# Software Development Engineer Interview Questions

Software development engineer interview questions shared by candidates

## Top Interview Questions

Write an algorithm to determine if 2 linked lists intersect 15 AnswersThe first answer is simply looping through every item in list one checking it against all items in list 2 until you find a match. This is O(n2) and you'll be asked to improve it. Think about other data structures with faster access to improve this algorithm. ^ Use a HashMap? We could traverse and put every node we see in a hashmap @PixelPerfect3 Yes, a hashtable would do the job. Just put every node from one of the lists into a hashtable then traverse the other list checking to see if each node exists in the hashmap. This would then be in O(n) time with the downside of using more memory for the hashtable. Show More Responses I don't understand why we would need extra space for this problem. If two linked list intersects, that means their end are the same. Traverse until the end of both list and check if the address of the last nodes are the same. @Anonymous - you are right. All we need to do is check if the ends are the same. My solution would be useful if we want to find the node they intersect at. @PixelPerfect3 & @Anon - Sorry guys, that's not correct. It's not that the end of the lists are the same - intersecting means if any nodes within the linked list are the same. For example: List 1 = 1 -> 3 -> 5 -> 6 -> 7 -> 9 List 2 = 2 -> 4 -> 6 -> 8 -> 10 In this case, the 4th element of list 1 and the 3rd element of list 2 are "intesecting". Notice how the ends are different yet still they intersect. The extra space used by the hashtable is made up for by the speed of lookup O(1) in the hashtable. If space is an issue and speed not, you'd go for the O(n2) solution which is to traverse through List 1 and for every node check it against all the nodes in List 2. @Ja, would it be more clear to describe this question as "Check two LinkedLists, to see if they have one node sharing the same value." ? @Ron Perhaps, yes. But take a look online for other people who have been asked this question from Amazon/Microsoft/Google. They tend to ask for "intersecting" linked lists, which means the lists share one or more of the same node. In my simple case above it might look as if it's just the value of each node in the list but I think technically intersecting means they share the same node, i.e. the object. My example was just for illustration but if you were writing this for real you'd want to check the node->next pointer to see if it's the same object in both lists. @Ja, Your example doesn't really make sense: how can the node with value 6 point to a node with value 7 AND a node with value 8? It can only point to one node: either 7 or 8. That's why I think Anonymous' answer is correct. @PixelPerfect3 - It's not the nodes value that's important but the actual node itself, i.e. the value of the next pointer will be the same for a node in both lists. Simply saying "the last node in the list will be the same" is incorrect! Linked lists can intersect at any point in the lists and not share the same last node. Actually, you know I think you guys are right after some thought! My only concern was to find the actual node they intersect at but PixelPerfect3 had a point - being that a singly linked list only points to one next node, if at any point they intersect then they must have the same node at the end of the list. Sorry for adding to the confusion. If you wish to know exactly where they intersect then my solution posted above will work but if you just need to know if they intersect, PixelPerfect3 and Anon solution of the same end element is correct. 1) len1=find length of linkedlist1 2) len2 =find length of linkedlist2. 3) move the bigger linked list to (len1-len2) position. 4) rightnow both linked lists are equal at distance from last node. that is they are n node away last node. 5) iterate both LL simulatenously and if they have same instance that is their intersection point. I think all of you guys missed one important problem. What if the linked lists have cycles? I believe this is one of the important points the interviewer want you to think about. Show More Responses Assumption that if one node intersects, all nodes from there till the end intersect is wrong. For example, my node definition is: typedef struct NODE { int value; NODE *ptr1; NODE *ptr2; } LISTNODE; If I use ptr1 only for first list and ptr2 only for second list; then I could have an intersection at the middle element but not in the end. Its a different question why one would want to design a node the way I mentioned above; but the assumption is wrong. Common answers: a) If lists aren't cyclic; use a visited flag in the NODE definition and traverse first list and mark all nodes visited. Then traverse second and read the flag. b) Use a hash-map with address as the key. Insert into hash-map while traversing first list. Check the hashmap while traversing second. c) If the list could have cycles, still b) and a) would work with any modifications. Thats a double linked list. Not a linked list. |

