Con trăn
Hoàn toàn cố gắng kết hợp các nếp gấp khác nhau trong vài lần đầu tiên, sau đó thực hiện các nếp gấp còn lại bằng cách sử dụng một cách tiếp cận tham lam.
Cách tiếp cận toàn diện được giới hạn trong phạm vi nếp gấp hợp lý ở trung tâm, sao cho nó sẽ không mất nhiều thời gian, trong khi không bỏ qua quá nhiều nếp gấp có thể mang lại mức tối thiểu tốt.
Ran sử dụng pypy trên macbook air của tôi.
Đáp án:
20*20D9R15R6D11R10R9D10R11
40*20D6D13D9R19R21R20D11D10
40*40D21R21R11D19R23R20D23D15
20*80D33D47D40R10D39D41R9R11
Đầu ra:
Exhaustive folds levels: 3
Percentage pruned from sides from exhaustive folds: 0.2
Time taken: 4.016076s
Score: 7.91125
20*20D9R15R6D11R10R9D10R11
Exhaustive folds levels: 3
Percentage pruned from sides from exhaustive folds: 0.2
Time taken: 28.529278s
Score: 16.34375
40*20D6D13D9R19R21R20D11D10
Exhaustive folds levels: 3
Percentage pruned from sides from exhaustive folds: 0.25
Time taken: 98.430465s
Score: 42.13
40*40D21R21R11D19R23R20D23D15
Exhaustive folds levels: 3
Percentage pruned from sides from exhaustive folds: 0.25
Time taken: 234.873787s
Score: 32.30875
20*80D33D47D40R10D39D41R9R11
Tổng số điểm: 7.91125 + 16.34375 + 42.13 + 32.30875 = 98,69375
Mã số:
import time, math
from collections import deque
numberOfFolds = 8 # Total number of folds
startTime = time.clock()
exec "grid = ("+"""
1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1
1 1 0 0 0 1 0 1 1 0 0 0 1 0 1 1 1 0 1 1
0 1 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 0
0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1
0 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0
1 0 1 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 1
0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0
0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0
1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 1
1 1 0 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0
0 1 1 0 0 0 1 1 0 1 1 1 0 1 1 1 0 1 0 1
0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 1 1 0
0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1
0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1
1 1 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1
1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 1
0 0 1 0 1 1 1 1 0 1 1 0 1 0 1 0 0 1 1 0
0 1 1 0 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 0
0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 1 1 1
""".replace(" ",",").replace("\n","],[")[2:-2]+")"
def getAverage(grid):
count = total = 0
for j in grid:
for i in j:
count += 1
total += i
return total/float(count)
def getScore(grid, average):
score = 0
for j in grid:
for i in j:
score += abs(average-i)
return score
def downFoldedGrid(grid, row, width, height, copy=True):
if copy: grid = [r[:] for r in grid]
foldRange = min(row, height-row)
for j in xrange(foldRange):
rowRef1 = grid[row+j]
rowRef2 = grid[row-1-j]
for i in xrange(width):
rowRef1[i] = rowRef2[i] = (rowRef1[i] + rowRef2[i]) * .5
return grid
def downFoldedScore(grid, score, average, row, width, height):
foldRange = min(row, height-row)
average2 = 2*average
for j in xrange(foldRange):
rowRef1 = grid[row+j]
rowRef2 = grid[row-1-j]
a = b = c = 0
for i in xrange(width):
a = rowRef1[i]
b = rowRef2[i]
c = a+b
score += abs(average2-c) - abs(average-a) - abs(average-b)
return score
def rightFoldedGrid(grid, column, width, height, copy=True):
if copy: grid = [r[:] for r in grid]
foldRange = min(column, width-column)
for j in xrange(height):
rowRef = grid[j]
for i in xrange(foldRange):
