges. Return -1 if it is not possible. Example 1: Input: n = 6 arr [] = {0,0,5. Counting 102. Input: nums = {2, 8, 5, 4} Output: 1 Explanation: swap 8 with 4. So T will become “zzz” and we will remove letters from the left of S until all the z’s are removed. Your task is to complete the function print2largest () which takes the array of integers arr and n as parameters and returns an integer denoting the answer. Whenever we reach a node at the kth level, we add its value to a sum. e entry/exit points are unidirectional doors like valves). A linked list is called circular if it not NULL terminated and all nodes are connected in the form of a cycle. Allocate Minimum Spanning Tree. We need to find the max sum of sums of M subarrays of size K (non-overlapping) in the array. If e has one end in X and the other. Your Task: You don't need to read or print anything. Your task is to return maximum score possible in the given array Arr. entry/exit points are. Sum of array elements possible by appending arr [i] / K to the end of the array K times for array elements divisible by K. Find the product of the maximum product subarray. The size of the largest cycle is the value of the largest cached value. Examples: Input: N = 4, Edge [] = {1, 2, 0, -1} Output: 3 Given an array Arr[] of N integers. After partitioning, each subarray has their values changed to become the maximum value of that subarray. The assertion is clearly true for a graph with at most one edge. Given two strings denoting non-negative numbers X and Y. i] having length i + 1. Let this value be x. Geek lost the password of his super locker. If max_so_far is less than max_ending_here then update max_so_far to max_ending_here. Approach: The Idea is to compute the indices of the largest three elements in the array. The path may start and end at any node in the tree. A plus (+) shape has atleast five elements which are { (x-1, y), (x, y-1. Note: The above code assumes that there is at least one positive element in the array. The idea is we will maintain a integer variable maxsum. You are given a weighted undirected graph having n vertices numbered from 1 to n and m edges describing there are edges between a to b with some weight, find the shortest path between the vertex 1 and the vertex n and if path does not. 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. Problem Submissions Comments. Auxiliary Space: O(n), where N represents the size of the given array. Question: Converging Maze: Largest Sum Cycle 1. Once the graph traversal is completed, push all the similar marked numbers to an adjacency list and print the adjacency list accordingly. The task is to find the sum of weights of the edges of the Minimum Spanning Tree. Instructions. First we store the prefix sum in a separate array so that any subarray sum can be calculated in constant time. 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. 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. The task is to find subtree with maximum sum in the tree and return its sum. 2. Example 1: Input: N = 5 Arr [. We know that the path should turn clockwise whenever it would go out of bounds or into a cell that was previously visited. gfg potd gfg potd todaygfg problem of the dayProblem Link:-Link:-h. Function Description: The sum of the largest sum cycle in the maze. Cycles of length n in an undirected and connected graph. Finally, we return the largest sum of digits. Linked List 72. Efficient Approach: Find the second largest element in a single traversal. Back to. @Mingle_Tech @Code_Star #mingletech #Mingle_Tech Thank you for watching this video 💛 geeks for geeks, Missing Number in matrix, Absolute List Sorting, Balanced String,. More than 100 million people use GitHub to discover, fork, and contribute to over 330 million projects. Output: 3. In this post, a solution using the approach of Largest Sum Contiguous Subarray is discussed. . 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. Suppose we have x as 6, then the numbers which are less than 6 and have remainders which add up to 6 gives sum as 6 when added. Simulation 132. Every cell of the maze contains these numbers 1, 2 or 3. Largest Sum. We also add end to previous sum. So now S will become “awa”. For a given number of the form ‘nr/dr’ where dr > nr, first find the greatest possible unit fraction, then recur for the remaining part. From the above three questions, I was able to solve the 2 questions completely, and a 7/10 test in the remaining one. The solution is based on Maximum sum rectangle in a 2D matrix. The task is to check if the linked list has a loop. 2) Start traversing the array from array [1],. Therefore the output will be 3. Static data structure: Static data structure has a fixed. -----. Algorithm for solving this problem: Find the sum of all elements of in individual stacks. We can solve this problem similar to two pointers method. Proof: Let there be a unique Min-Cut of given graph and let there be C edges in the Min-Cut and the edges be {e 1, e 2, e 3, . Time Complexity: O(N 2 log K) Auxiliary Space: O(N), but this can be reduced to O(K) for min-heap and we can store the prefix sum array in the input array itself as it is of no use. The cells are named with an integer value from 0 to N−1. Find the maximum of the sums of all such subsequences. From a given cell, we are allowed to move to cells (i+1, j) and (i, j+1) only. next is the next greater element for the popped element. entry/exit points are unidirectional doors like valves). Each cell may have multiple entry points but not more than one exit (i. 26. Largest number with given sum | Practice | GeeksforGeeks. You have to find the K-th largest sum of contiguous subarray within the array elements. 