Binary'Tree'- Recursion
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Recursion
• 01$%2#"&'("#(341(#3253167(8&2(#&9:"'6(;2&<91=#(>4121(5(=134&?($599#(
"3#198@
• A;;2&5$4
B C8(341(;2&<91=("#(#325"6438 &2>52?D(#&9:1("3(?"2 1$397(E<5#1($5#1(F 341(95#3(#31;(3&(
#3&;(341(21$%2#"&'G@
B H9#1(E21$%2#":1(#31;G
.@ I"=;9"87(341(;2&<91=("'3&(#=59912(;2&<91=#@
,@ I&9:1(341(#"=;912(;2&<91=#(%#"'6(341(#5=1(596&2"34=@
J@ K&=<"'1(341(#&9%3"&'#(&8(341(#=59912(;2&<91=#(3453(#&9:1(341(61'1259(;2&<91=@
Recursion'– Array'Addition'Example
• L":1'(5'(522 57(&8(M,D(JD(ND(OD(*D(/PD("=;91=1'3(5(21$%2#":1(=134&?(5??E"'3MP(
5G(3453($59$%9531#(341(#%=(&8(599("'31612#("'(341(52257@
• A'#>12Q
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213%2'(5??S419;12E5D()GT((((((++U 11?(5(419;12(= 134&?(3&(5$$1##(15$4(
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V
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"8(E"'?1W(XX(5@91'634 B .G(213%2'(5M"'?1 WPT(++Y5#1($5#1
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V
Binary'Tree
• !18"'"3"&'Q(Y"'527([211("#(5(?535(#32%$3%21(3453(45#(5(2&&3('&?1(5'?(
15$4('&?1("'(341(3211(45#(53(=&#3(3>&(#%<3211#D(>4"$4(521(2181221?(3&(
341(9183($4"9?(5'?(2"643($4"9?@
• HW5=;91Q
Binary'Tree'Traversal
• Y215?34B8"2#3(325:12#59(EY\IG(:"#"3#('&? 1(5$$&2?"'6(3&(4&>(852(5>57(
82&=(341(2&&3@
• !1;34B8"2#3(325:12#59( E!\IG(:"#"3#('&?1#(5#(852( 5415?(5#(;&##"<91(<18&21(
<5$]"'6(%;@([4121(521(34211(37;1#(&8(!\I(8&2(<"'527(3211#Q
• ^21&2?12(32 5:12#59(:"#"3#(5('&?1D(341'("3#(9183($4"9?D(341'("3#(2"643($4"9?@
• C'&2?12 325:12#59(:"#"3#(5('&?1_#(91 83($4"9?D(341'(341('&?1("3#198D(341'("3#(2"643(
$4"9?@
• ^&#3&2?12 325:12#59(:"#"3#(5('&?1_#(9183($4"9?D(341'("3#(2"643($4"9?D(341'("3#198@
Binary'Tree'Traversal'Example
Y215?34B8"2#3Q(
^21&2?12Q
C'&2?12Q
^&#3&2?12Q
Binary'Tree'Traversal'Example
Y215?34B8"2#3Q(ND(JD(*D(OD(/
^21&2?12Q(ND(JD(*D(OD(/
C'&2?12Q(JD(ND(OD(*D(/
^&#3&2?12Q(JD(OD(/D(*D(N
`"#%59"a53"&'(9"']Q(433;#Q++:"#%596&@'13+1'+<#3
Which'one'of'these'is'breadth-first'traversal?
A@ .D(,D(JD(ND(OD(*D(/D(bD(-
Y@ OD(,D(*D(.D(ND(bD(JD(/D(-
K@ .D(JD(ND(,D(/D(-D(bD(*D(O
!@ OD(JD(,D(ND(JD(*D(bD(/D(-(
Which'one'of'these'is'breadth-first'traversal?
A@ .D(,D(JD(ND(OD(*D(/D(bD(-
Y@ OD(,D(*D(.D(ND(bD(JD(/D(-
K@ .D(JD(ND(,D(/D(-D(bD(*D(O
!@ OD(JD(,D(ND(JD(*D(bD(/D(-(
Which'one'of'these'is'postorder traversal?
A@ .D(JD(ND(,D(/D(-D(bD(*D(O
Y@ OD(,D(*D(.D(ND(bD(JD(/D(-
K@ .D(,D(JD(ND(OD(*D(/D(bD(-
!@ OD(JD(,D(ND(JD(*D(bD(/D(-(
Which'one'of'these'is'postorder traversal?
A@ .D(JD(ND(,D(/D(-D(bD(*D(O
Y@ OD(,D(*D(.D(ND(bD(JD(/D(-
K@ .D(,D(JD(ND(OD(*D(/D(bD(-
!@ OD(JD(,D(ND(JD(*D(bD(/D(-(
Which'one'of'these'is'inorder traversal?