a = column+i
b = column-1-i
rowRef[a] = rowRef[b] = (rowRef[a] + rowRef[b]) * .5
return grid
def rightFoldedScore(grid, score, average, column, width, height):
foldRange = min(column, width-column)
average2 = 2*average
for j in xrange(height):
rowRef = grid[j]
a = b = c = 0
for i in xrange(foldRange):
a = rowRef[column+i]
b = rowRef[column-1-i]
c = a+b
score += abs(average2-c) - abs(average-a) - abs(average-b)
return score
def bestFoldsGreedy(grid, average, maxFolds, width, height):
score = getScore(grid, average)
folds = []
append = folds.append
for z in xrange(maxFolds):
bestFold = 0
bestFoldScore = score
bestFoldGrid = grid
for i in xrange(1, width): #Try all right folds
foldScore = rightFoldedScore(grid, score, average, i, width, height)
if foldScore < bestFoldScore:
bestFold = i
bestFoldScore = foldScore
for i in xrange(1, height): #Try all down folds
foldScore = downFoldedScore(grid, score, average, i, width, height)
if foldScore < bestFoldScore:
bestFold = -i
bestFoldScore = foldScore
if bestFold:
append(bestFold)
score = bestFoldScore
if bestFold > 0: rightFoldedGrid(grid, bestFold, width, height, False)
else: downFoldedGrid(grid, -bestFold, width, height, False)
return score, folds
# Get the height and width
height = len(grid)
width = len(grid[0])
# Transpose the grid if height > width for better locality of reference
transposed = False
if height > width:
grid = [[grid[i][j] for i in range(height)] for j in range(width)]
transposed = True
height, width = width, height
# The exhaustive grids and folds attempted
exhaustiveGridsAndFolds = deque([(grid,[])])
popleft = exhaustiveGridsAndFolds.popleft
append = exhaustiveGridsAndFolds.append
# Set the bounds to exhaustively test for
exhaustiveLevels = 3
prunePadding = [0.2, 0.25][width*height > 1000]
leftBound = int(max(width*prunePadding, 1))
rightBound = int(width*(1.0-prunePadding))
topBound = int(max(height*prunePadding, 1))
bottomBound = int(height*(1.0-prunePadding))
# Populate the exhaustive grids and folds
while 1:
grid, folds = popleft()
if len(folds) == exhaustiveLevels:
append((grid, folds))
break
for i in xrange(leftBound, rightBound):
if i not in folds:
append((rightFoldedGrid(grid, i, width, height), folds+[i]))
for i in xrange(topBound, bottomBound):
if -i not in folds:
append((downFoldedGrid(grid, i, width, height), folds+[-i]))
# Test all the exhaustive grids and folds greedily
average = getAverage(grid)
bestFinalScore = getScore(grid, average)
bestFinalFolds = []
numberOfGreedyFolds = numberOfFolds-exhaustiveLevels
while exhaustiveGridsAndFolds:
grid, exhaustiveFolds = popleft()
finalScore, greedyFolds = bestFoldsGreedy(grid, average, numberOfGreedyFolds, width, height)
if finalScore <= bestFinalScore:
bestFinalScore = finalScore
bestFinalFolds = exhaustiveFolds + greedyFolds
# Repeat the last fold till the total number of folds if needed
if len(bestFinalFolds) < numberOfFolds:
bestFinalFolds += [bestFinalFolds[-1]]*(numberOfFolds-len(bestFinalFolds))
# Print the best result
foldsString = ""
down = "D"
right = "R"
if transposed:
down, right = right, down
width, height = height, width
for fold in bestFinalFolds:
if fold > 0: foldsString += right+str(fold)
elif fold < 0: foldsString += down+str(-fold)
print "Exhaustive folds levels: " + str(exhaustiveLevels)
print "Percentage pruned from sides from exhaustive folds: " + str(prunePadding)
print "Time taken: " + str(time.clock()-startTime) + "s"
print "Score: " + str(bestFinalScore)
print str(width) + "*" + str(height) + foldsString