I got this document from one of my collegue, it has interesting and very complex (interview) questions on datastructures. I'm pasting the document here as it is:

Q1: How would you find a cycle in a linked list? Try to do it in O(n) time. Try it using constant amount of memory.

A1: p2 is guaranteed to reach the end of the list before p1 and every link will be tested by the while condition so no chance of access violation. Also, incrementing p2 by 2 and p1 by 1 is the fastest way of finding the cycle. In general if p1 is incremented by 'n' and p2 by 'm', ('n' not == 'm'), then if we number the nodes in the cycle from 0 to k-1 (k is the number of nodes in the cycle), then p1 will take values given by i*n (mod k) and p2 will take values i*m (mod k). These will collide every n*m iterations. Clearly, n*m is smallest for n==1 and m==2.

bool

HasCycle(Node *pHeadNode)

{

Node

*p1, *p2;

p1 =

p2 = pHeadNode;

while (p2 && p2->Next) {

p1 = p1->Next;

p2 = p2->Next->Next;

if(p1 == p2)

return true;

}

return false;

}

Q2: Given a history of URLs, how would you determine if a particular URL had been seen before?

A2: Hash Table is the most efficient way to do this. You can use several hashing algorithms. For example, checksum of a link can be used as a key for hashing. This will ensure o(1) order provided good checksum algorithm is used which is always unique. Whenever page loads we can parse all URL's from the page and take their checksum and compare them w/ the hashtable. Whichever links matches are displayed in some different color.

Hashtable is the correct answer, but a constant order algo. sounds too fantastic. URLs are by themselves unique and so hash function should not add to the redundancy by being unique. O/w it becomes nothing but a linear sort of search, while binary can do better.

Though URLs are not inherently alphabetically ordered, one might think of ordering them that way, or making the hash function that utilizes this. This will entail a combined binary + linear search which sounds optimal and is open to complexity calculations. A good data structure can be a hash table pointing to a binary tree (an array pointing to a binary tree).

Q3: Since pages can have multiple URLs pointing to them, how can you make sure you've never seen the same CONTENT before?

A3: Keep a list (or a binary tree) of hashes (using MD5, SHA1 or similar hash/digest algorithm) of pages you've visited. Then just compare digest of current page to the hashes in the tree.

Q4: Come up with the plan on how to traverse a graph, as well as to quickly determine if a given URL is one of the million or so you've previously seen.

A4: Use prim's algorithm; Kruskal's algorithm is faster than Prim's. For checking for an already seen url, use dictionary search tree. It is the most efficient i.e. O(1) for whatever number of urls you have in the database.

Q5: The Web can be modeled as a directed graph. Come up with a graph traversal algorithm. Make the algorithm non-recursive and breadth-first.

Q6: Write a function to print the Fibonacci numbers

int fib (int n)

{

assert(n>=1);

return (n<=2 ? 1: (fib(n-1) + fib(n-2)));

}

int fibonacci (int n)

{

if (n <= 2) return 1;

int current, one_back 1, two_back = 1;

for(int i = 3; i <= n; i++) {

current = one_back + two_back;

one_back = two_back;

two_back = current;

} /*the end of for loop */

return current;

}

Q7: Write a function to print all of the permutations of a string.

map<string,int> map_StrInt;

void PermuteString(char* str, int n)

{

char ch = str[n-1];

for(int i = 0; i < n; i++)

{

swap(str[i], str[n-1]);

PermuteString(str, n-1);

swap(str[i], str[n-1]);

}

if(n == 1) map_StrInt[string(str)]++;

}

Q8: Design a memory management scheme.

Q9: Give a one-line C expression to test whether a number is a power of 2. Now implement it without using loops.

A9:

x = ((x > 0) & !(x & x - 1));

Q10: How can I swap two integers in a single line statement?

A10: Use xor operator to accomplish this: a ^= b ^= a ^= b;

Q11: Implement an algorithm to sort a linked list.

