MORE ON RECURSION - GitHub Pages0 1 2 3 4 5 6 7 8 91011121314 61314253343515364728493959697 Binary...

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MORE ON RECURSION Problem Solving with Computers-I 6 10 40 12 32 47 43 45 41

Transcript of MORE ON RECURSION - GitHub Pages0 1 2 3 4 5 6 7 8 91011121314 61314253343515364728493959697 Binary...

Page 1: MORE ON RECURSION - GitHub Pages0 1 2 3 4 5 6 7 8 91011121314 61314253343515364728493959697 Binary Search: Efficient search in a sorted array lo •Binary search.Given valueand sorted

MORE ONRECURSION

Problem Solving with Computers-I 6

10

40

12

32 4743

45 41

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Page 3: MORE ON RECURSION - GitHub Pages0 1 2 3 4 5 6 7 8 91011121314 61314253343515364728493959697 Binary Search: Efficient search in a sorted array lo •Binary search.Given valueand sorted

Final Exam: Monday 12/09, noon-3:00p, Embarcadero Hall

Final Exam Review Session:

Day: Friday (12/06)Time: 5:00p - 7:00p

Location: Phelps 3526

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int fac(int N){

if (N <= 1)return 1;

else{int rest = fac(N-1);return rest * N;

}

Basecase

Recursivecase

Thinking recursively !

Human: Basecaseand1step Computer: Everythingelse

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int fac(int N){

if (N <= 1)return 1;

elsereturn fac(N-1)* N;

}

Basecase

Recursivecase

(shorterversion)

Thinking recursively !

Human: Basecaseand1step Computer: Everythingelse

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Behind the curtain…

cout<<fac(1);

Result: 1 The base case !

int fac(int N){

if (N <= 1)return 1;

elsereturn N * fac(N-1);

}

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Behind the curtain…

fac(5)

int fac(int N){

if (N <= 1)return 1;

elsereturn N * fac(N-1);

}

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fac(5)

5 * fac(4)

Behind the curtain…int fac(int N){

if (N <= 1)return 1;

elsereturn N * fac(N-1);

}

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fac(5)

5 * fac(4)

4 * fac(3)

Behind the curtain…int fac(int N){

if (N <= 1)return 1;

elsereturn N * fac(N-1);

}

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fac(5)

5 * fac(4)

4 * fac(3)

3 * fac(2)

Behind the curtain…int fac(int N){

if (N <= 1)return 1;

elsereturn N * fac(N-1);

}

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fac(5)

5 * fac(4)

4 * fac(3)

3 * fac(2)

2 * fac(1)

Behind the curtain…int fac(int N){

if (N <= 1)return 1;

elsereturn N * fac(N-1);

}

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fac(5)

5 * fac(4)

4 * fac(3)

3 * fac(2)

2 * fac(1)

1

"The Stack"

Remembers all of the individual calls

to fac

Behind the curtain…int fac(int N){

if (N <= 1)return 1;

elsereturn N * fac(N-1);

}

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fac(5)

5 * fac(4)

4 * fac(3)

3 * fac(2)

2 * 1

Behind the curtain…int fac(int N){

if (N <= 1)return 1;

elsereturn N * fac(N-1);

}

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fac(5)

5 * fac(4)

4 * fac(3)

3 * 2

Behind the curtain…int fac(int N){

if (N <= 1)return 1;

elsereturn N * fac(N-1);

}

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fac(5)

5 * fac(4)

4 * 6

Behind the curtain…int fac(int N){

if (N <= 1)return 1;

elsereturn N * fac(N-1);

}

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fac(5)

5 * 24

Behind the curtain…int fac(int N){

if (N <= 1)return 1;

elsereturn N * fac(N-1);

}

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fac(5)

Result: 120

Behind the curtain…int fac(int N){

if (N <= 1)return 1;

elsereturn N * fac(N-1);

}

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821 3 4 65 7 109 11 12 14130641413 25 33 5143 53 8472 93 95 97966

Binary Search: Efficient search in a sorted array

lo

• Binary search. Given value and sorted array v[], find index i such that v[i] == value, or return -1 indicating that no such index exists.

• Invariant. Algorithm maintains v[lo] £ value £ v[hi].

• Ex. Binary search for 33.

hi

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Binary Search• Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130641413 25 33 5143 53 8472 93 95 97966

lo himid

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Binary Search• Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130641413 25 33 5143 53 8472 93 95 97966

lo hi

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Binary Search• Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130641413 25 33 5143 53 8472 93 95 97966

lo mid hi

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Binary Search• Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130641413 25 33 5143 53 8472 93 95 97966

lo hi

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Binary Search

• Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130641413 25 33 5143 53 8472 93 95 97966

lo himid

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Binary Search

• Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130641413 25 33 5143 53 8472 93 95 97966

lohi

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Binary Search

• Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130641413 25 33 5143 53 8472 93 95 97966

lohimid

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Binary Search

• Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130641413 25 33 5143 53 8472 93 95 97966

lohimid

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Write the recursive implementation of Binary search

int binarySearch(int v[], int value, int lo, int hi);

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if(hi<=lo){return -1;

}

int mid = (lo + hi)/2;if(v[mid] == value){

return mid;}

Which of the following is a valid base case?int binarySearch(int v[], int value, int lo, int hi){

A:

B:

C: Both A and B

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Fill in the blanksint binarySearch(int v[], int value, int lo, int hi){

if(hi < lo)return -1;

int mid = (lo + hi)/2;if(v[mid] == value)

return mid; if(v[mid] < value){

binarySearch(v, value, _____, hi);}

}

A: loB: mid - 1C: midD: mid + 1E: hi

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Searching a linked listGiven a linked list, implement a recursive search function- Return true if a given value is present in the linked list- Otherwise return false

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Recursive function to free nodes in a linked listGiven a linked list, implement a recursive function to delete all the nodes in the linked list

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Is this a correct implementation?int binarySearch(int v[], int value, int lo, int hi){

if(hi<lo)return -1;

int mid = (lo + hi)/2;if(v[mid] == value)

return mid; if(v[mid] < value){

binarySearch(v, value, mid + 1, hi);}else{

binarySearch(v, value, lo, mid - 1);}

}

A: YesB: No


COURSE 9 Tree Structured Files. Database Management Systems2 Binary Tree Organization K Data Pointer Left Pointer Right Heap and sorted files - useful.

