1. Short answer questions (5 questions in total, 100.0 points)
1 Write a function to implement selection method sorting. (Upload code and screenshot of running result)
correct answer:
def selectSort(lst, reverse=False):
length = len(lst)
for i in range(0, length):
#假设剩余元素中第一个最小或最大
m = i
#扫描剩余元素
for j in range(i+1, length):
#如果有更小或更大的，就记录下它的位置
exp = 'lst[j] < lst[m]'
if reverse:
exp = 'lst[j] > lst[m]'
if eval(exp):
m = j
#如果发现更小或更大的，就交换值
if m!=i:
lst[i], lst[m] = lst[m], lst[i]
my answer:
def sort(A):
for i in range(len(A)):
min = i
for j in range(i + 1, len(A)):
if A[min] > A[j]:
min = j
A[i], A[min] = A[min], A[i]
print ('排序后的数组：', A)
A=list(map(int, input("输入要排序的数:").split()))
sort(A)
operation result:
Enter the number to sort: 5 4 78 36 1 6
Sorted array: [1, 4, 5, 6, 36, 78]
2 Write a function to realize the dichotomy search. (Upload code and screenshot of running result)
correct answer:
def binarySearch(lst, value):
start = 0
end = len(lst)
while start < end:
#计算中间位置
middle = (start + end) // 2
#查找成功，返回元素对应的位置
if value == lst[middle]:
return middle
#在后面一半元素中继续查找
elif value > lst[middle]:
start = middle + 1
#在前面一半元素中继续查找
elif value < lst[middle]:
end = middle - 1
#查找不成功，返回False
return False
my answer:
d
ef sort(A):
for i in range(len(A)):
min = i
for j in range(i + 1, len(A)):
if A[min] > A[j]:
min = j
A[i], A[min] = A[min], A[i]
print ('排序后的数组：', A)
A=list(map(int, input("输入要排序的数:").split()))
sort(A)
def Search(alist, item):
n = len(alist)
if n == 0:
return False
else:
mid = n // 2
if alist[mid] == item:
return True
elif item < alist[mid]:
return Search(alist[: mid], item)
else:
return Search(alist[mid + 1:], item)
item = int(input("搜索值:"))
print(Search(A,item))
operation result:
Enter the number to sort: 8 9 1 4 2 3
Sorted array: [1, 2, 3, 4, 8, 9]
Search value: 1
True
3 Write a function to find the longest increasing subsequence of a given sequence. (Upload code and screenshot of running result)
correct answer:
from itertools import combinations
from random import sample
def subAscendingList(lst):
'''返回最长递增子序列'''
for length in range(len(lst), 0, -1):
#按长度递减的顺序进行查找和判断
for sub in combinations(lst, length):
#判断当前选择的子序列是否为递增顺序
if list(sub) == sorted(sub):
#找到第一个就返回
return sub
def getList(start=0, end=1000, number=20):
'''生成随机序列'''
if number > end-start:
return None
return sample(range(start, end), number)
def main():
#生成一个包含10个随机数的列表进行测试
lst = getList(number=10)
if lst:
print(lst)
print(subAscendingList(lst))
main()
operation result:
[608, 543, 915, 787, 545, 128, 930, 852, 844, 322]
(608, 915, 930)
4 Write a function to find the two numbers with the smallest difference in a given sequence. (Upload code and screenshot of running result)
correct answer:
import random
def getTwoClosestElements(seq):
#先进行排序，使得相邻元素最接近
#相差最小的元素必然相邻
seq = sorted(seq)
#无穷大
dif = float('inf')
#遍历所有元素，两两比较，比较相邻元素的差值
#使用选择法寻找相差最小的两个元素
for i,v in enumerate(seq[:-1]):
d = abs(v - seq[i+1])
if d < dif:
first, second, dif = v, seq[i+1], d
#返回相差最小的两个元素
return (first, second)
seq = [random.randint(1, 10000) for i in range(20)]
print(seq)
print(sorted(seq))
print(getTwoClosestElements(seq))
operation result:
Original sequence: [2462, 6108, 330, 1112, 9219, 8152, 5373, 3708, 4292, 7772, 6783, 2107, 8479, 4355, 9791, 2815, 1456, 8381, 406, 6948]
After sorting: [330, 406, 1112, 1456, 2107, 2462, 2815, 3708, 4292, 4355, 5373, 6108, 6783, 6948, 7772, 8152, 8381, 8479, 9219, 9791]
Results: (4292, 4355)
5 Use Monte Carlo method to calculate the approximate value of pi. (Upload code and screenshot of running result)
correct answer:
from random import random
def estimatePI(times):
hits = 0
for i in range(times):
x = random()*2 – 1 #random()生成介于0和1之间的小数
y = random()*2 - 1 #该数字乘以2再减1，则介于-1和1之间
if x*x + y*y <= 1: #落在圆内或圆周上
hits += 1
return 4.0 * hits/times
print(estimatePI(10000))
print(estimatePI(1000000))
operation result:
3.1444
3.141404