A11: The merge sort algorithm:

#include <cassert>

typedef struct MNode *PNODE;

struct MNode

{

int Key;

struct MNode *Next;

};

PNODE Merge(PNODE p, PNODE q)

{

assert(p);

assert(q);

PNODE pHead;

if(p->Key < q->Key)

{

pHead = p, p = p->Next;

}

else

{

pHead = q, q = q->Next;

}

PNODE r = pHead;

while (p && q)

{

if(p->Key < q->Key)

{

r->Next = p, r = r->Next, p = p->Next;

}

else

{

r->Next = q, r = r->Next, q = q->Next;

}

}

if(!p) r->Next = q;

if(!q) r->Next = p;

return pHead;

}

PNODE Partition(PNODE pNode)

{

PNODE p1 = pNode;

PNODE p2 = pNode->Next->Next;

while (p2 && p2->Next)

{

p2 = p2->Next->Next;

p1 = p1->Next;

}

PNODE pSav = p1->Next;

p1->Next = NULL;

return pSav;

}

PNODE Merge_Sort(PNODE p)

{

if(!p || !p->Next) return p;

PNODE q = Partition(p);

p = Merge_Sort(p);

q = Merge_Sort(q);

p = Merge(p, q);

return p;

}

Q12:Implement strstr(), strcat(), strtok(), strrchr, and strcmp

char* strstr (const char *str1, const char *str2)

{

char *cp = (char *)str1;

char *endp = cp + (strlen(cp) - strlen(str2));

while (*cp & (cp <= endp))

{

char *s1 = cp;

char *s2 = (char *)str2;

while ( *s1 & *s2 && (*s1 == *s2) )

s1++, s2++;

if (!(*s2)) return(cp); // success!

cp++; // bump pointer to next char

}

return(NULL);

}

char *strcat (char * dst, const char * src)

{

char *cp = dst;

while (*cp) cp++; // find end of dst

while (*cp++ = *src++); // Copy src to end of dst

return (dst); // return dst

}

char *strcpy (char * dst, const char * src)

{

char* cp = dst;

while (*cp++ = *src++); // Copy src over dst

return(dst);

}

char *strtok (char *string, const char *control)

{

char *str;

const char *ctrl = control;

char map[32];

int count;

static char *nextoken;

/* Clear control map */

for(count = 0; count < 32; count++)

map[count] = 0;

//Set bits in delimiter table

do{

map[*ctrl >> 3] |= (1 << (*ctrl & 7));

}

while (*ctrl++);

//Initialize str. If string is NULL, set str to the saved pointer

//(i.e., continue breaking tokens out of the string from the last strtok call)

if(string)

str= string;

else

str = nextoken;

//Find beginning of token (skip over leading delimiters). Note that there is

//no token iff this loop sets str to point to the terminal null (*str =='\0')

while (*str && (map[*str >> 3] & (1 << (*str & 7))))

str++;

string = str;

//Find the end of the token. If it is not the end of the string, put a null there.

for( ; *str ; str++)

if(map[*str >> 3] & (1 << (*str & 7)))

{

*str++ = '\0';

break;

}

//Update nextoken

nextoken = str;

//Determine if a token has been found.

if(string == str)

return NULL;

else

return string;

}

int strcmp(const char *src, const char* dst)

{

int ret = 0;

while (!(ret = (*src - *dst)) & *dst);

++src, ++dst;

if (ret < 0)

ret = -1;

else

ret = 1;

return ret;

}

char *strrev (char *string)

{

char *start = (char *)string;

char *left = (char *)string;

while (*string++); // find end of string

string -= 2;

while (left < string)

{

char ch = *left;

*left++ = *string;

*string-- = ch;

}

return start;

}

char* strrchr (const char *string, int ch)

{

char *start = (char *)string;

while (*string--); // find end of string

// search forward front

while (--string != start && *string != (char)ch);

if(*string == (char)ch) // char found ?

return (char *)string;

else

return (NULL);

}

Q13: Given a linked list which is sorted, how will you insert in sorted way.

void Insert(PNODE &pHead, PNODE pThing)

{

if(pHead == 0)

pHead = pThing;

else

{

bool fComesFirst = true;

PNODE pCurrent = pHead;

PNODE pPrevious;

while (pCurrent)

{

if (pThing->Key < pCurrent->Key)

break;

pPrevious = pCurrent;

pCurrent = pCurrent->Next;

fComesFirst = false;

}

if(fComesFirst)

pHead = pThing;

else

pPrevious->Next = pThing;

pThing->Next = pCurrent;

}

}

Q14: Give me an algorithm and C code to find the subarray with the largest sum given an array containing both positive and negative integers.

