刷到歸併，就此開坑，歸併似乎用的是分治的思維
👉圖解歸併算法
👉參考詳解 ：其中詮釋出，通過分治的方法，降低對比交換的次數，來降低時間複雜度
分治！就是把大問題肢解成同類小問題解決（遞歸）
二分法查詢（用於有序數列）
通過設立center，把長數列中查詢或計數的工作分到每一個部分當中去完成，最後合併（求和）
代碼略
歸併排序
def mergeSort(temp_list, number_list, left, right):
if left == right:
return
elif left < right:
center = (left + right)//2
mergeSort(temp_list, number_list, left, center)
mergeSort(temp_list, number_list, center+1, right)
merge(temp_list, number_list, left, center, right)
return number_list
pass
def merge(temp_list, number_list, left, center, right):
idx_l = left
idx_r = center + 1
idx_ct = 0
while idx_r <= right:
if number_list[idx_r] >= number_list[idx_l]:
temp_list[idx_ct] = number_list[idx_l]
idx_l += 1
idx_ct += 1
pass
else:
temp_list[idx_ct] = number_list[idx_r]
idx_r += 1
idx_ct += 1
if idx_l > center:
while idx_r <= right:
temp_list[idx_ct] = number_list[idx_r]
idx_r += 1
idx_ct += 1
while idx_l <= center:
temp_list[idx_ct] = number_list[idx_l]
idx_l += 1
idx_ct += 1
for i in range(idx_ct):
number_list[left+i] = temp_list[i]
for i in range(len(temp_list)):
temp_list[i] = 0
pass
def testMergesort():
number_list = [364,637,341,406,747,995,234,971,571,219,993,407,416,366,315,301,601,650,418,355,460,505,360,965,516,648,727,667,465,849,455,181,486,149,588,233,144,174,557,67,746,550,474,162,268,142,463,221,882,576,604,739,288,569,256,936,275,401,497,82,935,983,583,523,697,478,147,795,380,973,958,115,773,870,259,655,446,863,735,784,3,671,433,630,425,930,64,266,235,187,284,665,874,80,45,848,38,811,267,575]
temp_list = [0 for i in range(len(number_list))]
print(mergeSort(temp_list, number_list, 0, len(number_list)-1))
testMergesort()
輸出爲：[3, 38, 45, 64, 67, 80, 82, 115, 142, 144, 147, 149, 162, 174, 181, 187, 219, 221, 233, 234, 235, 256, 259, 266, 267, 268, 275, 284, 288, 301, 315, 341, 355, 360, 364, 366, 380, 401, 406, 407, 416, 418, 425, 433, 446, 455, 460, 463, 465, 474, 478, 486, 497, 505, 516, 523, 550, 557, 569, 571, 575, 576, 583, 588, 601, 604, 630, 637, 648, 650, 655, 665, 667, 671, 697, 727, 735, 739, 746, 747, 773, 784, 795, 811, 848, 849, 863, 870, 874, 882, 930, 935, 936, 958, 965, 971, 973, 983, 993, 995]
* merge函數還可以做重構
逆序對應用
逆序對指的是在一串數字中前大後小的數字對。歸併的交換不重複，交換次數就可以用來統計逆序對的數量。
與排序的差別在於多了計數
寫的時候一定要注意count的計數的位置，以及left和right的限制！
def InversePairs(data):
# write code here
temp = [0 for i in range(len(data))]
count = mergeCount(data, temp, 0, len(data) - 1)
print(temp)
return count
def mergeCount(data, temp, left, right):
count = 0
if left == right:
return 0
center = (left + right) // 2
count += mergeCount(data, temp, left, center)
count += mergeCount(data, temp, center + 1, right)
idx_l = left
idx_r = center + 1
idx_ct = 0
while idx_r <= right and idx_l <= center:
if data[idx_r] >= data[idx_l]:
temp[idx_ct] = data[idx_l]
idx_ct += 1
idx_l += 1
pass
else:
count += center + 1 - idx_l
temp[idx_ct] = data[idx_r]
idx_ct += 1
idx_r += 1
pass
pass
while idx_r <= right:
temp[idx_ct] = data[idx_r]
idx_ct += 1
idx_r += 1
pass
while idx_l <= center:
temp[idx_ct] = data[idx_l]
idx_ct += 1
# count += center + 1 - idx_l
idx_l += 1
pass
for i in range(idx_ct):
data[left + i] = temp[i]
pass
return count
def testInversePairs():
data = [364,637,341,406,747,995,234,971,571,219,993,407,416,366,315,301,601,650,418,355,460,505,360,965,516,648,727,667,465,849,455,181,486,149,588,233,144,174,557,67,746,550,474,162,268,142,463,221,882,576,604,739,288,569,256,936,275,401,497,82,935,983,583,523,697,478,147,795,380,973,958,115,773,870,259,655,446,863,735,784,3,671,433,630,425,930,64,266,235,187,284,665,874,80,45,848,38,811,267,575]
print(InversePairs(data))
輸出爲：正常排序如上
逆序數爲：2519