1. 插入排序（章节2.1）
def insertion_sort(A):
for i in range(1, len(A)):
key = A[i]
while i > 0 and key < A[i-1]: //遍历前序元素，并和当前key进行比较如果比key大则将该元素后移
A[i] = A[i-1]
i -= 1
A[i] = key
return A
P = [3, 2, 1, 4, 6, 5, 9]
print(insertion_sort(P))
2. 归并排序（章节2.3.1）
def merge(A, p, r, q):
L = []
R = []
for i in range(p, r+1):
L.append(A[i])
L.append(float('inf'))
print(L)
for j in range(r+1, q+1):
R.append(A[j])
R.append(float('inf'))
print(R)
i = 0
j = 0
for k in range(p, q+1):
if L[i] < R[j]:
A[k] = L[i]
i += 1
else:
A[k] = R[j]
j += 1
return A
def merge_sort(A, p, q):
if p < q:
r = (p + q) // 2 #integer division
merge_sort(A, p, r)
merge_sort(A, r+1, q)
print(merge(A, p, r, q))
P = [5, 2, 3]
merge_sort(P, 0, 2)
3. 最大子数组问题暴力解法（章节4.1）
def violent_solution(A):
profit = 0
buy = ''
sale = ''
for key1 in A:
for key2 in A:
if int(key1) < int(key2) and A[key1] < A[key2] and profit < (A[key2] - A[key1]):
profit = A[key2] - A[key1]
buy = key1
sale = key2
return buy, sale, profit
P = {'0': 100, '1': 113, '2': 110, '3': 85, '4': 105, '5': 102,
'6': 86, '7': 63, '8': 81, '9': 101, '10': 94, '11': 106,
'12': 101, '13': 79, '14': 94, '15': 90, '16': 97}
print(violent_solution(P))
4. 最大子数组问题分治策略解法（mid算在左侧）（章节4.1）
import math
def find_max_crossing_subarray(A, low, mid, high):
left_sum = float('-inf')
s = 0
max_left = 0
for i in range(low, mid+1)[::-1]:
s = s + A[i]
if left_sum < s:
left_sum = s
max_left = i
right_sum = float('-inf')
s = 0
max_right = 0
for j in range(mid+1, high+1):
s = s + A[j]
if right_sum < s:
right_sum = s
max_right = j
return max_left, max_right, left_sum + right_sum
def find_maximum_subarray(A, low, high):
if low == high:
return low, high, A[low]
else:
mid = math.floor((low + high) / 2)
left_low, left_high, left_sum = find_maximum_subarray(A, low, mid)
right_low, right_high, right_sum = find_maximum_subarray(A, mid+1, high)
cross_low, cross_high, cross_sum = find_max_crossing_subarray(A, low, mid, high)
if left_sum >= right_sum and left_sum >= cross_sum:
return left_low, left_high, left_sum
elif right_sum >= left_sum and right_sum >= cross_sum:
return right_low, right_high, right_sum
else:
return cross_low, cross_high, cross_sum
P = [100, 113, 110, 85, 105, 102, 86, 63, 81, 101, 94, 106, 101, 79, 94, 90, 97]
P_C = []
for i in range(1, P.__len__()):
P_C.append(P[i] - P[i-1])
print(find_maximum_subarray(P_C, 0, 15))
5. 最大子数组问题分治策略解法（mid算在右侧）（章节4.1）
（此时除了需要改变区间，还需将mid的取值改为向上取整）
import math
def find_max_crossing_subarray(A, low, mid, high):
left_sum = float('-inf')
s = 0
max_left = 0
for i in range(low, mid)[::-1]:
s = s + A[i]
if left_sum < s:
left_sum = s
max_left = i
right_sum = float('-inf')
s = 0
max_right = 0
for j in range(mid, high+1):
s = s + A[j]
if right_sum < s:
right_sum = s
max_right = j
return max_left, max_right, left_sum + right_sum
def find_maximum_subarray(A, low, high):
if low == high:
return low, high, A[low]
else:
mid = math.ceil((low + high) / 2) //改为向上取整即可
left_low, left_high, left_sum = find_maximum_subarray(A, low, mid-1)
right_low, right_high, right_sum = find_maximum_subarray(A, mid, high)
cross_low, cross_high, cross_sum = find_max_crossing_subarray(A, low, mid, high)
if left_sum >= right_sum and left_sum >= cross_sum:
return left_low, left_high, left_sum
elif right_sum >= left_sum and right_sum >= cross_sum:
return right_low, right_high, right_sum
else:
return cross_low, cross_high, cross_sum
P = [100, 113, 110, 85, 105, 102, 86, 63, 81, 101, 94, 106, 101, 79, 94, 90, 97]
P_C = []
for i in range(1, P.__len__()):
P_C.append(P[i] - P[i-1])
print(find_maximum_subarray(P_C, 0, 15))
6. 产生随机排列（章节5.3）
import random
def randomize_in_place(A):
for i in range(len(A)):
r = random.randint(i, len(A)-1)
A[i], A[r] = A[r], A[i]
return A
P = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
print(randomize_in_place(P))