/* Give me an algorithm and C code to find the subarray with the largest sum given an array containing both positive and negative integers.

For each position i in the array we can find out the sub array ending exactly at that position and having the largest sum. At the beginning for the first element the only possible sub array it that one containing the first element so initially the largest amount is a[1]. (For algorithm sake let assume that the array is 1-indexed). Following the principle of dynamic programming it will be proved that the best sub array( with the largest sum) ending in position i+1 is somehow related to best sub array ending in position i.

Let be k the starting index of the best sub array ending in position i and S the sum of this sub array. Let be t an index strictly less than k. The sum from the index t to i+1 is T + S + a[i+1] where T is the sum of elements from t to k-1 indexes. Because of the properties of index k T+S <= S otherwise k will not point to best sub array ending in i so each sub array starting in t

Similarly , let choose an index t between k+1 and i. The sum from index t to i+1 is T+a[i+1], where is the sum of elements between t and i positions. Again T < S according to the optimality of k index so the best sub array ending in i+1 is that one starting from k and that has S+a[i+1] as sum of array elements. But there is one more situation to analyse. If S is less then zero is obvious that S+a[i+1] < a[i+1] so in this case the best sub array ending in i+1 position is exactly the sub array containing only that element. In fact this situation direct you to start a new sub array that will be candidate for the best sub array of the entire array.

In conclusion the information to be kept while going through the array only once (O(n)) is the best sub array ending in the current position and best sub array found for the entire array until the current step.(if it necessary also the starting and ending position for these sub array can be kept). After the processing of the last element the algorithm will have determined the sub array having the largest sum.

Note: The algorithm works fine even there is no negative number in the array and it will produce of course as the largest sum the sum of all array elements.

Algorithm: arr is the array of n integer; the function will return the largest sum and the limits of the sub array producing that value */

#include <iostream>

using namespace std;

int GetLargestSubArray(int* arr, int n, int &iBeginRet, int

&iEndRet)

{

int iBeginSaved=0, iEndSaved=0; // the start/end positions of the saved sub array

int iBegin, iEnd; // the start/end positions of the current sub array

int nSumSaved=0, nSum=0; // the sums of whole saved largest and current sub arrays

int i = 0; // index to loop in the array

if(0 == n) // Nothing to analyze, return invalid array indexes

{

iEndRet = iBeginRet = -1;

return 0;

}

nSumSaved = nSum = arr[i];

for(i = 2; i < n; i++)

{

/*Compute the current largest sum */

if(nSum<0)

{

nSum = arr[i];

iBegin = iEnd = i;

}

else

{

nSum += arr[i];

iEnd= i;

}

if(nSum > nSumSaved)

{

nSumSaved = nSum;

iBeginSaved = iBegin;

iEndSaved = iEnd;

}

}

iBeginRet = iBeginSaved;

iEndRet = iEndSaved;

return nSumSaved;

}

Q15: Given an array of size N in which every number is between 1 and N, determine if there are any duplicates in it.

A15: I'll try to do it in O(N) w/o using any additional memory. The key is to use content of the array as index into array, checking in O(1) if that number has been seen already.

bool HasDups(int * a, int N)

{

bool fHasDup = false;

for(int i = 0; i < N; i++) {

int index = a[i] % N;

if(a[index] > N) {

fHasDup = true;

break;

}

a[index] += N;

}

//restore the array

for(int j = 0; j < i; j++)

if(a[j] > N) a[j] %= N;

return fHasDup;

}

Q16: A square picture is cut into 16 squares and they are shuffled. Write a program to rearrange the 16 squares to get the original big square.

Q17: Implement an algorithm to reverse a singly linked list. (with and without

recursion)

Node*RevSList(Node *pCur, Node *pRev) {

if(!pCur) return pRev;

Node*pNext = pCur->Next;

pCur->Next = pRev;

pRev= pCur;

return (RevSList(pNext, pRev));

}

Node* RevSList(Node *pCur) {

Node*pRev = NULL;

while (pCur)

{

Node*pNext = pCur->Next;

pCur->Next = pRev;

pRev= pCur;

pCur= pNext;

}

return pRev;

}

Q18:Implement an algorithm to reverse a doubly linked list.