A@ .D(,D(JD(ND(OD(*D(/D(bD(-
Y@ OD(,D(*D(.D(ND(bD(JD(/D(-
K@ .D(JD(ND(,D(/D(-D(bD(*D(O
!@ OD(JD(,D(ND(JD(*D(bD(/D(-(
Which'one'of'these'is'inorder traversal?
A@ .D(,D(JD(ND(OD(*D(/D(bD(-
Y@ OD(,D(*D(.D(ND(bD(JD(/D(-
K@ .D(JD(ND(,D(/D(-D(bD(*D(O
!@ OD(JD(,D(ND(JD(*D(bD(/D(-(
Which'one'of'these'is'preorder'traversal?
A@ .D(JD(ND(,D(/D(-D(bD(*D(O
Y@ OD(,D(*D(.D(ND(bD(JD(/D(-
K@ .D(,D(JD(ND(OD(*D(/D(bD(-
!@ OD(JD(,D(ND(JD(*D(bD(/D(-(
Which'one'of'these'is'preorder'traversal?
A@ .D(JD(ND(,D(/D(-D(bD(*D(O
Y@ OD(,D(.D(ND(JD(*D(bD(/D(-
K@ .D(,D(JD(ND(OD(*D(/D(bD(-
!@ OD(JD(,D(ND(JD(*D(bD(/D(-(
Tree'Construction'Algorithm
.@ L13(341(2&&3(82&=(34 1(;21(E; &#3G(&2?12(325:12#59@
,@ c&$531(341(2&&3("'(341("'&2?12 325:12#59@
J@ !1312="'1(341(#"a1#( &8(7&%2(9183(5'?(2"643(#%<3211#(82&=(341("'&2?12
325:12#59D(5'?(&<35"'(341("'&2?12 325:12#59(&8(341(9183(5'?(2"643(
#%<3211#@
N@ K&=;%31(341(#;9"3("'?1W(& 8(7&%2(;21(E;&#3G(&2?12(325:12#59(3&(613(341(
9183(5'?(2"643(;21&2?12( 3 25:12#59(&8(7&%2(9183(5'?(2"643(#%<3211#@
O@ K21531(34 1( 2&&3('&?1( 5'?(# &9:1(21$%2#":197(8&2("3#(9183(5'?(2"643(
#%<3211#@
Binary'Tree
HW12$"#1(.Q(C=;91=1'3(8"'?d5WI%=EG(=134&?(3453(8"'?(341(=5W"=%=(#%=(&8(599(;534#(E15$4(;534(45#(
341"2(&>'(#%=(5'?(8"'?(=5W(#%=(&8(34&#1(#%=#G@(\&2(1W5=;91D(341(;534(.Be,BeO(=5]1#(341(=5W(#%=(
&8(b(5'?(b("#(341(21#%93@
"'3 8"'?d5WI%=EU&?1('G(R
V
Binary'Tree
HW12$"#1(.Q(C=;91=1' 3 (8"'?d5WI%=EG(=134&?(3453(8"'?(341(=5W"=%=(#%=(&8(599(;534#(E15$4 (;534(
45#(341"2(&>'(#%=(5'?(8"'?(=5W(#%=(&8(34&#1(#%=#G@(\&2(1W5= ;91D(341(;534(.Be,BeO(=5]1#(#%=(
&8(bT(.Be,eN(=5 ]1#(#%=(&8(/T(5'?(.BeJ(=5]1#(#%=(&8(N@([41218&21D(b("#(341(21#%93@
"'3 8"'?d5WI%=EU&?1('G(R
"8(E'(XX('%99G(213%2'()T
19#1(R
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"'3 #%=2"643 X(8"'?d5WI%=E'@2"643GT
"8(E#%=9183 e(#%=2"643G(213%2'('@?535 Z(#%=9183T
19#1(213%2'('@?535 Z(#%=2"643T
V
V
Binary'Tree
• HW12$"#1(,Q(C=;91=1'3(="22&2EG(=134&?(3453(21;95$1# ( 3 41($%221'3(
<"'527(3211(>"34("3#(&>'(="22&2(:12#"&'@
:&"?(="22&2EU&?1('G(R
V(
Binary'Tree
• HW12$"#1(,Q(C=;91=1'3(="22&2EG(=134&?(3453(21;95$1#(341($%221'3(<"'527(3211(>"34("3#(&>'(
="22&2(:12#"&'@
:&"?(="22&2EU&?1('G(R
"8(E'(fX('%99G(R
="22&2E'@9183GT
="22&2E'@2"643GT
U&?1(31=;(X('@2"643T
'@2"643 X('@9183T
'@9183 X(31=;T
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