Data Structures (Classroom Practice Booklet Solutions)

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2 Dt Strutures (Clssroom Prtie Booklet Solutions). Arrys. Ans: o of A [] = +(+) = Here, j is Vrying lo. of Ai, j i rows j C In (i ) rows no. of elements, (i ) = i (i )/ lo of Ai, j [i(i ) / (j )] C. (i) By RMO, the lo. of A [, ] = + [ (+) + (-)] = + = (ii) By CMO, the lo of. () RMO: A [, ] = + [( ) + (+)] = Storge: 7 Eg: Retrievl: lo of A[i, j] D D = i rows j j C () CMO: Storge: 7 Retrievl: lo of Ai, j D D j ols i i In eh ol., il = j. o. of i, j [(j) ols (i j)] C A In (j ) ols The no. of elements is n n... n j j n... j n j lo. of A[i, j] nj j j j j C i j C ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

3 : : Dt Strutures. () RMO: Storge: 7 Retrievl: lo of Ai, j D D numer of elements in i rows j j euse j is Vrying Row jl exept st row i th (i ) lo. of i, j i j i A C () CMO: Storge: i j C 7 Retrievl: lo. of A[i, j] = + D + D Sine i is Vrying Col il j ols i i exept st olumn j th j- j j i j C j i C lo of A i, () Storge & Retrievl: 7 If i j = lo of Ai, j i i or (j jl) i.e., lo. of Ai, j i or j If i j = lo. of Ai, j (n ) i or j If i j = lo. of Ai, j n i or j ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

4 : : CSIT Postl Cohing Solutions. Z Mtrix:,,, re ntidigonl elements where i + j = N + Storge: st row lst row remining elements re 7 If i = lo of Ai, j j If i = n j lo of Ai, j n j If i + j = n + lo of Ai, j n i Algorithm: if (i = = ) return A[j ]; else if ( i = = n) return A[n + j ]; else if ( i + j = = n + ) return A [n + i ]; else return ;. 7 If i = o. of A[i, j] = + + j = j If i = n o. of A[i, j] = + n + j = n + j - If j = o. of A[i, j] = + n + n + i = n + i n n (n ) = ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

5 : : Dt Strutures. () A sequene mtrix of order n n is sid to e Toeplitz mtrix. If T [i, j] = T [i, j ], for ll i >, j >. Size = n x 7 7 x x x Ex: A [, ] = A[, ] ( = ) size of memory required for Toeplitz mtrix of order nn x 7 7 x x x n+ n = n () Storge nd retrievl: i j i > j If i j o. of A [i,j] = + [ + (j )] If i > j o. of A [i,j] = + [n+(i j )] if (i j) else return A[j i]; return A [n+i j ];. () Squre Bnd Mtrix: It is denoted y D n, where n is size of mtrix is (-) s digonls exists ove nd elow the mtrix digonl. D, = Size:- N (digonl elements ) + [N +N +N-+.+N ( )] = N+[( )N (+++.+ )] Totl no. of elements = n+ [n + n +. + n ( )] = n + [( ) n [++. + ( )]] n n = n+n( ) ( ) = n + ( ) [n ] ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

6 : : CSIT Postl Cohing Solutions Ex: In D, = + [ ] = + = elements () D, In D, A (,) in rd digonl In D, A (,) in th digonl (i) i j vlue is remined onstnt through out the digonl (ii)as vlue hnges, ordingly K vlue lso hnges. K vlue = (i j) lo. of A[i,j] = + no. of elements in(k ) dig + D ross Store D, : No. of elements in (k ) digonls is [n (-)]+[n ( )+] + [n ( ) + ] +. [n +(k )] [n ( )] st digonl euse it is( ) th digonl (n ( )+) nd digonl [n ( )+] rd digonl n +(k ) (k ) th term i.e. (k ) th digonl = (k ) (n ) k k(k ) = (k ) (n ) + lo. of A[i, j] = + k n k k j 7 lo. of A[i, j] = +no. of element in (k ) dig + (i il) or (j jl) ut here il is vrying digonl y digonl so prefer jl whih is lwys in eh digonl = + no. of elements in (k ) dig +(j ) ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