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). If we calculate A 3, then the number of triangles in Undirected Graph is equal to trace (A 3) / 6. Given an array of 0s and 1s. Exclusively for Freshers! Participate for Free on 21st November & Fast-Track Your Resume to Top Tech Companies. This is the best place to expand your knowledge and get prepared for your next interview. Now let’s see how the two-pointer technique works. I try to upload the daily code which i practice daily and also upload GFG POTD (Java,Cpp,Python3) - GitHub - shibam120302/GFG_POTD: I try to upload the daily code which i practice daily and also upload GFG POTD (Java,Cpp,Python3). 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). Note: edges [i] is defined as u, v and weight. Explanation: The product of the subarray {1, 5, -6, 9} is -270 which is the minimum possible. Given two strings denoting non-negative numbers X and Y. nirazv April 20, 2021, 8:32am 8. But in the case of the number of elements being large, the array in which we store the contiguous. Find the total count of sub-arrays having their sum equal to 0. Length of the longest common span with same sum is 6. Solve. Maximum sum path in a matrix from top-left to bottom-right. Among them { 9, 2, 7 } is longest. Back to Explore Page. The task is to find the connected chain with the maximum sum of values among all the connected components in the graph. Find the contiguous sub-array(containing at least one number) which has the maximum sum and return its sum. , we use Topological Sorting . Find the maximum for each and every contiguous subarray of size K. You are given an array arr[] of size n. the used approach of using sum at each node until the node is again repeated in the cycle. 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. Else return false. Example 1: Input: N = 3 K = 2 Arr = {3,2,1} Output: 5 Explanation: The different subarray sums we can get from the array are = {6,5,3,2,1}. If total array size is not multiple of k, then we can take partial last array. 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. Two Sum Using remainders of the elements less than x: The idea is to count the elements with remainders when divided by x, i. . . Follow the steps mentioned. While finding all subarray calculate their size and sum of all elements of that subarray. The idea is to check if R is odd or even and calculate Kth largest odd number accordingly. Example 2: Input: N = 2,K = 2 A [] = {10 5} Output: -1 Explanation: Can't make any increasing subsequence of length 2. This is the best place to expand your knowledge and get prepared for your next interview. Given an integer array arr, partition the array into (contiguous) subarrays of length at most k. Initialize a Max-Heap using a priority queue, say. Take the sum of all the values after subtraction. 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. For a better experience, watch the video at 1. We one by one remove every edge from the graph, then we find the shortest path between two corner vertices of it. Sliding Window 100. Start your problem-solving journey today! You can now create your own custom sprints by adding problems to it. . 25 or 1. Menu. Input: L = -3, R = 3, K = 1. Inputs to queries are left top and right bottom indexes of submatrix whose sum is to find out. Analysis of Graph Coloring Using Greedy Algorithm: The above algorithm doesn’t always use minimum number of colors. We get maximum sum by adding subarray {4, 2, 10, 23} of size 4. Examples : Input : 313551 Output : 531135 Explanations : 531135 is the largest number which is a palindrome, 135531, 315513 and other numbers can also be formed but we need the highest of all of the palindromes. Clearly, if this is the max sum formed then the. Find if there is any subarray with a sum equal to zero. Thus, the explicit formula is . Else, we will calculate the maximum value of max_so_far and (sum – min_so_far) and return it. Calculate the sum of X and Y. (Order of array remains unchanged). 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. 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. If current_sum is greater than max_sum, update max_sum, end to the current index, and max_start and max_end to start and end respectively. Solve company interview questions and improve your coding intellectBack to Explore Page. Solved the problem of finding the starting point of a cycle in Linked list; Day 78. Algorithm: First create an queue structure and push k elements inside it and calculate the sum of the elements (let’s say su) during pushing. Follow the steps below to solve the problem: If the given array is sorted in ascending order, then print “-1” as it is not possible to find lexicographically the largest permutation. Run. Example 1: Input: 1 / 2 3 / / 4 5 6 7 Output: 28 ExplanationYour 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. This is the best place to expand your knowledge and get prepared for your next interview. It's uses O (N) additional storage. Longest subarray