### Software Development Engineer at Amazon was asked...

Find the deepest common ancestor of two nodes in a tree structure. 13 AnswersThis interview was frustrating because it felt like the woman couldn't write code in C++. I first asked whether I could assume a standard Tree node structure (as I've built several custom structures and they all have many of the same basic components) and she was pretty much dumbstruck and told me ti write the implementation for one. So i did. Then I started walking through my solution and practically had to spell the word iterator when I said I declared one. My solution was basically to just descend in the tree toward the first value until the two values are on different sides of the current node or you fall out the bottom of the tree. I had to repeat the conditional statements character by character for the interviewer. Isn't the root node always the "deepest" common ancestor? Either the question is worded wrong, or you answered it incorrectly, but I think it's most likely that it's worded wrong. @mliu the question is correct. u r thinking wrong. depth of a tree grows towards its leaves. root is the least deep node in a tree. Show More Responses @nunnu is right here what the question wanted was the common ancestor furthest from the root. Again, I'm pretty sure (by subsequent conversations with friends) that my answer was right but that the interviewer and I just couldn't communicate struct node { int value; struct node *right; struct node *left; }mynode; mynode *closestAncestor(mynode* root, mynode* p, mynode* q) { mynode *l, *r, *tmp; if(root == NULL) { return(NULL); } if(root->left==p || root->right==p || root->left==q || root->right==q) { return(root); } else { l = closestAncestor(root->left, p, q); r = closestAncestor(root->right, p, q); if(l!=NULL && r!=NULL) { return(root); } else { tmp = (l!=NULL) ? l : r; return(tmp); } } } Smiles, my ancestors don't sit in trees. - Do yours? We have grown used to sitting under them and have great picnics... Suppose we need to find common ancestor for the nodes with values A an B. start from the root and compare value of the root node with both A and B. If A an B are both below/above the node's value then go down to the next node. Repeat until we find a node where A and B "go" to different links. This node seems to be 'common ancestor'. Traverse up the tree for both the nodes and add them to the explored list. If there is a common element in the explored list of both the nodes, that's the common ancestor. Hari, if the answer was the root your approach would have n^2*lg(n) complexity where mine had lg(n) in the worst case solution with O(h) time and memory complexity (h - height of the tree) Node * dca(const Node * a, const Node * b) { stack qa, qb; while (a) { qa.push(a); a = a->p; } while (b) { qb.push(b); b = b->p; } Node * result = NULL; while (qa.top() == qb.top()) { result = qa.top(); qa.pop(); qb.pop(); } return result; } To find the common ancestor. O(lg N) public Node GetCommonParent(Node root, int key1, int key2) { while (root != null) { int key = root.iData; if (key key1 && key > key2) root = root.LeftChild; else return root; } return null; } @Joarder: your answer is both really bad coding practice and only works for very specifically-structured trees (binary search trees based in integer keys). The approach is a good one, but you should not override a parameter being passed in and you should use Node.isLeft(Node) and Node.isRight(Node) rather than comparing keys directly. Remember that a tree can be made from a collection of any comparable object, keys are not required. Why was the first answer down voted? I think thats the best answer.. There is no better way.. And its O(log n) complexity. |

