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96 lines
2.6 KiB
Python
96 lines
2.6 KiB
Python
from collections import defaultdict
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import inspect
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N = 32
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f = lambda x: (2*x-1) ^ (x&7)
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table = [f(i) & (N-1) for i in range(N)]
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rtable = [table.count(i) for i in range(N)]
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def getPath(v):
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if table[v] is None:
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return [v]
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bak = table[v]
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table[v] = None
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r = [v] + getPath(bak)
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table[v] = bak
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return r
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def getPaths():
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visited = set()
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paths = list()
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for i in range(N):
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if rtable[i] == 0:
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paths.append(getPath(i))
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for path in paths:
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for i in path:
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visited.add(i)
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for i in range(N):
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if i not in visited:
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paths.append(getPath(i))
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for j in paths[-1]:
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visited.add(j)
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return paths
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pathsByLidx = defaultdict(set)
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loopsByIdx = dict()
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loopsByLidx = dict()
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for path in getPaths():
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i = path.index(path[-1])+1
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head, loop, lidx = tuple(path[:i]), tuple(path[i:]), max(path[i:])
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pathsByLidx[lidx].add((head, loop))
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print()
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print("The %d-bit function f(x) produces %d loops:" % (N.bit_length()-1, len(pathsByLidx)))
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print(" ", inspect.getsource(f).strip())
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for lidx, paths in pathsByLidx.items():
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loop = None
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for path in paths:
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for i in path[0] + path[1]:
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loopsByIdx[i] = lidx
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if loop is None or path[1][0] > loop[0]:
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loop = path[1]
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loopsByLidx[lidx] = loop
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print()
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print("%d-Element Loop:" % len(loop))
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print(" ", " ->- ".join(["%2d" % i for i in loop + (loop[0],)]))
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lines = []
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lastPath = []
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for path in sorted([tuple(reversed(p[0])) for p in paths]):
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line = ""
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for i in range(len(path)):
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if i < len(lastPath) and lastPath[i] == path[i]:
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line += " %s " % (" " if i == 0 else "| ")
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else:
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line += " %s %2d" % (" " if i == 0 else "`<-" if len(lastPath) else "-<-", path[i])
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lastPath = []
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lastPath = path
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lines.append(line)
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for i in range(len(lines)-1, -1, -1):
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line, nextline = list(lines[i]), "" if i == len(lines)-1 else lines[i+1]
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if len(nextline) < len(line): nextline = nextline.ljust(len(line))
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for k in range(len(line)):
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if line[k] == "|" and nextline[k] in " -":
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line[k] = " "
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lines[i] = "".join(line)
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print("%d Lead-Ins:" % len(lines))
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for line in lines:
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print(line)
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print()
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print("Loop Membership:")
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for lidx in pathsByLidx:
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print("%18s |" % (loopsByLidx[lidx],), end="")
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for i in range(N):
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print("*" if loopsByIdx[i] == lidx else ".", end="")
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print("|")
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print()
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