of only 0's or 1's with atmost K flips. Now we will use Kadane’s Algorithm to find the maximum subarray sum and minimum subarray sum. Return -1 if there are no cycles. Below is the dry run of the above approach: Follow the given steps to solve the problem: Create a deque to store K elements. We can generate Egyptian Fractions using Greedy Algorithm. If the sum of all three stacks is the same, then this is the maximum sum. Given head, the head of a singly linked list, find if the linked list is circular or not. Practice. For example, the number 190 will be represented by the linked list, 1->9-. Follow the below steps to Implement the idea: Initialize the variables max_so_far = INT_MIN and max_ending_here = 0. The sum of right-subtree is 1 The sum of tree is 13. For the root node, sum of elements in left subtree is 40. 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. So, this DSA sheet by Love Babbar contains 450 coding questions which will help in: Understanding each and every concept of DSA. From subarray Arr [i. In the following code getTargetLeaf () does this by assigning the result to *target_leaf_ref. e 5 only. Declare a variable count with value 0 to store the final answer. Constraints: * 1 <= nums. Example 1: Input: X = "25", Y = "23" Output: 48 Explanation: The. Note: edges [i] is defined as u, v and weight. We can use Hashing to find maximum length of sub-array in 1-D array in O (n) time. Largest possible 5 digit number is 93000 with sum 12. 1) If count is equal to K, simply return current Node as it. Pre-requisite: BS-18. In case you need more clarity about a question, you may use the expected output button to see output for your given input. Time Complexity: O (N), where N is length of array. The value of currsum exceeds the desired sum by currsum – sum. 3) Do following while E is not empty. This is the best place to expand your knowledge and get prepared for your next interview. Step 1-> 12345 % 10 which is equal-too 5 + ( send 12345/10 to next step ) Step 2-> 1234 % 10. Where 5 is the 2nd largest. Floyd Warshall. Steps to implement: Declare a variable “ans” with value 0 because if no such subarray exists then 0 will be the answer. Do either BFS or DFS starting from every unvisited. Find the largest co-prime fraction less than the given fraction; Minimum count of numbers required ending with 7 to sum as a given number; Count 'd' digit positive integers with 0 as a digit; Find the closest Fraction to given fraction having minimum absolute difference; Extended Midy's theorem; Find all strings that match specific pattern. NOTE: If there is a tie, then compare with segment's length and return segment which has maximum length. Time Complexity: O (N) Below is the implementation of the above approach: C++. If there is a prefix with a sum equal to ( x – s), then the subarray with the given sum is found. 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. a strictly increasing. Instructions. Input : arr [] = {10, 1, 3, 15, 30, 40, 4, 50, 2, 1} K = 3 Output : 3 15 30 40 4 50. Given a weighted directed graph with n nodes and m edges. Now, the idea is to reduce the problem to 1-D array. Given a weighted directed graph with n nodes and m edges. This is based on the fact that in order to find the minimum contiguous sum we can first make the elements of the original array negative ie. A leaf node is also considered as SumTree. 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. Explanation: The largest subsequence with greatest sum is [12 -5 7 -9] with length 4. Here adj[i] contains vectors of size 2,Given a binary tree, the task is to find the maximum path sum. Example 1: Input: N = 5 Arr[] = {1,2,3,-2,5} Output: 9 Explanation: Max subarray Welcome to my channel. Find the missing element. Practice. A-143, 9th Floor, Sovereign Corporate Tower, Sector-136, Noida, Uttar Pradesh - 201305The Range of a subarray of arr is the difference between the largest and smaller element in the subarray. 0 = arr [i+1] + arr [i+2] + . Monotonic Stack 55. Input: n = 7 k = 3 arr = [1,15,7,9,2,5,10] Output: 84 Explanation: arr becomes [15. Time Complexity: O(N 2) Auxiliary Space: O(1) Efficient Approach: We can optimize the above approach by using the below steps. Now run your algorithm to get the maximum weight cycle. This is the highest possible sum of a. . All the above paths are of length 3, which is the shortest distance between 0 and 5. 1) Initialize the. Create Largest Sum Cycle. For example, consider 6/14, we first find ceiling of 14/6, i. Solved the problem of finding the starting point of a cycle in Linked list; Day 78. 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. A sequence, sorted in increasing order is. Take two variables min and max to store the minimum and maximum elements of. The task is to complete the function maxSubarraySum() which takes Arr[] and N as input parameters and returns the sum of subarray with maximum sum. The largest value in the left subtree (of x) is smaller than the value of x. Maximize product of array by replacing array elements with its sum or product with element from another array. Solution Approach. Given the graph, Print out the maximum weight Cycle of the graph. Longest Increasing Subsequence having sum value atmost K. Time Complexity: O(N*2 N). 594 views 1 month ago GFG POTD series. Linked list can contain self loop. Inversion Count: For an array, inversion count indicates how far (or close) the array is from being sorted. 