Proposition de corrigé
Code:
from typing import List, Dict, Set, Tuple
from dataclasses import dataclass
import math
print("\n----------------------------")
print("------- Exercice 3 -------")
print("----------------------------\n")
xs: List[float] = [0.0, 5.0, 6.0, 9.0, 10.0]
ys: List[float] = [0.0, 5.0, 1.0, 1.0, 8.0]
### 3 (a)
# Ajout d'une erreur dans les données:
# ceci ajoute une valeur à ys sans ajouter une valeur
# correspondante dans xs et crée ainsi une incohérence
ys.append(1000)
p = len(xs)
if p == len(ys):
print("Data OK")
else:
print("Correcting length mismatch")
p = min(p, len(ys))
xs = xs[:p]
ys = ys[:p]
### 3 (b)
print("Considered points: ", end="")
for i in range(p - 1):
print(f"({xs[i]}, {ys[i]})", end=", ")
print(f"({xs[p - 1]}, {ys[p - 1]})")
### 3 (c)
def is_monotonic_increasing(values: List[float]) -> bool:
for i in range(1, len(values)):
if values[i] <= values[i - 1]:
return False
return True
print(f"xs is monotonic inscreasing: {is_monotonic_increasing(xs)}")
print(f"ys is monotonic inscreasing: {is_monotonic_increasing(ys)}")
### 3 (d)
def interpolated_y(x: float) -> float:
for i in range(1, p):
if xs[i - 1] <= x <= xs[i]:
y = ys[i - 1] + (ys[i] - ys[i - 1]) * (x - xs[i - 1]) / (xs[i] - xs[i - 1])
return y
return float("nan")
### 3 (e)
for i in range(100 + 1):
x = i / 10
y = interpolated_y(x)
print(f"x={x} -> y={y}")
### 3 (f)
num_mismatch = 0
for i in range(p):
x, y = xs[i], ys[i]
y_int = interpolated_y(x)
if y != y_int:
print(f"Mismatch for x={x}: should be {y}, but computed {y_int}")
num_mismatch += 1
if num_mismatch == 0:
print("No mismatch found")
### 3 (g)
def areas_under_curve(xs: List[float], ys: List[float]) -> List[float]:
areas: List[float] = []
for i in range(1, p):
mean_height = (ys[i] + ys[i - 1]) / 2
width = xs[i] - xs[i - 1]
local_area = mean_height * width
areas.append(local_area)
return areas
areas = areas_under_curve(xs, ys)
print(areas)
sum_areas = 0.0
for a in areas:
sum_areas += a
print(f"Total area: {sum_areas}")
print("\n----------------------------")
print("------- Exercice 4 -------")
print("----------------------------\n")
### 4 (a) & (b)
@dataclass
class Task:
person: str
title: str
start_day: int
duration: int
difficulty: float
tasks = [
Task("Bernard", "Overview", 0, 2, 0.5),
Task("Heidi", "Frontend", 1, 4, 0.9),
Task("Gabriel", "Kickoff", 0, 1, 0.2),
Task("Morgane", "Backend", 0, 3, 0.8),
Task("Bernard", "Demos", 3, 2, 0.7),
Task("Gabriel", "Database", 1, 3, 0.8),
Task("Morgane", "Tests", 3, 2, 0.65),
]
for task in tasks:
print(task)
### 4 (c)
occupations: Dict[str, List[str]] = {}
for task in tasks:
if task.person not in occupations:
occupations[task.person] = ["", "", "", "", ""]
for day in range(task.start_day, task.start_day + task.duration):
occupations[task.person][day] = task.title
for person, occupation in occupations.items():
print(f"{person}'s occupation: {occupation}")
### 4 (d)
for person, occupation in occupations.items():
for i, title in enumerate(occupation):
if len(title) == 0:
print(f"{person} has nothing to do on day {i}")
### 4 (e)
days_booked: Dict[str, Set[int]] = {}
num_conflicts = 0
for task in tasks:
if task.person not in days_booked:
days_booked[task.person] = set()
persons_days = days_booked[task.person]
for day in range(task.start_day, task.start_day + task.duration):
if day in persons_days:
print(f"{task.person} should work on “{task.title}” on day {day} but is already busy")
num_conflicts += 1
else:
persons_days.add(day)
if num_conflicts == 0:
print(f"No conflicts detected")
### 4 (f)
difficulties: Dict[str, float] = {}
for task in tasks:
if task.person not in difficulties:
difficulties[task.person] = 0
difficulties[task.person] += task.difficulty * task.duration
max_diff = 0.0
max_person = ""
for person, total_difficulty in difficulties.items():
if total_difficulty > max_diff:
max_diff = total_difficulty
max_person = person
print(f"{max_person} has the largest sum of difficulties: {max_diff}")
