Space complexity
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The document discusses space complexity, which is the amount of computer memory required during program execution based on input size. Space complexity includes fixed space requirements like instruction space and simple variables, as well as variable space requirements that depend on input instance characteristics like input/output size and values. It provides examples of calculating space complexity for different algorithms, showing that space complexity can be a constant plus a variable component related to input size.
![Space Complexity
Amount of computer memory that is required during program execution as a function of input
size.
OR
Space complexity is the amount of memory it needs to run to completion
Space=Fixed part +Variable part
Fixed: varies from problem to problem. Includes space needed for storing instructions
variables , constants and structured variables.[arrays , struct]
Variable: varies from program to program. Includes space needed for stack and for
structured variables that are dynamically allocated during run time.
219-01-2017 VNRVJIET::CSE Author: Y.Bhanusree, Assistant Professor](https://image.slidesharecdn.com/spacecomplexity-170119071255/85/Space-complexity-2-320.jpg)
![Algorithm abc(a,b,c)
{
return a+b*c+(a-b-)/a+b+4.0
}
Algorithm Sum(a,n)
{
s:=0
for i:=1 to n do
s:=s+a[i];
return s;
}
19-01-2017 VNRVJIET::CSE Author: Y.Bhanusree, Assistant Professor 4](https://image.slidesharecdn.com/spacecomplexity-170119071255/85/Space-complexity-4-320.jpg)
![Ex:2
float sum(float list[ ], int n)
{
float tempsum = 0;
int i;
for (i = 0; i<n; i++)
tempsum += list [i];
return tempsum;
}
Ssum(I) = 0
19-01-2017 VNRVJIET::CSE Author: Y.Bhanusree, Assistant Professor 6](https://image.slidesharecdn.com/spacecomplexity-170119071255/85/Space-complexity-6-320.jpg)
![Ex:3 Recursive function for summing a list of numbers
float sum(float list[ ], int n)
{
if (n)
return sum(list, n-1) + list[n];
else
return 0;
}
8
Type Name Number of bytes
parameter: float
parameter: integer
return address:(used internally)
list [ ]
n
4
2
2(unless a far address)
TOTAL per recursive call 8
Ssum(I)=Ssum(n)=8n
19-01-2017 VNRVJIET::CSE Author: Y.Bhanusree, Assistant Professor](https://image.slidesharecdn.com/spacecomplexity-170119071255/85/Space-complexity-8-320.jpg)
Space complexity
- 1. Space complexity Unit I Part 2 Creative Commons License Space Complexity by Bhanusree Yalamanchili is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
- 2. Space Complexity Amount of computer memory that is required during program execution as a function of input size. OR Space complexity is the amount of memory it needs to run to completion Space=Fixed part +Variable part Fixed: varies from problem to problem. Includes space needed for storing instructions variables , constants and structured variables.[arrays , struct] Variable: varies from program to program. Includes space needed for stack and for structured variables that are dynamically allocated during run time. 219-01-2017 VNRVJIET::CSE Author: Y.Bhanusree, Assistant Professor
- 3. Fixed Space Requirements (C) Independent of the characteristics of the inputs and outputs instruction space(space for code) space for simple variables, fixed-size structured variable, constants Variable Space Requirements (SP(I)) depend on the instance characteristic I number, size, values of inputs and outputs associated with I recursive stack space, formal parameters, local variables, return address 3 S(P)=C+SP(I) 19-01-2017 VNRVJIET::CSE Author: Y.Bhanusree, Assistant Professor
- 4. Algorithm abc(a,b,c) { return a+b*c+(a-b-)/a+b+4.0 } Algorithm Sum(a,n) { s:=0 for i:=1 to n do s:=s+a[i]; return s; } 19-01-2017 VNRVJIET::CSE Author: Y.Bhanusree, Assistant Professor 4
- 5. Ex:1 float abc(float a, float b, float c) { return a + b + b * c + (a + b - c) / (a + b) + 4.00; } Sabc(I) = 0 519-01-2017 VNRVJIET::CSE Author: Y.Bhanusree, Assistant Professor
- 6. Ex:2 float sum(float list[ ], int n) { float tempsum = 0; int i; for (i = 0; i<n; i++) tempsum += list [i]; return tempsum; } Ssum(I) = 0 19-01-2017 VNRVJIET::CSE Author: Y.Bhanusree, Assistant Professor 6
- 7. Exercise Find space complexity for the following algorithms: • Swap • Maximum • Minimum • Selection sort • Matrix display • Matrix multiplication 19-01-2017 VNRVJIET::CSE Author: Y.Bhanusree, Assistant Professor 7
- 8. Ex:3 Recursive function for summing a list of numbers float sum(float list[ ], int n) { if (n) return sum(list, n-1) + list[n]; else return 0; } 8 Type Name Number of bytes parameter: float parameter: integer return address:(used internally) list [ ] n 4 2 2(unless a far address) TOTAL per recursive call 8 Ssum(I)=Ssum(n)=8n 19-01-2017 VNRVJIET::CSE Author: Y.Bhanusree, Assistant Professor