Node *RevDList(Node *pCur)

{

if(!pCur) return pCur;

pSav= pCur->Next;

pCur->Next = pCur->Prev;

pCur->Prev = pSav;

if(!pSav) return pCur;

return RevDList(pSav);

}

Node*RevDList(Node *pCur)

{

while (pCur)

{

Node*pSav = pCur->Next;

pCur->Next = pCur->Prev;

pCur->Prev = pSav;

if(!pSav) return pCur;

pCur= pSav;

}

return pCur;

}

Q19: Delete an element from a doubly linked list.

Node* DelDLLNode(Node *pNode)

{

if(!pNode) return pNode;

if(pNode->Next) pNode->Prev->Next =pNode->Next;

if(pNode->Prev) pNode->Next->Prev =pNode->Prev;

return pNode; // delete it if it's heap-based.

}

Q20: Implement an algorithm to sort an array.

Q21: Given a sequence of characters, how will you convert the lower case characters to upper case characters?

Q22: Count the number of set bits in a number without using a loop.

#define reverse(x) \

(x=x>>16 | (0x0000ffff&x)<<16, \

x=(0xff00ff00&x)>>8|(0x00ff00ff&x)<<8,\

x=(0xf0f0f0f0&x)>>4|(0x0f0f0f0f&x)<<4,\

x=(0xcccccccc&x)>>2|(0x33333333&x)<<2,\

x=(0xaaaaaaaa&x)>>1|(0x55555555&x)<<1)

#define count_ones(x) \

(x=((0xaaaaaaaa&x)>>1)+(0x55555555&x), \

x=((0xcccccccc&x)>>2)+(0x33333333&x), \

x=((0xf0f0f0f0&x)>>4)+(0x0f0f0f0f&x), \

x=((0xff00ff00&x)>>8)+(0x00ff00ff&x), \

x=(x>>16) + (0x0000ffff&x))

Q23: Give mean algorithm and C code to shuffle a deck of cards, given that the cards are stored in an array of ints. Try to come up with a solution that does not require any extra space.

for(Src = 0; Src < N; Src++)

{

Dest= rand() % N; // All N positions equally likely

Swap(X[Src], X[Dest]);

}

At first glance, it would appear that this algorithm generates all permutations with equal probability. On examination, though, one can see that this will generate N^{N} arrangements of elements---each of the N iterations of the loop positions a value among the N available positions. It is known, though, that there are only N! possible permutations of N elements: for each permutation there are multiple ways to generate that permutation---on average, N^{N}/N! ways.

for(Src = 0; Src < N; Src++)

{

Dest= rand() % N; // All N positions equally likely

Swap(X[Src], X[Dest]);

}

Examination of the structureof this loop shows that it will generate N! arrangements of elements. All permutations are equally likely, aside from the very minor deviation from uniform distribution by selecting a random value between 0 and Dest as (rand()

% (Dest+1)).

Q24: How would you print out the data in a binary tree, level by level,

starting at the top?

Q25: Do a breadth first traversal of a tree.

typedef int VertexType;

typedef class Vertex *LPVertex;

class Vertex

{

int index;

int weight;

LPVertex next;

public:

int GetIndex();

bool Visited();

Vertex &Visit();

Vertex &Mark();

Vertex *GetNext();

};

enum { kMaxVertices = 7 };

typedef LPVertex HeaderArray[kMaxVertices];

HeaderArray adjacencyList;

void BreathFirstSearch (HeaderArray adjacencyList, LPVertex pv)

{

queue Q;

pv->Visit().Mark();

Q.push(pv);

while (!Q.empty())

{

pv = Q.front(); Q.pop();

pv =adjacencyList[pv->GetIndex()];

for(; pv; pv = pv->GetNext())

if(!pv->Visited())

{

pv->Visit().Mark();

Q.push (pv);

}

}

}

void DepthFirstSearch (HeaderArray adjacencyList, LPVertex pv)

{

stack S;

pv->Visit().Mark();

S.push(pv);

while (!S.empty())

{

pv =S.top();

pv =adjacencyList[pv->GetIndex()];

for(; pv; pv = pv->GetNext())

if(!pv->Visited())

{

pv->Visit().Mark();

S.push(pv);

}

S.pop();

}

}

Q26: Write a routine to draw a circle given a center coordiante (x,y) and a radius (r) without making use of any floating point computations.

