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Félix MARQUET
@@ -1,121 +1,121 @@
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`````C
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||||
mergeSort(array, left, right){ (left = left index of the array, right = right index of the array)
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if left > right{
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return
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}
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middle = (left+right) / 2
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mergeSort(array, left, mid) T(n/2)
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mergeSort(array, mid+1, right) T(n/2)
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merge(array, left, mid, right) M(n)
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}
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``````
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`````C
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merge(array, left, mid, right){
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n1 = mid - left + 1
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n2 = right - mid
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leftArray[n1]
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rightArray[n2]
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for i = 0 to n1 - 1{
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leftArray[i] = array[left + i]
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}
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for j = 0 to n2 - 1{
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rightArray[j] = array[mid + 1 + j]
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}
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i = 0
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j = 0
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k = left
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while i < n1 and j < n2{
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if leftArray[i] <= rightArray[j]{
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array[k] = leftArray[i]
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i = i + 1
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}
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else{
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array[k] = rightArray[j]
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j = j + 1
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}
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k = k + 1
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}
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while i < n1{
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array[k] = leftArray[i]
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i = i + 1
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k = k + 1
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}
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||||
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||||
while j < n2{
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array[k] = rightArray[j]
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j = j + 1
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k = k + 1
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}
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}
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`````
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````C
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T(N) = 2 * T(N/2) + M(N) = 2 * T(N/2) + constant * N
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……
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= 2^k * T(N/2^k) + k * N * constant with k = number of sub array
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= N * T(1) + N * log(N) * constant
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= N + N * log(N)
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= N * log(N)
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````
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````C
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BubbleSort (array, size){SS
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O(n)for int = 1 to size{
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O(n)for j = 0 to size -1{
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if array[j] > array[j+1]{
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swap(array[j], array[j+1])
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}
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}
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}
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}
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````
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````C
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swap (elemA, elemB){
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var = elemA
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elemA = elemB
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elemB = var
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}
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````
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||||
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````C
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Counter = {0} * k
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execution time: k (initialization of all the values from the counter to zero, to begin counting at 0)
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````
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|
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````C
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for (i=0; i < array size ; i++){
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counter ++
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}
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execution time: n (size of the array)
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````
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||||
|
||||
````C
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||||
for (i=0; i < k; i++){
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for (j=0; j < number of letter counted; j++){
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array[index] = i;
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}
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}
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execution time: k + n, the first for repeat k time, for each assume value. And there is only n number how’s been counted.
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||||
````
