ProgrammingOneHour_2018

Programming-One-Hour Activity By Tongji Google Camp, Fall Semester, 2018

Part One: Fibonacci with Sliding Array

1. Reversion Version

$F(1)=1\F(2)=1\F(3)=F(1)+F(2)=2\F(4)=F(2)+F(3)=F(2)+F(1)+F(2)=3\F(5)=F(4)+F(3)=F(3)+F(2)+F(2)+F(1)=F(2)+F(1)+F(2)+F(2)+F(1)=5\...$

Analysis:

Time complexity: $O(1.618^n)$

Space complexity: $O(n)$

Problem: Duplicate calculation

2. Sliding Array Version

$F(1)=1\F(2)=1\F(3)=F(2)+F(1)=2\F(4)=F(3)+F(2)=3\F(5)=F(4)+F(3)=5\...$

F(n)	Cell 0	Cell 1	Cell 2
F(1)	[1]	-	-
F(2)	1	[1]	-
F(3)	1	1	[2]
F(4)	[3]	1	2
F(5)	3	[5]	2

Analysis:

Time complexity: $O(n)$

Space complexity: $O(1)$

Part Two: Doubled Array

1. Two facts

Fact 1: Allocated memory block cannot be modified dynamically

Fact 2: Sometimes we need to change the size of array we have allocated to fit elements in different numbers

Conclusion: Resize the array

2. Analysis

Key Point: Tradeoff between space utilization and operation time

2.1 Space utilization

Scenario 1: 1 element in an array of 10000 elements long

Scenario 2: 9000 element in an array of 10000 elements long

2.2 Operation time

To expand an array from 10 elements long to 10000 elements long

Scenario 1: increase the size of the array by 1 every time

result 1: 9900 times, 10000 elements long

Scenario 2: increase the size of the array by doubling it

result 1: 10 times, 10240 elements long

3. One more thing

C library function - realloc()

Description

The C library function *void *realloc(void ptr, size_t size) attempts to resize the memory block pointed to by ptr that was previously allocated with a call to malloc or calloc.

Declaraion

Following is the declaration for realloc() function.

void *realloc(void *ptr, size_t size)

Parameters

ptr − This is the pointer to a memory block previously allocated with malloc, calloc or realloc to be reallocated. If this is NULL, a new block is allocated and a pointer to it is returned by the function.
size − This is the new size for the memory block, in bytes. If it is 0 and ptr points to an existing block of memory, the memory block pointed by ptr is deallocated and a NULL pointer is returned.

Return value

This function returns a pointer to the newly allocated memory, or NULL if the request fails.

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