Q27: Given an array of characters which form a sentence of words, give an efficient algorithm to reverse the order of the words in it.

char

*ReverseWords (char *string)

{

char*start = strrev(string);

char*left;

char*right;

char ch;

while (*string)

{

while (*string == ' ' & *string)

string++;

left= string;

while (*string != ' ' & *string)

string++;

right = string-1;

while (left < right)

{

ch =*left;

*left++ = *right;

*right-- = ch;

}

}

return start;

}

Q28: Implement a TIC-TAC-TOE game assuming Computer as one of the player. Optimize it for fast computer play time and space. Do some analysis on memory and processing requirements.

Q29: Write a function to find the depth of a binary tree.

long findDepth(Node *pNode)

{

if(!pNode) return 0;

long depthLeft = findDepth(pNode->Left);

long depthRight = findDepth(pNode->Right);

return (depthLeft>depthRight ? ++depthLeft:

++depthRight);

}

Q30: You aregiven two strings: S1 and S2. Delete from S2 all those characters which occur in S1 also and create a clean S2 with the relevant characters deleted.

char *strtokrem (char *string, const char *control)

{

char*start = string;

char*str = string;

const char *ctrl = control;

char map[32];

int count;

/*Clear control map */

for(count = 0; count < 32; count++)

map[count] = 0;

//Set bits in delimiter table

do

{

map[*ctrl >> 3] |= (1 << (*ctrl & 7));

}

while (*ctrl++);

//Remove each token whenever it matches

while (*str)

if(map[*str >> 3] & (1 << (*str & 7)))

{

for(char *pch = str; *pch; pch++)

*pch= *(pch+1);

}

else

str++;

return start;

}

Q31: Write a small lexical analyzer for expressions like "a*b" etc.

bool is_astarb(char* string)

{

//expressions: b, ab, aab, aaab, ...

bool bRet = false;

while (*string == 'a')

++string;

if(*string == 'b')

bRet= (*++string == '\0');

return bRet;

}

Q32: Given an array t[100] which contains numbers between 1 and 99. Return the duplicated value. Try both O(n) and O(n-square).

Q33: Write efficient code for extracting unique elements from a sorted list of

array.

void PrintUniqueElements(int rgNumb[], int cNumb)

{

assert(cNumb>0);

int iSav;

cout << (iSav = rgNumb[0]) << "\t";

for (int i = 1; i < cNumb; i++)

if (iSav != rgNumb[i])

cout<< (iSav = rgNumb[i]) << "\t";

}

Q34: Given a list of numbers (fixed list) Now given any other list, how can you efficiently find out if there is any element in the second list that is an element of the first list (fixed list).

Q35: Print an integer using only putchar. Try doing it without using extra

storage.

void putDigits(int val)

{

if(val < 0) { cout << "-"; val = -val; }

stack<int> S;

S.push(val);

while (!S.empty())

{

val= S.top(); S.pop();

if(val >= 10)

{

S.push(val%10);

S.push(val/10);

}

else

cout.put(val+'0');

}

}

Q36: Write a function that allocates memory for a two-dimensional array of given size(parameter x & y).

Q37: Write source code for printHex(int i) in C/C++

void putHex(int val)

{

if(val < 0) {

printf("-");

val= -val;

}

if(val >= 0 & val < 16) {

printf("%c", val > 9 ? (val-10)+'A' :val+'0');

return;

}

putHex(val/16);

printf("%c", val%16 > 9 ? (val%16-10)+'A' :val%16+'0');

}

Q38: What sort of technique you would use to update a set of files over a network, where a server contains the master copy.

Q39: How do you handle deadlock on a table that is fed with a live serial feed?

Q40: Do the class/structure description for a Hash table, and write the source

code for the insert function.

Q41: How would you implement a hash table? How do you deal with collisions.?

Q42: What would you suspect if users report they are seeing someone else'sdata on their customized pages?