The Game of Nim worded diffently. 11 AnswersThe Name of the Game. The anwer is 'Take' from the german word nimm. There is a game called 'The Game of Nim' that has a specific mathematical equation that must be utilized in order to win the game. Nimm is the German word for Take, so you must figure out the best way to take the matches without your opponent beating you at it. Show More Responses The Game of Nim is a simple board game in which you and your opponent take turns removing a number of matches from one of the rows (normally about 5 rows) of matches on the board. The person to take the last match off the board is the winner. The reason why it is of interest to us as prospective software engineers (and why you probably asked this question) is that it has some interesting binary number properties making it fairly trivial to write computer code to ensure a win every time (every time there is a starting advantage, that is). Would you like me to go into more detail? Ok, well in brief then, basically the trick is to take the number of matches in each row and represent this as a binary number. Then, either by hand or with a program, do an Exclusive Or operation on the numbers. Then whenever you take some matches, just ensure that the remaining total is always zero after your turn and you will be sure to win by the end of the game. Maybe I should also add (and I'm thinking out the box here), that sometimes we as people are up against a challenge or opponent where succeeding or beating them is seemingly reliant on chance or luck. However, with careful analysis of the problem and good strategising, it turns out it is actually possible to ensure success just about every time. On the other hand, there are times when the odds are against us from the start. Then either we must stand up for what we believe is fair (i.e. be aware and vocalise that we cannot possibly win), or else acknowledge that our opponent is worthy and will ultimately get the better of us. Yet it should be noted that we can still stay strong and be competitive from the beginning allowing us to possibly take advantage of any mistakes or weaknesses our opponents or challenges might display. That is the Game of Nim worded differently. What does this question have to do with Quality? Nim's Game If I was interviewing you and asked you that question, I would be trying to determine if you could take a simple problem and provide a simple solution. If you went off into the weeds like Andrew_Bryce did, I would be wondering how effective you would be solving tons of simple issues. Also, if you answered the wrong question (what is the Game of Nim?) and not the question I asked (how would you word differently the phrase The Game of Nim?), I would be wondering how good your communication skills were. If I were being interviewed, I would wonder about the interviewer's communication skills. "The game of Nim worded differently" isn't a question. It isn't even a sentence. "Foaming Theme" 1) I cheated 2) I didn't even know what Nim was before I looked it up Here's how I would interpret some answers and the job I would recommend for them Anonymous: Huh? I think you're trying to be a smartass, but I don't get it - Cafeteria Worker Ryan: Knowledgeable - Content provider SelenityHyperion: Knowledgeable, informative and relatively succinct - Writer Andrew_Bryce: Detail oriented and a perfectionist - Software tester, some forms of coder Astrochimp: Focused - Project Manager OneEye: Thinks his answer is the only correct one - Clearly VP material Count Negroni: Nit Picker - Editor I don't think there's supposed to be one correct answer Ha ha, jokes on me. "The Game of Nim worded differently." is not the actual question, just a vague description. I would answer: "Are you talking to me?" Because it sure sounds like you're high. Then I'd get up and leave. Strategic domination |

Most of them were expected. Almost all are problem solving questions. 1. Given a BST with following property find the LCA of two given nodes. Property : All children has information about their parents but the parents do not have information about their children nodes. Constraint - no additional space can be used 15 AnswersHint - detect the level at which the given nodes are present. Then travel upwards from that position. How about traversing from one node to root, adding each node to hashset, Then try do the same with second one, on collision return node. No, you cannot do that since you need extra space for hashset which is not allowed, I am going to post my solution in a min Show More Responses function findLCA(Node node1, Node node2) { int counter1 = 0; int counter2 = 0; Node temp; //Find the level for each node, use a temp node to //traverse so that we don't lose the info for node 1 and node 2 temp = node1; while( temp.parent ! = null) { temp = temp.parent; counter1++; } temp = node2; while( node2.parent ! = null) { node2 = node2.parent; counter2++; } /* * We wanna make them at the same level first */ if(counter1 > counter2) { while(counter1 != counter2) { node1 = node1.parent; counter1--; } } else { while(counter2 != counter1) { node2 = node2.parent; counter2--; } } while (node1.parent != node2.parent) { node1 = node1.parent; node2 = node2.parent; } System.out.println("Found the LCA: " + node1.parent.info); } //correction temp = node2; while( temp.parent ! = null) { temp = temp.parent; counter2++; } @chmielsen : your solution would work... but as said by Hamid, due to the constraint of space, you have to consider some other technique. I seems really like the question of finding intersection of two linked lists 1)consider node1 as p1. see if p1=p2 , p1->parent=p2, p2->parent=p1 2)now for a value p1 try to see recursively if p2->parent ever becomes equal to p1 or p2=root 3)set p1=p1->parent and continue till p1=p2 or p1= root temp1 = node1; temp2 = node2; while( temp1.parent != null && temp2.parent != null){ if(temp1.value == temp2.value){ return temp1; // temp1 and temp2 point to same node so pick one } temp1 = temp1.parent; temp2 = temp2.parent; } System.out.println("no such ancestor"); Consider this is a BST, where max node is always on the right of min node, we can traverse max upward one node at a time while comparing min nodes as it traverse upward toward root. BinaryNode findBSTLCA( BinaryNode min, BinaryNode max ) { BinaryNode tempMax = max; BinaryNode tempMin = min; while( tempMax != null ) { while( tempMin != null ) { if( tempMin.element == tempMax.element ) return tempMin; tempMin = tempMin.parent; } tempMin = min; // reset tempMin tempMax = tempMax.parent; // traverse tempMax upward 1 node } return null; // no LCA found } Consider that the lowest common ancestor in a binary search tree means the node value would be between the two values passed in. Because everything left is less than and everything right is greater than, we can traverse the tree using this knowledge. Here's the solution in PHP for something different: function findLowestCommonAncestor(Node $root, $value1, $value2) { while ($root != null) { $value = $root->getValue(); if ($value > $value1 && $value > $value2) { $root = $root->getLeft(); } else if ($value getRight(); } else { return $root; } } return null; //the tree is empty } howardkhl - your solution works, but this is O(n^2) complexity, making it too slow for large enough trees. Ja - your solution might work (haven't thoroughly checked it) but it violates the restriction that a parent node does not know about the child node. So this answer is invalid. The correct answer is the one given by Hamid Dadkhah, which, just like an anonymous responsder said, is the same problem as an intersecting list. you can use the following method *Node getLCA(Node *n1, Node* n2){ while(n1.parent!=null){ Node * p= n2; while(p.parent!=null){ if(n1.parent!=p.parent) p=p.parent; else return p.parent; } } } Show More Responses Pick one of the nodes in random. Keep traversing up until the property: new node is greater than one of the nodes and lesser than the other is satisfied. I was also interviewed with same question. They not only ask the solution they also ask for the time complexity of the solution. Make sure you to ask different questions and confirm the type of tree. They could give you binary search tree, binary tree, sorted binary tree. Solution will greatly depend on the type of the tree. |