COURSE 9 Tree Structured Files. Database Management Systems2 Binary Tree Organization K Data Pointer Left Pointer Right Heap and sorted files - useful.

JANUAR FSSMDMD 1 234567 8 91011121314 15 161718192021 22 23 30 24 31 25262728 29.

JANUAR FSSMDMD 1 234567 8 91011121314 15 161718192021 22 23 30 24 31 25262728 29.

Getting sorted

Getting sorted

Binary Heap Algorithms - CS Home - University of … Heap Algorithms ... Linked List Linear Linear Linear Sorted Linked List Logarithmic Logarithmic ... using this array representation

Binary Heap Algorithms - CS Home - University of … Heap Algorithms ... Linked List Linear Linear Linear Sorted Linked List Logarithmic Logarithmic ... using this array representation

Lecture 5: Scheduling and Binary Search Trees · Sorted list: Appending and sorting takes ( nlgn) time. However, it is pos- ... Lecture 5 Scheduling and Binary Search Trees 6.006

Lecture 5: Scheduling and Binary Search Trees · Sorted list: Appending and sorting takes ( nlgn) time. However, it is pos- ... Lecture 5 Scheduling and Binary Search Trees 6.006

nAmiBIA UniVERSITYexampapers.nust.na/greenstone3/sites/localsite/collect...Problem A7 Given a binary search tree, which traversal type would print the values in the nodes in sorted

nAmiBIA UniVERSITYexampapers.nust.na/greenstone3/sites/localsite/collect...Problem A7 Given a binary search tree, which traversal type would print the values in the nodes in sorted

Sorted Lists

Sorted Lists

Events Calendar Shanghai June 2014. SunMonTueWedThuFriSat 1234567 8 91011121314 1516161717181819192021 222324252627272828 292930 Circus Ballet&Dance Concert.

Events Calendar Shanghai June 2014. SunMonTueWedThuFriSat 1234567 8 91011121314 1516161717181819192021 222324252627272828 292930 Circus Ballet&Dance Concert.

web-cat.orgweb-cat.org/questionbank/QuestionBank.doc · Web viewCanterbury QuestionBank 633573 Suppose you try to perform a binary search on a 5-element array sorted in the reverse

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Events Calendar China April 2015. WedThuFriSatSunMonTue 1234567 8 91011121314 15161718192021 22232425262728 2930 Please Select & Click On Picture To See.

Events Calendar China April 2015. WedThuFriSatSunMonTue 1234567 8 91011121314 15161718192021 22232425262728 2930 Please Select & Click On Picture To See.

1 Prune-and-Search Method 2012/10/30. A simple example: Binary search sorted sequence : (search 9) 14579101215 step 1 step 2 step 3 Binary search.

1 Prune-and-Search Method 2012/10/30. A simple example: Binary search sorted sequence : (search 9) 14579101215 step 1 step 2 step 3 Binary search.

CSc 110, Spring 2017 - University of Arizona · Binary Search Binary search: a method of searching that takes advantage of sorted data. Consider a guessing game: Someone thinks of

CSc 110, Spring 2017 - University of Arizona · Binary Search Binary search: a method of searching that takes advantage of sorted data. Consider a guessing game: Someone thinks of

Events Calendar China March 2015. SunMonTueWedThuFriSat 1234567 8 91011121314 15161718192021 22232425262728 293031 Please Select & Click On Picture To.

Events Calendar China March 2015. SunMonTueWedThuFriSat 1234567 8 91011121314 15161718192021 22232425262728 293031 Please Select & Click On Picture To.

Ch5: Merge Sort - ecpe.nu.ac.th · Merge Sort vsCards • We have two sorted piles of a card deck. Sorted Sorted pills pills

Ch5: Merge Sort - ecpe.nu.ac.th · Merge Sort vsCards • We have two sorted piles of a card deck. Sorted Sorted pills pills

Gift ideas sorted -

Gift ideas sorted -

Sorted Array

Sorted Array

Maths Sorted New

Maths Sorted New

Binary Search - math.uic.edu › ~jan › mcs360 › binary_search.pdf · Binary Search 1 Recursive Problem Solving the towers of Hanoi recursive C++ code 2 Binary Search sorted vectors

Binary Search - math.uic.edu › ~jan › mcs360 › binary_search.pdf · Binary Search 1 Recursive Problem Solving the towers of Hanoi recursive C++ code 2 Binary Search sorted vectors

Sorted addition

Sorted addition

BINARY SEARCH TREES - UCSB CS24Binary Search • Binary search. Given value and sorted array a[], find index i such that a[i] = value, or report that no such index exists. • Invariant.

BINARY SEARCH TREES - UCSB CS24Binary Search • Binary search. Given value and sorted array a[], find index i such that a[i] = value, or report that no such index exists. • Invariant.