7 : : Dt Strutures. Stks & Queues. (i). Ans: () (ii). Ans: () Given rry size m, sy Numer of stks n, sy m i < n T[i] = B[i] = i. n i = T [] = B[] = = = i = T [] = B[] = = = i = T [] = B[] = = [] = when i = B [] = m = = (i) Push = overflow = size i B m T 7 th stk st stk nd stk m- 7 T B T B over flow ses T B T[i] = B [ i +] (ii) POP = under flow = initil B T 7 7 T[] T[] T[] B[] B[] B[] B[] T B T B under flow ses T[i] = B[i] T B. Ans: () Stk Stk Stk 7 7 B[] T[] T[] B[] Pop Pop Pop T[] B[] over flow B[] Arry ontents re,,,,,,, 7, ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

8 : 7 : CSIT Postl Cohing Solutions. Ans: () Queue one ontins elements. The element is to Pop is the th element of the queue. Dequeues from queue one + enqueues from queue one. enqueues from queue two + Dequeues from queue two the th element is nother Dequeue.. invotion til () T () = T () = T () = T () = stop Output:,, Totlly enqueues, Dequeues. Ans: (d) () Push () Push () Pop( ) Pop( ) Pop( ) () underflow Push () Push () Pop() Pop( ) :vlid Get top( ) = : vlid 7. hed (x) hed (x ) printf (x) hed (x ) hed() hed() printf(x) hed() repet () :vlid hed() print(x) hed() eft steps (d) Push () Push () Push () Pop( ) :Invlid Push() Pop Push() Pop( ) Is empty( ): true But given is flse so : Invlid hed () print (x) hed () Output:. Ans: (d) ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

9 . (i) x()=7 : : Dt Strutures Additions = f (n+) f() = f() = =. (i) (ii) x ( x [] ) x (7) 7 x() x() x() x() = x [] = 7 x(x[]) = 7 The no. of lls or invotions for evluting x(x[]) = Numer of lls for evluting f(n) = f (n+) x()+ x()+ + + = 7 n 7 Fi(n) Cll: Add:. (ii) Clulte the totl numer of lls in Fioni () = f() = = = 7 (iii) fi (7) fi () fi () fi () fi () fi () fi () fi () fi () fi () fi () fi () fi () Akermn(m, n) n if m Akermnm, if n Akermnm, Akermn(m, n ) otherwise (i) Akermn(, ) = A(, A(, )) = A(, 7) A(,) = A(, A(,)) = A(, ) = 7 A(,) = A(, A(,)) = A(, ) = A(, ) = A(,) = A(, ) = A(, A(, )) = A(, ) = + = ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

10 : : CSIT Postl Cohing Solutions A(, ) = A(, ) = A(, ) = + = A(,) = A(,A(, )) = A(, ) = + = A(,) = A(,A(, )) = A(, )= + = A(, ) = A(, A(, )) = A(, A(, A(, ))) = A(, A(, )) = A(, ) = + = 7 A(, 7) = A(, A(, )) = A(, A(, A(, ))) = A(, A(, 7)) = A(, ) = Akermn(, ) = (ii) Akermn(, ) = A(, A(, )) = A(, A(, A(, ))) = A(, A(, )) A(, ) = A(, ) = A(, A(, )) = A(, A(, A(, 7))) = A(, A(, )) = A(, ) = A(, ) = A(, A(, )) = A(, A(, A(, ))) = A(, A(, )) = A(, ) = Akermn(, ) = (iii) Akermn(, ) = (iv) Akermn(, ) = A(, ) A(,) = A(, A(, )) A(, ) = A(, ) A(, ) = A(, A(, )) A(, ) = A(, ) = A(, ) = A(, ) = A(, ) = A(, ) = A(, ) A(, ) = from (i) A(, ) = Akermn(, ) =. void TOH (int n, int ) { if (n! = ) { TOH (n,, R, M); } } void min ( ) { TOH (,,, ); } Eh disk moves for i where i =,, If there re disks then it moves for times = ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