Number of 1's in binary representation of integer? 13 AnswersRun a loop, in which you binary-AND the integer with 1, and increment a counter, if the result is 1. Then right-shift the input-integer by 1 bit, and start over in the loop unsigned int ones(unsigned int number) { unsigned int n; for (n = 0; number != 0; number >> 1) { if (number & 1) { n++; } } return n; } unsigned int ones(unsigned int number) { unsigned int n; for (n = 0; number != 0; number >> 1) { if (number & 1) { n++; } } return n; } Show More Responses i dnt knw wheather it correct or not.....do correct me if im wrng a=0 q=n/2 r=n%2 n=q if(r=1)then a=a++ continue.... ct = 0; while (val) { ct++; val = val & (val - 1); } Several of the above work, but use preincrement public static int population(int x) { x = (x & 0x55555555) + ((x >> 1) & 0x55555555); x = (x & 0x33333333) + ((x >> 2) & 0x33333333); x = (x & 0x0F0F0F0F) + ((x >> 4) & 0x0F0F0F0F); x = (x & 0x00FF00FF) + ((x >> 8) & 0x00FF00FF); x = (x & 0x0000FFFF) + ((x >>16) & 0x0000FFFF); return x; } in C++, how about: do { sum += n&1; } while (n>>=1); int ones( ) { int n; int number = 1100110111; n = 0; while (number!=0) { int temp = number % 10; if(temp ==1 ) n++; number = number/10; } return n; } Lets consider 14(1110) is the number int CountOnes(int Number) { int n=0; while(number !=0) { if(number%2==1) n++; number >> 1; } return n; } The function takes an int and returns the number of Ones in binary representation public static int findOnes(int number) { if(number < 2) { if(number == 1) { count ++; } else { return 0; } } value = number % 2; if(number != 1 && value == 1) count ++; number /= 2; findOnes(number); return count; } All the answers above will not get you to amazon... try code the function with o(m), where m is the number of 1's in the binary representation of an integer. (hint: look up "Programming Interviews Exposed") int num = 31; int mask = 1; int counter = 0; while (num > mask ) { if ((num & mask) == mask) { counter++; } mask = mask << 1; } Console.Write(counter); Console.ReadKey(); |

