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116 lines
3.6 KiB
Python
116 lines
3.6 KiB
Python
''' mbinary
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#########################################################################
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# File : rotate.py
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# Author: mbinary
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# Mail: zhuheqin1@gmail.com
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# Blog: https://mbinary.xyz
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# Github: https://github.com/mbinary
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# Created Time: 2018-05-19 21:54
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# Description: three methods of rotating a list
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1. 利用 ba=(br)^T(ar)^T=(arbr)^T，通过三次反转字符串: 即首先对序列前部分逆序，再对序列后部分逆序，再对整个序列全部逆序
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2. 分组交换(尽可能使数组的前面连续几个数为所要结果):a长度大于b，将 ab 分成 a0a1b，交换 a0 和 b，得 ba1a0，只需再交换 a1和 a0。若 a 长度小于 b，将 ab 分成 ab0b1，交换 a 和 b0，得 b0ab1，只需再交换 a 和b0。通过不断将数组划分，和交换，直到不能再划分为止。分组过程与求最大公约数很相似。
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3.所有序号为 (j+i*m) % n (j 表示每个循环链起始位置，i 为计数变量，m 表示左旋转位数，n 表示字符串长度)，会构成一个循环链（共有 gcd(n,m)个，gcd 为 n、m 的最大公约数），每个循环链上的元素只要移动一个位置即可，最后整个过程总共交换了 n 次（每一次循环链，是交换 n/gcd(n,m)次，总共 gcd(n,m)个循环链。所以，总共交换 n 次）。
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#########################################################################
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'''
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def rotate(s, k, right=False):
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def reverse(a, b):
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while a < b:
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s[a], s[b] = s[b], s[a]
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a += 1
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b -= 1
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n = len(s)
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k = k % n if not right else n-k % n
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reverse(0, k-1)
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reverse(k, n-1)
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reverse(0, n-1)
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return s
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def rotate2(s, k, right=False):
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def swap(a, b, c):
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for i in range(c):
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s[a+i], s[b+i] = s[b+i], s[a+i]
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def _rot(pl, pr):
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''' swap s[pl,pr) , s[pr:]'''
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if pr == n:
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return
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if pr-pl <= n-pr:
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swap(pl, pr, pr-pl)
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_rot(pr, 2*pr-pl)
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else:
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swap(pl, pr, n-pr)
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_rot(n-pr+pl, pr)
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n = len(s)
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k = k % n if not right else n-k % n
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_rot(0, k)
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return s
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def rotate3(s, k, right=False):
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def gcd(a, b):
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if b == 0:
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return a
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return gcd(b, a % b)
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n = len(s)
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k = k % n if not right else n-k % n
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r = gcd(n, k)
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for i in range(r):
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tmp = s[i]
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j = (i+k) % n
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while j != i:
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s[j-k] = s[j]
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j = (j+k) % n
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s[(j-k+n) % n] = tmp
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return s
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def test():
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def f(func, *args, right=False):
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print(' '.join(['testing:', func.__name__,
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str(args), 'right=', str(right)]))
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rst = func(*args, right=right)
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print('result', rst)
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print()
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return f
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if __name__ == '__main__':
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s = [i for i in range(10)]
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tester = test()
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tester(rotate, s, 4, right=True)
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tester(rotate, s, 4)
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tester(rotate2, s, 2, right=True)
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tester(rotate2, s, 2)
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tester(rotate3, s, 132, right=True)
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tester(rotate3, s, 132)
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'''
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testing: rotate ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 4) right= True
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result [6, 7, 8, 9, 0, 1, 2, 3, 4, 5]
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testing: rotate ([6, 7, 8, 9, 0, 1, 2, 3, 4, 5], 4) right= False
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result [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
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testing: rotate2 ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 2) right= True
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result [8, 9, 0, 1, 2, 3, 4, 5, 6, 7]
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testing: rotate2 ([8, 9, 0, 1, 2, 3, 4, 5, 6, 7], 2) right= False
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result [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
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testing: rotate3 ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 132) right= True
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result [8, 9, 0, 1, 2, 3, 4, 5, 6, 7]
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testing: rotate3 ([8, 9, 0, 1, 2, 3, 4, 5, 6, 7], 132) right= False
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result [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
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'''
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