11 : : Dt Strutures. () After N + lls we hve the first move. So fter lls we hve the first move. () After totl lls lls, we hve the lst move. () Totl moves N = 7 (d) Totl invotions = N+ = =. void TOH(int r, int, int m, int R) { if (n = =) printf : to R else { TOH (n,, R, M) printf( to R) TOH(n, M,, R) } void min( ) { TOH(,,, ); } moves = N lls = N+ ut with modified progrm. The numer of lls n e redued.. (i) Ans: (d) A * B CD + A * B C + D (ii) Ans: () A(B+C) * D (A * (B+C)) D A B+C D. = + * d/e + f g h i * j (i) Postfix: = + *d/e + fgh i*j = + *d/e + f g h i * j = +*d/e + f gh i*j = + d*e/+ fgh (i j *) = d * e/+fgh + ij* d*e/+fgh + ij* = (ii) Prefix: = + * d/e +( f gh) i * j = + *d/e + ( fgh) i * j = + /*de + fgh *ij = + /*de + fgh *ij = ++ /*defgh *ij = + + /*de fgh*ij = + + /*de f gh*ij ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

12 : : CSIT Postl Cohing Solutions. Ans: (d) 7. (i) * / + + * / + + / + + / ^ / * *. Ans: (),, +,,, /, *,, / = + = * = = (ii) ++ + / * ++ + / * ++ / ++ / ACE Engineering Pulitions Vlue of the postfix expression is. Ans: yz (i) (ii) (iii) yz (iv) yz Output is yz Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

13 : : Dt Strutures. R 7 F Size = u l + + = Given ondition () Bse (s) = Front (Q ) = () Front (Q ) = Bse (s) = = Until first is enountered, stk ontins So ++ = is enqueued in lo Until seond is enountered, stk ontins 7 So + 7 = is enqueued is Then simply nd re pushed in stk So the lotion of nd re nd. S Front. Ans () Suppose tht rry ontins Rer 7 7 Front S Initil onfigurtion: Dequeue( ) enqueue (x) nd enqueue (y) :. Ans: () The given reursive proedure simply reverses the order of elements in the queue. Beuse in every invotion the deleted q 7 7 Front q Rer R F Delete element F R Now two dded x y F R (R, F) = (,) Option (). Rer ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

14 : : CSIT Postl Cohing Solutions element is stored in i nd when the queue. eomes empty. Then the insert ( ) funtion ll will e ii exeuted from the very lst invoked d e f funtion ll. So, the lst deleted element will e inserted first nd the proedure goes first p i iii on Print = d. inked ists. It ompres the two lists ist nd ist if they re sme it returns true otherwise ist nd ist re different. () ist is ontented t the end of ist. () either uses null pointer dereferene or ppends list m to the end of list n.. P Q R S T - first The output is PQRST 7. Ans: () while (P) or while (P!= Null) while P is pointing to someody. Reursive routine for Count. It eomes irulr single inked ist euse loop termintes when temp = = Null.. ii d e f g first iii i p Print = d f d Return + Return + Return + Return + Return ll ll ll ll No. of nodes = ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

15 . Ans: () f f Before After ogi r q : : Dt Strutures. Ans: () inked stk push ( ) = insert front ( ) Initil Do( ) NU f Do() f. p Before f \. Do() f q v w x y z Opertion eft most Right most Middle Insert After Delete f v w x y z ontention of two single linked lists y hoosing lterntive nodes.. n link = M n Rlink = M Rlink n link Rlink = n n Rlink link = n. Ans: (d) Cur. Next = New Node (X, Cur. Next) iii iv (i) Strut Node * n = Get Node ( ) ; (ii) n dt = X ; (iii) n Next = Cur Next ; i x ii (iv) Cur Next = n n ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

16 : : CSIT Postl Cohing Solutions. Ans: (B) Inserts to the left of middle node in douly linked list.. Ans: () Before reverse: H d t : t link After reverse: H d 7. Ans: () It is n extension for the si single linked list. In irulr linked list insted of storing Null vlue in the lst node of single linked list, store the ddress of the st node (root) forms irulr linked list. Using irulr linked list it is possile to diretly trverse to the first node fter rehing the lst node nd so perform dditions nd deletions in O() time omplexity. For tht, rer node points to front node ut front node doesn t point to rer node. ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

17 : : Dt Strutures. Trees. void A (strut BTNode *t). { () Converse Preorder Algorithm Converse Preorder(node x) if(t) { { printf( %, t dt); if x Null B (t C); print(x.vlue) Converse Preorder(x.right) } B (t RC); A Converse Preorder(x. left) } B B } e A A () Converse Inorder f Algorithm Converse Inorder(node x) { if x NU B d A(t) = d f g e B g } Converse Inorder(x.right) Print(x.vlue) Converse Inorder(x.left) void B (strut BTNode *t) { if(t) { () Converse Postorder Algorithm Converse Postorder(node x) { if x NU Converse Postorder(x.right) Converse Postorder(x.left) Print(x.vlue) } } A (t C); printf( %, t dt); A (t RC); B A B B f A e } A A d g B(t) = d e f g ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