### Software Development Engineer at Amazon was asked...

Implement a function to validate whether a given binary tree is a BST (i.e. write an isBST() function). 9 AnswersI came up with a recursive solution something like this: boolean isBST(TreeNode node, int min = INT_MIN, int max = INT_MAX) { if (node != null) { if (node.left != null && node.left > max || node.right != null && node.right < min) { return false; } else { return (isBST(node.left, min, node.value) && isBST(node.right, node.value, max)); } } else { return false; } } How come this function never returns true? And why would you need min and max? Ok, so I should have spent a little more time posting this (I was admittedly rushing through it so I could get access to more questions/answers). Here's a revised version that should hopefully make more sense: boolean isBST(TreeNode node, int min = INT_MIN, int max = INT_MAX) { if(node == null) { return true; } if(node.value > min && node.value < max && IsValidBST(node.left, min, node.value) && IsValidBST(node.right, node.value, max)) { return true; } else { return false; } } The main change is that I decided to avoid checking the children of the tree in the body, and leave it to recursion to take care of that. Thus, we just have to look at the current "node" and that's it... the constraints will be handled by passing min and max down. @Alexander - in response to your questions, the original function does in fact return true, if the condition (isBST(node.left, min, node.value) && isBST(node.right, node.value, max)) happens to evaluate to true. Finally, the min and max values are required because a BST requires that each value in the left branch be smaller than ALL parent values on that branch (and similarly for those on the right branch being larger). Another way of saying this is that the entire left tree of any node must be smaller than the node's value, and the entire right tree must be larger than the node's value. Thus, in a recursive solution, you have to have a way to pass down the upper and lower bounds to the lower levels of the tree, otherwise the third level won't be able to check whether it's smaller/larger than the root two levels up. That's why we pass down the min and max values. Hope this helps. Show More Responses boolean isBST(TreeNode node) { if(node.isLeafNode( )) return true; else { if(node.value node.rightChild) return false; else return (isBST(node.leftChild) && isBST(node.rightChild)) } } traverse in order and see if they r same @Alexander - in response to your questions, the original function does in fact return true, if the condition (isBST(node.left, min, node.value) && isBST(node.right, node.value, max)) happens to evaluate to true. ============= Those are just two function calls and the function never returns true. Alexander is right - you are missing a terminating clause in your recursion. Forgot to add - your second solution is correct since it returns true. // For +ve number OR use INT_MIN instead of -1(s) bool BinarySearchTree::validate() { int minVal = -1; int maxVal = -1; return ValidateImpl(root, minVal, maxVal); } bool BinarySearchTree::ValidateImpl(Node *currRoot, int &minVal, int &maxVal) { int leftMin = -1; int leftMax = -1; int rightMin = -1; int rightMax = -1; if (currRoot == NULL) return true; if (currRoot->left) { if (currRoot->left->value value) { if (!ValidateImpl(currRoot->left, leftMin, leftMax)) return false; if (leftMax != currRoot->left->value && currRoot->value value; } if (currRoot->right) { if (currRoot->right->value > currRoot->value) { if(!ValidateImpl(currRoot->right, rightMin, rightMax)) return false; if (rightMin != currRoot->right->value && currRoot->value > rightMin) return false; } else return false; } else { rightMin = rightMax = currRoot->value; } minVal = leftMin rightMax ? leftMax : rightMax; return true; } // using inorder traverse based Impl bool BinarySearchTree::validate() { int val = -1; return ValidateImpl(root, val); } // inorder traverse based Impl bool BinarySearchTree::ValidateImpl(Node *currRoot, int &val) { if (currRoot == NULL) return true; if (currRoot->left) { if (currRoot->left->value > currRoot->value) return false; if(!ValidateImpl(currRoot->left, val)) return false; } if (val > currRoot->value) return false; val = currRoot->value; if (currRoot->right) { if (currRoot->right->value value) return false; if(!ValidateImpl(currRoot->right, val)) return false; } return true; } |