A42: Overflow; If we're talking about ASP, JSP, CFML that sort of thing, I would suspect unsynchronized access to session data in a multi-threaded Servlet, JavaBean or COM object -- i.e., a non-threadsafe bug in the server application.

Q43: How would you do conditional compilation?

A43: The #if directive, with the #elif, #else, and #endif directives, controls compilation of portions of a source file. If the expression you write (after the #if) has a nonzero value, the line group immediately following the #if

directive is retained in the translation unit. Plus, #ifdef and #ifndef identifier.

Q44: Write an algorithm to draw a 3D pie chart?

Q45: Prove that Dijkstra's MST algorithm indeed finds the overall MST.

A45: The two common MST algorithms are by Kruskal and Prim. Djikstra gave us

an algorithm for shortest path, not MST.

Q46: How would you implement a queue from a

stack?

stack stk1, stk2;

void push(element e)

{

push.stk1(e);

}

element pop()

{

if(stk2.empty())

while(!stk1.empty())

stk2.push(stk1.pop());

return stk2.pop();

}

Q47: Write a funtion that finds repeating characters in a string.

Q48: Write a routine to reverse a series of numbers without using an array.

int iReverse (int iNum)

{

int iRev =0;

while(iNum !=0)

{

iRev = iRev * 10 + iNum % 10;

iNum /= 10;

}

return iRev;

}

Q49: Write a function to find the nth item from the end of a linked list in a single pass.

A49: I would think keeping a gap of "n" between fptr and sptr would do. Then, advance both together till fptr->next (fptr is the one in front) = NULL.

Aren't you traversing the list twice - once with fptr and the second time with sptr. I think you should maintain an queue of pointers. Keep pushing a pointer into the queue and whenever the size of the queue becomes greater than n, remove a pointer at the head of the queue. When you reach the end of the list. The element at the head of the queue gives a pointer to the nth element from the end.

#include <queue>

PNODE GetNthLastElement (PNODE pCur, unsigned nOffset)

{

queue<PNODE> Q;

for(; pCur && Q.size() < nOffset; Q.push(pCur), pCur = pCur->Next);

if (Q.size() < nOffset) return NULL;

while (pCur){

Q.pop();

Q.push(pCur);

pCur= pCur->Next;

}

return (Q.front());

}

Q50: Give me an algorithm for telling me the number I didn't give you in a given range of numbers (Numbers

are given at random).

Q51: Write a random number generator in a specified range.

#include <algorithm>

int random_range(int lowest_number, int highest_number)

{

if(lowest_number > highest_number)

{

swap(lowest_number,highest_number);

}

int range = highest_number - lowest_number + 1;

return lowest_number + int(range * rand()/(RAND_MAX + 1.0));

}

Q52: Delete a node from a single linked list.

#include <algorithm>

int random_range(int lowest_number, int highest_number)

{

if(lowest_number > highest_number)

{

swap(lowest_number,highest_number);

}

int range = highest_number - lowest_number + 1;

return lowest_number + int(range * rand()/(RAND_MAX + 1.0));

}

Q53: Say you have three integers between 0 - 9. You have the equation: A! + B! + C! = ABC (where ABS is a three digit numbers, not A * B * C). Find A, B, and C that satisfies this equation.

Q54: Give 2 nodes in a tree, how do you find the common root of the nodes?

Q99: Write a small lexical analyzer for expressions like a(b|c)d*e+.

enum State {

s0 =0, s1, s2, s3, // states

m0 = 0, m1, m2, m3, acc, err // actions: matches, accept or error

};

State DecisionTable[4][6] = {

// a b c d e other // input

m1,err,err,err,err,err, // s0

err,m2, m2,err,err,err, // s1

err,err,err, m2, m3,err, // s2

acc,acc,acc,acc, m3,acc // s3

};

State IsAcceptable (char *&theIStream)

{

State stateCur = s0, State theDecision = err;

do

{

char theChar = *theIStream++;

int theInput = (theChar - 'a') % 6;

theDecision = DecisionTable[stateCur][theInput];

switch (theDecision)

{

default:

stateCur = theDecision;

break;

case err:

case acc:

; //do nothing

}

}

while (theDecision != err & theDecision != acc);

return theDecision;

}