18 . void A(strut BTNode *t) { if(t) { printf( %, t dt); B (t RC); B (t C); } } void B (strut BTNode *t) { if(t) { A (t RC); printf( %, t dt); A (t C); } } e : 7 : CSIT Postl Cohing Solutions Note: The numer of inry trees n e formulted with unleled nodes re n C n n.. Ans:. Preorder : A B C D E F G In-order : B D C A F G E Post-order: D C B G F E A B D C d d B D C A F G E F G E f D C F G d g B(t) = egfd D G. 7. Note: If pre-order is given, long with terminl node informtion & ll right hild informtion the unique pttern n e found. If post-order is given long with Totlly distint trees possile terminl informtion nd ll left hild ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

19 : : Dt Strutures informtion the unique pttern n e. () Ans: identified. = I(n-)+ V = = I + V d V V t = null e V f V I =. Ans: () =. = = = d e f g Post- order : defg Pre-order: defg In-order: defg. Minimum =, Mximum = x xr. () Ans: ef nodes () = Totl nodes internl nodes = In+-I x xr x xr d = I(n-)+ = I =? = I( ) + = I + t=nu x xr e xr x g xr I = x f ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

20 : : CSIT Postl Cohing Solutions.. Before Swp After swp (, (e (f, g, h)),d) e e Prent of f, g, h is e. i.e. internl prenthesis hs hildren of prent whih is out of prenthesis. IV d d d III e e e II f g h I step. v ++ d d e e v v d. Given re trees A p B C q r To get the onverted inry tree of these given trees prent is not given we hve to ssume virtul prent v t = Null v v v e f V A p B C q r ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

21 : : Dt Strutures While trversing left ut the right node from. prent nd onnet it to the first left hild similrly seond to first third to seond nd so on. () () log x log A x. B P q C r () x!! (d) log x! log! Count the numer of trees in forest. x x 7. Ans: (d) left left Most hild nd Right s Right Siling (e) = Def: A left-most hild, right-siling inry tree is inry tree representtion of k-ry + tree. To form inry tree from n ritrry k-ry tree, the root of the originl tree is mde the root of the inry tree. Then, strting with the root, eh node's leftmost hild in the originl tree is mde its left hild in the inry tree, nd its nerest siling to the right in the originl tree is mde its right hild in the inry tree. + * / d e f g h i * j It ounts numer of leves in tree.. Ans: Expnded s ((+) ( )) + (( ) + (+)) = + = ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

22 : : CSIT Postl Cohing Solutions. Ans: ( + ) ( ) + ( ) + ( + ) = + ( ) =. SUN. MON TUE FRI SAT THU WED 7. 7,,,, 7, insert into empty inry serh tree. Ans: () Preorder =,,,, 7,,,,,, 7, Inorder =,, 7,,,,,,, 7,,,, 7,,,,,7,, 7 7,, 7, 7,, Element in the lowest level is 7. Return mximum vlue of the BST BST =, 7,,,,,, 7,,,, min mx ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

23 : : Dt Strutures. Ans: (d) () 7 (d) Not possile IN: not sorted order () 7 () 7 Not possile Not possile 7. BST deletion:- Proedure: Cse (i): No hildren: simply delete it Cse (ii): only one hild (or) sutree: onnet hild to its grnd prent. Cse (iii): Both hildren (or) su trees: reple with defult tion. i. Inorder suessor = minimum of RST ii. Inorder predeessor = lrgest to ST.. NH min N H H H NH H N(H) = + N(H-) + N (H-) N() = + N() + N() = + + = N() = +N()+N() = + + = 7 ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

24 : : CSIT Postl Cohing Solutions N() = + N(7) + N() = + + =.,,,,,,,,,,,, 7 + H 7 N(H) R + - R R + + R R R ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

25 : : Dt Strutures + R A E I R T V A E I K O R T S V 7. Delete, A + 7. A, V,, T, R, E, I, S, O, K R 7 A R V + A + T R V + Delete 7 7 Delete,, ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

