1.伪代码
'''MERGE(A,p,q,r)'''
n1 = q - p + 1 //L.length
n2 = r - q //R.length
let L[1..n1+1] and R[1..n2+1] be new arrays
for i = 1 to n1
L[i] = A[p + i - 1]
for j = 1 to n2
R[j] = A[q + j]
L[n1 + 1] = ∞
R[n2 + 1] = ∞
i = 1
j = 1
for k = p to r
if L[i] <= R[j]
A[k] = L[I]
i = i + 1
else
A[k] = R[j]
j = j + 1
'''MERGE-SORT(A, p, r)'''
if p < r
q = [(p+r)/2]
MERGE-SORT(A, p, q)
MERGE-SORT(A, q+1, r)
MERGE(A,p,q,r)
MERGE算法图示
2.Python代码
def merge(A, p, q, r):
#A[p:q+1] , A[q+1:r+1]
L = A[p:q+1]
R = A[q+1:r+1]
i = 0
j = 0
for k in range (p, r+1):
if i < len(L) and j < len(R):
if L[i] <= R[j]:
A[k] = L[I]
i = i + 1
else:
A[k] = R[j]
j = j + 1
elif i < len(L):
A[k] = L[I]
i = i + 1
else:
A[k] = R[j]
j = j + 1
return A
def merge_sort(A, p ,r):
if p < r:
q = (p+r)/2
merge_sort(A, p, q)
merge_sort(A, q+1, r)
merge(A,p,q,r)
result:
Before:
[34, 45, 12, 32, 100, 46, 82, 11]
After:
[11, 12, 32, 34, 45, 46, 82, 100]
循环不变性对于归并算法
- 初始化: 在循环之前,子数组为空,L和R数组升序排列, i=j=1, 分别指向数组最小值
- 保持: 每次循环从L和R中取出当前指向两者中小的值,此值为L和R所有值中的最小值,被取用值的数组的指针向后指,保证L和R是为归并的值,此时子数组升序排列且最大值 <= L和R的最小值
- 终止: 结束时 子数组,L和R数组均指向数组最大值,此时子数组为L和R中的数值升序排列
归并算法递归部分:MERGE_SORT(A,p,r)
递归二分数组,直到p<=r, 即细分到单元素数组,所以已经排好序.
递归归并子数组,直到将所有数据合并完.
MERGE_SORT算法图示
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