from dataclasses import dataclass
import math
print("\n----------------------------")
print("------- Exercice 3 -------")
print("----------------------------\n")
xs: List[float] = [0.0, 5.0, 6.0, 9.0, 10.0]
ys: List[float] = [0.0, 5.0, 1.0, 1.0, 8.0]
### 3 (a)
# Ajout d'une erreur dans les données:
# ceci ajoute une valeur à ys sans ajouter une valeur
# correspondante dans xs et crée ainsi une incohérence
ys.append(1000)
p = len(xs)
if p == len(ys):
print("Data OK")
else:
print("Correcting length mismatch")
p = min(p, len(ys))
xs = xs[:p]
ys = ys[:p]
### 3 (b)
print("Considered points: ", end="")
for i in range(p - 1):
print(f"({xs[i]}, {ys[i]})", end=", ")
print(f"({xs[p - 1]}, {ys[p - 1]})")
### 3 (c)
def is_monotonic_increasing(values: List[float]) -> bool:
for i in range(1, len(values)):
if values[i] <= values[i - 1]:
return False
return True
print(f"xs is monotonic inscreasing: {is_monotonic_increasing(xs)}")
print(f"ys is monotonic inscreasing: {is_monotonic_increasing(ys)}")
### 3 (d)
def interpolated_y(x: float) -> float:
for i in range(1, p):
if xs[i - 1] <= x <= xs[i]:
y = ys[i - 1] + (ys[i] - ys[i - 1]) * (x - xs[i - 1]) / (xs[i] - xs[i - 1])
return y
return float("nan")
### 3 (e)
for i in range(100 + 1):
x = i / 10
y = interpolated_y(x)
print(f"x={x} -> y={y}")
### 3 (f)
num_mismatch = 0
for i in range(p):
x, y = xs[i], ys[i]
y_int = interpolated_y(x)
if y != y_int:
print(f"Mismatch for x={x}: should be {y}, but computed {y_int}")
num_mismatch += 1
if num_mismatch == 0:
print("No mismatch found")
### 3 (g)
def areas_under_curve(xs: List[float], ys: List[float]) -> List[float]:
areas: List[float] = []
for i in range(1, p):
mean_height = (ys[i] + ys[i - 1]) / 2
width = xs[i] - xs[i - 1]
local_area = mean_height * width
areas.append(local_area)
return areas
areas = areas_under_curve(xs, ys)
print(areas)
sum_areas = 0.0
for a in areas:
sum_areas += a
print(f"Total area: {sum_areas}")
print("\n----------------------------")
print("------- Exercice 4 -------")
print("----------------------------\n")
### 4 (a) & (b)
@dataclass
class Task:
person: str
title: str
start_day: int
duration: int
difficulty: float
tasks = [
Task("Bernard", "Overview", 0, 2, 0.5),
Task("Heidi", "Frontend", 1, 4, 0.9),
Task("Gabriel", "Kickoff", 0, 1, 0.2),
Task("Morgane", "Backend", 0, 3, 0.8),
Task("Bernard", "Demos", 3, 2, 0.7),
Task("Gabriel", "Database", 1, 3, 0.8),
Task("Morgane", "Tests", 3, 2, 0.65),
]
for task in tasks:
print(task)
### 4 (c)
occupations: Dict[str, List[str]] = {}
for task in tasks:
if task.person not in occupations:
occupations[task.person] = ["", "", "", "", ""]
for day in range(task.start_day, task.start_day + task.duration):
occupations[task.person][day] = task.title
for person, occupation in occupations.items():
print(f"{person}'s occupation: {occupation}")
### 4 (d)
for person, occupation in occupations.items():
for i, title in enumerate(occupation):
if len(title) == 0:
print(f"{person} has nothing to do on day {i}")
### 4 (e)
days_booked: Dict[str, Set[int]] = {}
num_conflicts = 0
for task in tasks:
if task.person not in days_booked:
days_booked[task.person] = set()
persons_days = days_booked[task.person]
for day in range(task.start_day, task.start_day + task.duration):
if day in persons_days:
print(f"{task.person} should work on “{task.title}” on day {day} but is already busy")
num_conflicts += 1
else:
persons_days.add(day)
if num_conflicts == 0:
print(f"No conflicts detected")
### 4 (f)
difficulties: Dict[str, float] = {}
for task in tasks:
if task.person not in difficulties:
difficulties[task.person] = 0
difficulties[task.person] += task.difficulty * task.duration
max_diff = 0.0
max_person = ""
for person, total_difficulty in difficulties.items():
if total_difficulty > max_diff:
max_diff = total_difficulty
max_person = person
print(f"{max_person} has the largest sum of difficulties: {max_diff}")
Modifié le: vendredi, 22 octobre 2021, 09:55