Given a set of numbers -50 to 50, find all pairs that add up to a certain sum that is passed in. What's the O notation for what you just wrote? Can you make it faster? Can you find an O(n) solution? Implement the O(n) solution 17 AnswersO(n^2) solution is just two double for loops. O(n log n) solution will use a binary tree O(n) solution will use a hash table O(n) solution possibility (no need for a data structure) void findpairs(int sum) { //given a set of numbers -50 to 50, find all pairs that add up to a certain sum that is passed in. if (sum == 0) { cout 0) { for(int i = 0; i((sum/2)-1) && i>-26; i--) { if( (i - sum+i) == sum) { cout << i << " " << sum+i << "\n"; } } } } @Mike "if( (i + sum-i) == sum)" will always give you "sum". Show More Responses @Mike: if (sum == 0) does not imply 0,0. It implies -50,50; -49,49; -48,48,... Has anyone found the O(n) solution??? I'm having trouble with this one... Put all the numbers from the array into a hash. So, keys will be the number and values of the keys be (sum-key). This will take one pass. O(n). Now, foreach key 'k', with value 'v': if k == v: there is a match and that is your pair. this will take another O(n) pass totale O(2n) ~ O(n) Easiest way to do it. Written in python. If you consider the easiest case, when our summed value (k) is 0, the pairs will look like -50 + 50 -49 + 49 -48 + 48 etc.... etc... So what I do is generalize the situation to be able to shift this k value around. I also allow us to change our minimums and maximums. This solution assumes pairs are commutative, i.e. (2, 3) is the same as (3, 2). Once you have the boundaries that you need to work with, you just march in towards k / 2. This solution runs in O(n) time. def pairs(k, minimum, maximum): if k >= 0: x = maximum y = k - maximum else: x = k + maximum y = minimum while x >= k / 2 and y <= k / 2: print str(x) + " , " + str(y) + " = " + str(x + y) x = x - 1 y = y + 1 here is my solution using hash table that runs in O(2n) => O(n): public static String findNums(int[] array, int sum){ String nums = "test"; Hashtable lookup = new Hashtable(); for(int i = 0; i < array.length; i++){ try{ lookup.put(array[i], i); } catch (NullPointerException e) { System.out.println("Unable to input data in Hashtable: " + e.getMessage()); } } int num2; int num1; for (int i = 0; i < array.length; i++){ num2 = sum - array[i]; Integer index = (Integer)lookup.get(num2); if ((lookup.containsKey(num2)) && (index != i)){ num1 = array[i]; nums = array[i] + ", and " + num2; return nums; } } //System.out.println(lookup.get(-51)); return "No numbers exist"; } The number you're looking for is T. You can just create an array of size 101. Then you loop through the array, and drop each number i in cell of index i-50. Now you do a second pass, and for each number, you look at the number at index T-i-50. If there's something there, you have a pair. typedef pair Pair; list l; //create an empty list of tuples pairofsum(l,10); // an example of how to call the function which adds to your list of tuples the possible pairs of the sum void pairofsum(list& l,int sum) { if(sum==0) { Pair p; loadPair(p,0,0); l.push_back(p); for(int i=1;i<51;i++) { loadPair(p,i, -i); l.push_back(p); } } else if (sum<0) { Pair p; for(int i=0;i+-sum<51;i++) { loadPair(p,i,-(i+-sum)); l.push_back(p); } for(int i=1;i<=-sum/2;i++) { loadPair(p,-i,sum+i); l.push_back(p); } } else { Pair p; for(int i=1;sum+i<51;i++) { loadPair(p,-i,sum+i); l.push_back(p); } for(int i=0;i<=sum/2;i++) { loadPair(p,i,sum-i); l.push_back(p); } } } void loadPair(Pair& p, int f, int s) { p.first=f; p.second=s; } Here is my C# implementation. It runs O(N) and doesn't include duplicate pairs (e.g. including [50,-50] as well as [-50,50]). static void FindPairs(int sum) { for (int i=-50; i=-50) { Console.WriteLine(i + " " + otherNum); } } } Solution with no duplicates: @Test public void findPairsTest() { // TestCases // Alternately you can put this test cases in dataprovdier findPairs(50); findPairs(20); findPairs(-20); findPairs(-50); findPairs(0); } private void findPairs(Integer sum) { HashMap inputPair = new HashMap(); HashMap outputPair = new HashMap(); for(int i=-50; i<=50; i++) { inputPair.put(i, sum-i); } // print pairs for(Integer key : inputPair.keySet()) { Integer potentialOtherNum = inputPair.get(key); if(inputPair.containsKey(potentialOtherNum) && potentialOtherNum < key) { outputPair.put(key, potentialOtherNum); } } System.out.println(outputPair.entrySet().toString()); } Here is the solution in O(n) time complexity. http://www.knowsh.com/Notes/NotesSearch/NotesDetail/140226/Program-To-Find-All-The-Pairs-In-The-Given-Set-That-Add-Up-To-A-Certain-Sum Please let me know if there is any thing I missed. Show More Responses Use two pointers, one at the begin, one at the end, let us call the pointer begin and end, the array is named nums. If nums[begin]+nums[end]>target, end--;if end Half=sum/2; i=1; While (half+i -51) { first = half-i; second = half+i; System.out.println(“” + first + “, “ + second); } half=sum/2; i=1; While (half+i \ -51) { first = half-i; second = half+i; System.out.println(“” + first + “, “ + second); } Weirdly the less than and greater than signs make the text between them invisible. The conditional statement is supposed to say Half=sum/2; i=1; While (half+i LESSTHAN 51 && half-i GREATERTHAN -51) |