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, . Given an array containing N integers and a positive integer K, find the length of the longest sub array with sum of the elements divisible by the given value K. Example 1: Input: A[] = {2, 7, 6, 1, 4, 5} K = 3 Output: 4 Explanation: The subarray is {7, 6, 1, 4} with sum 18, which is divisible by 3. Split the given array into K subarrays such that the maximum subarray sum achievable out of K subarrays formed is minimum. As in this problem we have to choose one element which is the maximum in the subarray. Given a boolean 2D array of n x m dimensions where each row is sorted. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. The idea is simple, we find all divisors of a number one by one. This gives sum = 13. In that case you must submit your solution again to maintain the streak and earn a Geek Bit. Maximize array product by changing any array element arr [i] to (-1)*arr [i] - 1 any number of times. Given an array a [] of size N, and Q queries of two types 1 and 2. The solution is based on the fact that “ If a graph has no odd length cycle then it must be Bipartite, i. ; Sort the array in descending order. This problem is mainly an extension of Largest Sum Contiguous Subarray for 1D array. A disjoint-set data structure is defined as one that keeps track of a set of elements partitioned into a number of disjoint (non-overlapping) subsets. Below are steps to find the first node of the loop. Design 123. How to find the smallest number with given digit sum s and number of digits d ? Examples : Input : s = 9, d = 2 Output : 18 There are many other possible numbers like 45, 54, 90, etc with sum of digits as 9 and number of digits as 2. Note:- You have to return an ArrayList consisting of two. 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. If their sum is smaller than X then we shift the left pointer to right or if their sum is. geeksforgeeks. Find elements in given Array that are a factor of sum of remaining elements. An empty linked list is considered as c. P: If ‘a’ is the initial term and ‘d’ is a common difference. The sum is 110 and no two elements are adjacent. Given an array arr [] of N elements and a number K. 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). Follow the steps below to solve the given. A sheet that covers almost every concept of Data Structures and Algorithms. For example below graph have 2 triangles in it. e. The cells are named with an integer value from 0 to N−1. e c} is. 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. Maximize the minimum difference between any element pair by selecting K elements from given Array. The questions will be featured from a pool of public problems from the GFG Practice Portal. Given an array arr[] of size N and an integer K. Given a weighted, undirected and connected graph of V vertices and an adjacency list adj where adj [i] is a list of lists containing two integers where the first integer of each list j denotes there is edge between i and j , second inte. Return the sum of all subarray ranges of arr. The task is to find subtree with maximum sum in the tree and return its sum. The questions will be featured from a pool of public problems from the GFG Practice Portal. Follow the steps below to solve the problem: Initialize an adjacency list to create a graph from the given set of edges Edges [] []. . We would like to show you a description here but the site won’t allow us. If “n==1” ,then return arr [0]th element. Follow the steps below to solve the problem: Initialize a variable, say maxm, to store the largest element of the given array. Tree. To convert, we do following. All DSA Problems; Problem of the Day; GFG SDE Sheet; Curated DSA Lists. Pick the rest of the elements one by one and follow the following steps in the loop. We will soon be covering solution for the problem where duplicate elements are allowed in subarray. Sub-array A is greater than sub-array B if sum (A) > sum (B). A cycle is a path that starts and ends at the same node. Example 1: Input: N = 4, Level up your coding skills and quickly land a job. The solution is based on the fact that “ If a graph has no odd length cycle then it must be Bipartite, i. Find the first non-repeating element in a given array of integers. Example 1: Input: X = "25", Y = "23" Output: 48 Explanation: The. Print out the node having the maximum number of inorder weights. The element should occur more than once and the index of its first occurrence should be the smallest. Suppose S = “zzwzawa” and K = 2. Auxiliary Space: O (V+E) If you like GeeksforGeeks and would like to contribute, you can also write an article using write. Given a binary tree, find the largest value in each level. Can you solve this real interview question? Binary Tree Maximum Path Sum - Level up your coding skills and quickly land a job. Let e = uv be an edge of G and consider the graph H = G – uv. The result is going to be very large, hence return the result in the form of a string. Algorithm. Count 1’s in a sorted binary array using binary search iteratively: Check if arr [mid] is less than 1 then move the high to left side (i. Easy 224K 27. A back edge is an edge that is from a node to itself (selfloop) or one. 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.