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````C
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T(n) = k + n + n + k
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O(n) = n + k
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````
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[[TP1 Exercice 1.canvas|TP1 Exercice 1]]
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[[MergeSort.png]]
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[[MergeSort.canvas|MergeSort]]
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`````C
|
||||
mergeSort(array, left, right){ (left = left index of the array, right = right index of the array)
|
||||
if left > right{
|
||||
return
|
||||
}
|
||||
middle = (left+right) / 2
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mergeSort(array, left, mid) T(n/2)
|
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mergeSort(array, mid+1, right) T(n/2)
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merge(array, left, mid, right) M(n)
|
||||
}
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||||
``````
|
||||
|
||||
|
||||
`````C
|
||||
merge(array, left, mid, right){
|
||||
n1 = mid - left + 1
|
||||
n2 = right - mid
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||||
leftArray[n1]
|
||||
rightArray[n2]
|
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for i = 0 to n1 - 1{
|
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leftArray[i] = array[left + i]
|
||||
}
|
||||
for j = 0 to n2 - 1{
|
||||
rightArray[j] = array[mid + 1 + j]
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||||
}
|
||||
i = 0
|
||||
j = 0
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||||
k = left
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||||
|
||||
while i < n1 and j < n2{
|
||||
if leftArray[i] <= rightArray[j]{
|
||||
array[k] = leftArray[i]
|
||||
i = i + 1
|
||||
}
|
||||
else{
|
||||
array[k] = rightArray[j]
|
||||
j = j + 1
|
||||
}
|
||||
k = k + 1
|
||||
}
|
||||
|
||||
while i < n1{
|
||||
array[k] = leftArray[i]
|
||||
i = i + 1
|
||||
k = k + 1
|
||||
}
|
||||
|
||||
while j < n2{
|
||||
array[k] = rightArray[j]
|
||||
j = j + 1
|
||||
k = k + 1
|
||||
}
|
||||
}
|
||||
`````
|
||||
|
||||
````C
|
||||
T(N) = 2 * T(N/2) + M(N) = 2 * T(N/2) + constant * N
|
||||
|
||||
……
|
||||
|
||||
= 2^k * T(N/2^k) + k * N * constant with k = number of sub array
|
||||
|
||||
= N * T(1) + N * log(N) * constant
|
||||
|
||||
= N + N * log(N)
|
||||
|
||||
= N * log(N)
|
||||
|
||||
````
|
||||
|
||||
````C
|
||||
BubbleSort (array, size){SS
|
||||
O(n)for int = 1 to size{
|
||||
O(n)for j = 0 to size -1{
|
||||
if array[j] > array[j+1]{
|
||||
swap(array[j], array[j+1])
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
````
|
||||
|
||||
````C
|
||||
swap (elemA, elemB){
|
||||
var = elemA
|
||||
elemA = elemB
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||||
elemB = var
|
||||
}
|
||||
````
|
||||
|
||||
````C
|
||||
Counter = {0} * k
|
||||
|
||||
execution time: k (initialization of all the values from the counter to zero, to begin counting at 0)
|
||||
````
|
||||
|
||||
````C
|
||||
for (i=0; i < array size ; i++){
|
||||
counter ++
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||||
}
|
||||
|
||||
execution time: n (size of the array)
|
||||
````
|
||||
|
||||
````C
|
||||
for (i=0; i < k; i++){
|
||||
for (j=0; j < number of letter counted; j++){
|
||||
array[index] = i;
|
||||
}
|
||||
}
|
||||
execution time: k + n, the first for repeat k time, for each assume value. And there is only n number how’s been counted.
|
||||
````
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||||
|
||||
````C
|
||||
T(n) = k + n + n + k
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||||
O(n) = n + k
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||||
````
|
||||
|
||||
[[TP1 Exercice 1.canvas|TP1 Exercice 1]]
|
||||
[[MergeSort.png]]
|
||||
[[MergeSort.canvas|MergeSort]]
|
||||
|
||||
@@ -1,72 +1,72 @@
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{"id":"dd916430cd46a533","type":"text","text":"12","x":-60,"y":540,"width":100,"height":60}
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"edges":[
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{"id":"990eae9f88be03c2","fromNode":"4b4451abb50ed86b","fromSide":"bottom","toNode":"92e75ec2709bfad3","toSide":"top"},
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{"id":"b56e4df4db1d2b4a","fromNode":"5bf01a505a245357","fromSide":"bottom","toNode":"2c5beeeced9ff053","toSide":"top"},
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{"id":"507cde8b3ac55c26","fromNode":"92e75ec2709bfad3","fromSide":"bottom","toNode":"2c5beeeced9ff053","toSide":"top"},
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{"id":"3d94792d94dbc02c","fromNode":"2c5beeeced9ff053","fromSide":"bottom","toNode":"b4d443cf3670a80e","toSide":"top"},
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{"id":"a592ae78e7de07ab","fromNode":"b4d443cf3670a80e","fromSide":"bottom","toNode":"9fe17f4ffac0c8ab","toSide":"top"},
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]
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}
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@@ -1,21 +1,21 @@
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{
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"nodes":[
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{"id":"f86006360714173b","x":-500,"y":-300,"width":50,"height":60,"type":"text","text":"1"},
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{"id":"6a37a402fc5dd7a0","x":-350,"y":-420,"width":150,"height":60,"type":"text","text":"Selection"}
|
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],
|
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"edges":[]
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{
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"nodes":[
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{"id":"f86006360714173b","x":-500,"y":-300,"width":50,"height":60,"type":"text","text":"1"},
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{"id":"722870a59dc4222f","type":"text","text":"3","x":-300,"y":160,"width":50,"height":60},
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],
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||||
"edges":[]
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||||
}
|
||||
@@ -1,30 +1,30 @@
|
||||
# Set separator of data lines
|
||||
set datafile separator ";"
|
||||
set grid
|
||||
|
||||
# Set names of stuff
|
||||
set title "Execution Time vs Complexity"
|
||||
set xlabel "number of elements"
|
||||
set ylabel "time in milliseconds"
|
||||
|
||||
# Set line style, color, width, blabla
|
||||
set style line 1 linecolor rgb '#ff0000' linetype 1 linewidth 2
|
||||
set style line 2 linecolor rgb '#00ff00' linetype 1 linewidth 2
|
||||
|
||||
#### Prepare the function
|
||||
c = 0.000004 # to fit with the data !