26 : : CSIT Postl Cohing Solutions 7 + Delete. () Sequene of explortion V V V V V V V V 7 DFS Spnning tree is () Sequene of stk ontents. V V V V V V V. Grphs Delete 7 7 R Delete () Not pushed verties re V, V 7 (d) Verties re not pushed in more thn one V, V, V, V, V. () Sequene of explortion V V V V V V V 7 V () Sequene of stk ontents () Not pushed verties re V, V 7 (d) Verties re not pushed in more thn one V, V, V, V, V. () Sequene of explortion V V V V V V V 7 V () Sequene of stk ontents V V V V V V V V V V V V V V () Not pushed verties re V, V 7, V (d) Verties re not pushed in more thn one V, V, V ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

27 : : Dt Strutures. () invlid () vlid () (d) () vlid (d) vlid () () 7 7. Ans: (d) Step k only when lredy explored verties re there V V V () 7 (d) 7 V Trversl: BFS V V V V 7. () vlid () vlid V () invlid (d) vlid V V () () V V V V V ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

28 : 7 : CSIT Postl Cohing Solutions queue V V Dequeue queue V V V Dequeue queue V V V V 7 Dequeue queue V V V 7 V 7. () vlid () vlid () invlid (d) vlid. 7 g f e d strt Minimum possile reursion depth = (The dshed link nodes re explored while stepping kwrd.). Hshing. Ans: (d). Ans: (d). Ans: 7. Ans: () key: o:- 7 No. of ollisions = Mximum possile reursion depth = (The dshed link nodes re explored while stepping kwrd.) ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

29 : : Dt Strutures. Ans: () Keys Fold shifting h(k) = k% += + = + = ++ = ++ = () = ++ = ++ = 7 () = () ++ = Numer of Collisions =. (i) Hshing: (ist size: ) Modulo Division Collision Resolution: iner Proe Hshing Clultions % = 7 % = % = % = () 7 % = % = 7 % = () % = % = 7 Hshed ist (Collision) () () Collisions:. ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

30 : : CSIT Postl Cohing Solutions (ii) Hshing: (ist size: ) Digit Extrtion (,, ) + Modulo Division Collision Resolution: Qudrti Proe Hshing Clultions % = 7 7 % = % = + % = () % = 7 7 % = % = 7 % = % = + % = () () () Collisions:. % = Hshed ist (Collision) ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

31 : : Dt Strutures (iii). Hshing: (ist size: ) Mid Squre Collision Resolution: Rndom Numer ( * ddress ) % Hshing Clultions = % = 7 7 = 7 7 % = = % = ( * ) % () = % = 7 = % = ( * ) % ( * ) % () = % = 7 = % = 7 = % = ( * ) % ( * ) % ( * ) % ( * ) % ( * ) % () Hshed ist (Collision) () - - () () () Collisions:. ( * ) % () = % = ( * ) % ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

32 : : CSIT Postl Cohing Solutions (iv). Hshing: (ist size: ) Fold Shift Collision Resolution: iner Proe Hshing Clultions ( + + ) % = 7 ( ) % = ( + + ) % = ( + + ) % = 7 ( + + 7) % = ( + + ) % = 7 ( + + 7) % = ( + + ) % = ( + + ) % = 7 Hshed ist (Proe) Collisions:. (v). Hshing: (ist size: ) Rottion (right ), extrt (,, ),% + Collision Resolution: iner Proe Hshing Clultions % = % = % = 7 () ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

33 : : Dt Strutures % = % = % = 7 7 % = % = % = () - - Collisions:. () Hshed ist (Collision). Ans: () () Mximum Minimum (verge). Ans: () Resultnt hsh tle. In liner proing, we serh hsh tle sequentilly strting from the originl ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt

34 : : CSIT Postl Cohing Solutions lotion. If lotion is oupied, we hek the next lotion. We wrp round from the lst tle lotion to the first tle lotion if neessry. Cse (II): To store Vrile prt Fixed prt 7. Ans: () A 7 B C D. Ans: () Cse (I): To store Vrile prt Fixed prt! = Sine is not getting ollided with ny other key, it n e moved to the vrile prt. Cse (I) & Cse (II) re mutully exlusive Cse (I) + Cse (II) = + = Totl different insertion sequenes. Ans: Slots = Elements = od ftor = = elements slots =! = ACE Engineering Pulitions Hyderd Delhi Bhopl Pune Bhuneswr uknow Ptn Bengluru Chenni Vijywd Vizg Tirupti Kuktplly Kolkt