### Software Development Engineer at Amazon was asked...

List all anagrams in a file. Assumptions: case-insensitive, a-z characters only, one word per line. For example, if the file contains dog, cat, ddd, goo, act, god -- output dog, god, act, cat 10 AnswersThankfully I was taking a theory course and one trick used in the course was "encoding" programs as a large natural number using product of primes. 1. Adapt the encoding as follows -- generate the first 26 primes and assign a prime to each letter 2a. For each word, take the product of each letter's prime. So #(act) = 2*5*prime(t) 2b. As you can see, #(cat) = 5*2*prime(t) = #(act) 3. Insert a handwavey argument about inserting the number/word pairing into a HashMap> Sort the words. Anagrams appear next to each other in the sorted list. Sorry, sort the letters in each word, then sort the words. Anagrams appear next to each other in the list. For example the sorted list for the input would be: act act ddd dgo dgo goo Show More Responses Thanks for sharing Bill For this set of input, the expected output should contain only [cat, act, god, dog]. I'm curious to see what "next steps" your algorithm will perform to provide this expected output You keep track of the mapping from the sorted word to the actual word in a pair, for example: [act, cat] [act, act] [ddd, ddd] [dgo, god] [dgo, dog] [goo, goo] Then you go through this list and count if you have a duplicate entry or not. If you do, like for act, you print out those duplicate entries: cat, act. Bill, your algorithm is O(n*log(n)) while the candidates would be O(n) - provided he uses a decent hash function donutello, bills algo is not n log n it is n*log(k) where as candidates algo is n * k again (multiplications for each word) where k = length of the longest word on top of that calculating primes is expensive anyway I would go with bills answer Bills algo is nlogk + nlgn. After sorting the k letters for n times you also have to sort the n words. #Get inputs a = [] f = open('input.txt','r') for line in f: line = line.strip() a.append(line) #Sort letters in a word def sort_letter(s): r = [] for i in s: r.append(i) t = sorted(r) v = ''.join(t) return v #Find anagrams d = {} for v in a: sv = sort_letter(v) if sv in d: d[sv].append(v) else: d[sv] = [v] #Print results for k,v in d.items(): if len(v) > 1: for s in v: print s think of each line as a set of characters, not a word, then create set of sets of characters which you fill from the input. then print the set (order does not matter as its not specified) |