|
||||
f(x) = c * x**2
|
||||
|
||||
title_f(c) = sprintf("f(x) = c*n^2, c = %f", c)
|
||||
|
||||
# Automatic scaling of axes
|
||||
set autoscale xy
|
||||
|
||||
#### Plot data only
|
||||
# plot 'd:\Desktop\Cours\tuto_graficos\data.csv' title 'data'
|
||||
|
||||
#### Plot both data and function (data with continuous line)
|
||||
# plot 'd:\Desktop\Cours\tuto_graficos\data.csv' title 'data' with lines linestyle 1, f(x) title title_f(c) with lines linestyle 2
|
||||
|
||||
#### Plot both data and function (data with points)
|
||||
plot 'd:\Desktop\Cours\tuto_graficos\data.csv' title 'data', f(x) title title_f(c) with lines linestyle 2
|
||||
# Set separator of data lines
|
||||
set datafile separator ";"
|
||||
set grid
|
||||
|
||||
# Set names of stuff
|
||||
set title "Execution Time vs Complexity"
|
||||
set xlabel "number of elements"
|
||||
set ylabel "time in milliseconds"
|
||||
|
||||
# Set line style, color, width, blabla
|
||||
set style line 1 linecolor rgb '#ff0000' linetype 1 linewidth 2
|
||||
set style line 2 linecolor rgb '#00ff00' linetype 1 linewidth 2
|
||||
|
||||
#### Prepare the function
|
||||
c = 0.000004 # to fit with the data !
|
||||
f(x) = c * x**2
|
||||
|
||||
title_f(c) = sprintf("f(x) = c*n^2, c = %f", c)
|
||||
|
||||
# Automatic scaling of axes
|
||||
set autoscale xy
|
||||
|
||||
#### Plot data only
|
||||
# plot 'd:\Desktop\Cours\tuto_graficos\data.csv' title 'data'
|
||||
|
||||
#### Plot both data and function (data with continuous line)
|
||||
# plot 'd:\Desktop\Cours\tuto_graficos\data.csv' title 'data' with lines linestyle 1, f(x) title title_f(c) with lines linestyle 2
|
||||
|
||||
#### Plot both data and function (data with points)
|
||||
plot 'd:\Desktop\Cours\tuto_graficos\data.csv' title 'data', f(x) title title_f(c) with lines linestyle 2
|
||||
|
||||
@@ -1,33 +1,33 @@
|
||||
# Set separator of data lines and grid to plot
|
||||
set datafile separator ";"
|
||||
set grid
|
||||
|
||||
# Set names of stuff
|
||||
set title "Execution Time vs Complexity"
|
||||
set xlabel "number of elements"
|
||||
set ylabel "time in milliseconds"
|
||||
|
||||
# Set line style, color, width, blabla
|
||||
set style line 1 linecolor rgb '#ff0000' linetype 1 linewidth 2
|
||||
set style line 2 linecolor rgb '#00ff00' linetype 1 linewidth 2
|
||||
|
||||
#### Prepare the function
|
||||
f(x) = c * x ** 2
|
||||
|
||||
#### Fit the function to data
|
||||
fit f(x) 'd:\Desktop\Cours\tuto_graficos\data.csv' via c
|
||||
|
||||
# Save value of c to show in the function
|
||||
|
||||
title_f(c) = sprintf("f(x) = c*n^2, c = %f", c)
|
||||
|
||||
# Automatic scaling of axes
|
||||
set autoscale xy
|
||||
|
||||
#### Plot both data and function (data with continuous line)
|
||||
# plot 'd:\Desktop\Cours\tuto_graficos\data.csv' title 'data' with lines linestyle 1, f(x) title title_f(c) with lines linestyle 2
|
||||
|
||||
#### Plot both data and function (data with points)
|
||||
plot 'd:\Desktop\Cours\tuto_graficos\data.csv' title 'data', f(x) title title_f(c) with lines linestyle 2
|
||||
|
||||
|
||||
# Set separator of data lines and grid to plot
|
||||
set datafile separator ";"
|
||||
set grid
|
||||
|
||||
# Set names of stuff
|
||||
set title "Execution Time vs Complexity"
|
||||
set xlabel "number of elements"
|
||||
set ylabel "time in milliseconds"
|
||||
|
||||
# Set line style, color, width, blabla
|
||||
set style line 1 linecolor rgb '#ff0000' linetype 1 linewidth 2
|
||||
set style line 2 linecolor rgb '#00ff00' linetype 1 linewidth 2
|
||||
|
||||
#### Prepare the function
|
||||
f(x) = c * x ** 2
|
||||
|
||||
#### Fit the function to data
|
||||
fit f(x) 'd:\Desktop\Cours\tuto_graficos\data.csv' via c
|
||||
|
||||
# Save value of c to show in the function
|
||||
|
||||
title_f(c) = sprintf("f(x) = c*n^2, c = %f", c)
|
||||
|
||||
# Automatic scaling of axes
|
||||
set autoscale xy
|
||||
|
||||
#### Plot both data and function (data with continuous line)
|
||||
# plot 'd:\Desktop\Cours\tuto_graficos\data.csv' title 'data' with lines linestyle 1, f(x) title title_f(c) with lines linestyle 2
|
||||
|
||||
#### Plot both data and function (data with points)
|
||||
plot 'd:\Desktop\Cours\tuto_graficos\data.csv' title 'data', f(x) title title_f(c) with lines linestyle 2
|
||||
|
||||
|
||||
|
||||
@@ -1,35 +1,35 @@
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
int main (int argc, char** argv)
|
||||
{
|
||||
int taille;
|
||||
int i;
|
||||
int j;
|
||||
|
||||
// Lecture de la taille du carre.
|
||||
printf ("Donnez la taille du carre ? ");
|
||||
scanf ("%d", &taille);
|
||||
printf ("\n");
|
||||
|
||||
// Dessin de la bande du haut.
|
||||
for (i = 0; i < taille; i++)
|
||||
printf ("*");
|
||||
printf ("\n");
|
||||
|
||||
// Dessin des cotés.
|
||||
for (i = 1; i < taille - 1; i++)
|
||||
{
|
||||
printf ("*");
|
||||
for (j = 1; j < taille - 1; j++)
|
||||
printf (" ");
|
||||
printf ("*\n");
|
||||
}
|
||||
|
||||
// Dessin de la bande du bas.
|
||||
for (i = 0; i < taille; i++)
|
||||
printf ("*");
|
||||
printf ("\n");
|
||||
|
||||
return EXIT_SUCCESS;
|
||||
}
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
int main (int argc, char** argv)
|
||||
{
|
||||
int taille;
|
||||
int i;
|
||||
int j;
|
||||
|
||||
// Lecture de la taille du carre.
|
||||
printf ("Donnez la taille du carre ? ");
|
||||
scanf ("%d", &taille);
|
||||
printf ("\n");
|
||||
|
||||
// Dessin de la bande du haut.
|
||||
for (i = 0; i < taille; i++)
|
||||
printf ("*");
|
||||
printf ("\n");
|
||||
|
||||
// Dessin des cotés.
|
||||
for (i = 1; i < taille - 1; i++)
|
||||
{
|
||||
printf ("*");
|
||||
for (j = 1; j < taille - 1; j++)
|
||||
printf (" ");
|
||||
printf ("*\n");
|
||||
}
|
||||
|
||||
// Dessin de la bande du bas.
|
||||
for (i = 0; i < taille; i++)
|
||||
printf ("*");
|
||||
printf ("\n");
|
||||
|
||||
return EXIT_SUCCESS;
|
||||
}
|
||||
|
||||
@@ -1,10 +1,10 @@
|
||||
all: program
|
||||
|
||||
program: main.o util.o
|
||||
gcc -o program main.o util.o
|
||||
|
||||
main.o: main.c
|
||||
gcc -c main.c
|
||||
|
||||
util.o: util.c
|
||||
all: program
|
||||
|
||||
program: main.o util.o
|
||||
gcc -o program main.o util.o
|
||||
|
||||
main.o: main.c
|
||||
gcc -c main.c
|
||||
|
||||
util.o: util.c
|
||||
gcc -c util.c
|
||||
Reference in New Issue
Block a user