Determine if an array from 1..n has a duplicate in constant time and space. 12 AnswersCorrect answer is to place each value in the array in its corresponding index (i.e. if array[x] = 3, put 3 into array[3]). If an index already contains its corresponding value, there's a duplicate. ^^ Sorry, that's linear time *and* at best linear space, you fail. What are the properties of an array that affect time complexity? Usually we're talking about the size of the array, N, such that linear time operations, O(N), are those that perform an operation on each of the elements in the array. However, an important thing to consider is that you can evaluate N (the size of the array) itself in constant time. The only way this can be done in constant time is if the input satisfies the precondition that "1..n" means there are no *missing* values in that range. In other words, such an array from "1..5" must contain at least one instance of the numbers 1, 2, 3, 4, and 5. With that precondition, you know that the length of the array will be 5 if no duplicates and greater than 5 if it does contain duplicates. Show More Responses SUM(array) - (N(N+1)/2) = missing number. @Facebook Intern: That wont help .. In case there are 2 duplicates this can be broken. {1, 1, 4, 4} I attach pseudo code here: FindDuplicate(A) i = A.length j = 1 count = 0 while j < i if A[--j] - j == 0 j++ else count++ return count count holds the number of duplicated items This cannot be done in linear time unless the data-structure used to hold the integers has a property that immediately flags duplicates upon insertion. For e.g. like in a Dictionary/HashMap. I'm pretty sure OP posted something wrong there, and they were probably asking to do it in linear time and not constant. If it's constant, the way I would do it would be using a HashSet to check if the key (value in array) is contained, and if not add it to the set. If at any time I find an element that's already inside, return false; If an array has elements from 1 to n the size of the array will be n, thus if the size of the array is greater than n, there must exist a duplicate. I think they are just asking to determine if there is any duplicate number ir not. Its not mentioned to find out which number it is. So that we can find out by using sum of n numbers I think they are just asking to determine if there is any duplicate number ir not. Its not mentioned to find out which number it is. So that we can find out by using sum of n numbers They asked for constant time. So checking sum will not work. For zero indexed arrays, Check if arr[len(arr)-1] == len(arr) - 1. |

To find and return the common node of two linked lists merged into a 'Y' shape. 13 Answershow did the two linked lists make their poses to merge into a 'Y' shape, one's head attached to the waist? please explain more to help understand the question The two linked lists were something like: 1->2->3->4->5 and 3->4->5->6->7->8. For a Y shaped like this: 1 -> 2 -> 3 -> 4 ->7 -> 8 -> 9 5 -> 6 -> 7 -> 8 -> 9 where the trunk portion is of constant length, it is easy. Get the length of the first list. In our case 7. Get the length of the second list: 5. Difference is 2. This has to come from the legs. So, walk the difference in the larger list. Now node1 points to 3. node 2 points to 5. Now, walk through the two lists until the next pointers are the same. Show More Responses @kvr what if the lists are 1-2-3-4-7-8-9 and 12-13-14-5-6-8-9 Can this be done using hash tables? Or is there anything more efficient? i think that kvr's answer is the best. @snv if the two lists are linked by the very last two nodes, then you would find out after you are checking the values of the second two last two nodes. you just got unlucky and basically have to check until the very end. so basically, as a diagram with your example, it would look like this 1 -2 -3 -4-7-8-9 x -x -x -x -x-o 12-13-14-5-6-8-9 (sorry about spacing) but because you know the difference in length is 0, you can start comparing the two lists of nodes one by one. from the very beginning. HASH TABLE seems the only efficient wt. 1. add each element's address (of the smallest list)and push it to the hash table. 2. start walking second list. 3. get element compar eits address with hash table if match is found in hash table, return 4. if list is not exhausted, go to step 2. 5. return NULL Hashtable is complete overkill. The point is to realize that the two linked lists have the same tail. That means if you traverse them with the same index but from the right you will eventually find the first similar node. It's almost as easy if the problem said the two linked lists had the same prefix, find the first node on which they split. Here you walk them with the same index from the left. First reverse both list and find point where both gets diverged For Y condition the list could be List 1: 1->2->3->4->5->6 List 2: 7->8->9->4->5->6 So reverse list would be 6->5->4->3->2->1 6->5->4->9->8->7 now compare two list and move forward the position where you find next node of both are different is the point of merging Some of the above will work for doubly linked list. If not, travel node by node simultaneously from each end. When one traversal ends and the postion of cursor at the traversal is the answer kvr's answer is good but I think it could be optimized better by using 2 stacks. Traverse both lists putting each value into 2 separate stacks. Then when both are fully traversed, the head of each stack will match. Pop one off each at a time till they don't match, return the last popped. But I suppose it comes down to where the first match is at. If its the beginning of the list, kvr's answer will be better, if its at the end or bottom half 2 stacks would be better. Let's say L1 is the list starting with the lower number, and L2 is the other Set X = Head of L1 Set Y = Head of L2 While X <= Y Set X = Next(L1) End While If (X==Y) Return X Else While Y<=X Set Y = Next(L2) End While If X==Y Return X End If End If Repeat until you reach the end of either list. |

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