def merge(arr, aux, low, mid, high): # 05:00-06:00
"""Merge 2 sorted arrays into 1 sorted array."""
assert _isSorted(
arr, low, mid) # precondition: arr[low .. mid] are sorted subarrays
assert _isSorted(
arr, mid + 1,
high) # precondition: arr[mid+1 .. high] are sorted subarrays
aux[low:high + 1] = arr[low:high + 1] # copy to aux[]
# merge back to arr[] in sorted order
i = low # index of sorted arr[low .. mid] ( left-half)
j = mid + 1 # index of sorted arr[mid+1 .. high] (right-half)
## print('RRRRRRRRRRRRRRRRR', range(low, high+1), aux[j], aux[i])
for k in range(low, high + 1): # k is current entry in the sorted result
# i ptr is exhausted - this copying is unnecessary
if i > mid:
arr[k] = aux[j]
j += 1
# j ptr is exhausted
elif j > high:
arr[k] = aux[i]
i += 1
elif __lt__(aux[j], aux[i]):
arr[k] = aux[j]
j += 1
else:
arr[k] = aux[i]
i += 1
# _vis_merge(arr, aux, low, mid, high)
assert _isSorted(arr, low,
high) # postcondition: arr[low .. high] is sorted
def merge(a, aux, lo, mid, hi): # 05:00-06:00
"""Merge 2 sorted arrays into 1 sorted array."""
assert _isSorted(a, lo,
mid) # precondition: a[lo .. mid] are sorted subarrays
assert _isSorted(a, mid + 1,
hi) # precondition: a[mid+1 .. hi] are sorted subarrays
aux[lo:hi + 1] = a[lo:hi + 1] # copy to aux[]
# merge back to a[] in sorted order
i = lo # index of sorted a[lo .. mid] ( left-half)
j = mid + 1 # index of sorted a[mid+1 .. hi] (right-half)
for k in range(lo, hi + 1): # k is current entry in the sorted result
if i > mid:
a[k] = aux[j]
j += 1 # this copying is unnecessary
elif j > hi:
a[k] = aux[i]
i += 1 # j ptr is exhausted
elif __lt__(aux[j], aux[i]):
a[k] = aux[j]
j += 1
else:
a[k] = aux[i]
i += 1
#_vis_merge(a, aux, lo, mid, hi)
assert _isSorted(a, lo, hi) # postcondition: a[lo .. hi] is sorted
def merge(a, aux, lo, mid, hi): # 05:00-06:00
"""Merge 2 sorted arrays into 1 sorted array."""
assert _isSorted(a, lo, mid) # precondition: a[lo .. mid] are sorted subarrays
assert _isSorted(a, mid+1, hi) # precondition: a[mid+1 .. hi] are sorted subarrays
aux[lo:hi+1] = a[lo:hi+1] # copy to aux[]
# merge back to a[] in sorted order
i = lo # index of sorted a[lo .. mid] ( left-half)
j = mid+1 # index of sorted a[mid+1 .. hi] (right-half)
for k in range(lo, hi+1): # k is current entry in the sorted result
if i > mid: a[k] = aux[j]; j += 1 # this copying is unnecessary
elif j > hi: a[k] = aux[i]; i += 1 # j ptr is exhausted
elif __lt__(aux[j], aux[i]): a[k] = aux[j]; j += 1
else: a[k] = aux[i]; i += 1
#_vis_merge(a, aux, lo, mid, hi)
assert _isSorted(a, lo, hi) # postcondition: a[lo .. hi] is sorted
def Sort(ARR, array_history=None):
"""Rearranges the array in ascending order, using the natural order."""
N = len(ARR)
# 00:57 Everything to the left is in acending order
# Everything to the right, we have not seen at all
for i in range(N):
j = i
# Exchange the curr Elem with every element to the left that is > 01:21
while j > 0 and __lt__(ARR[j], ARR[j-1]): # Iterate from i back towards 0
if array_history is not None: array_history.add_history(ARR, {j:'*', j-1:'*'})
_exch(ARR, j, j-1)
j -= 1
assert _isSorted(ARR, 0, i)
assert _isSorted(ARR);
if array_history is not None: array_history.add_history(ARR, None)
def Sort(a, array_history=None): # 09:30 """Rearranges the array in ascending order, using the natural order.""" # At most N lg N compares and 6 N lg N array accesses to sort any array of size N aux = [None for i in range(len(a))] # Create aux outside _sort to avoid extensive costs. _add_history(array_history, a, aux) # Record initial state of arrays _sort(a, aux, lo=0, hi=len(a)-1, array_history=array_history) assert _isSorted(a)
def Sort(ARR, array_history=None):
"""Rearranges the array in ascending order, using the natural order."""
N = len(ARR)
# 00:57 Everything to the left is in acending order
# Everything to the right, we have not seen at all
for i in range(N):
j = i
# Exchange the curr Elem with every element to the left that is > 01:21
while j > 0 and __lt__(ARR[j],
ARR[j - 1]): # Iterate from i back towards 0
if array_history is not None:
array_history.add_history(ARR, {j: '*', j - 1: '*'})
_exch(ARR, j, j - 1)
j -= 1
assert _isSorted(ARR, 0, i)
assert _isSorted(ARR)
if array_history is not None: array_history.add_history(ARR, None)
def Sort(arr, array_history=None): # 09:30
"""Rearranges the array in ascending order, using the natural order."""
# At most N lg N compares and 6 N lg N array accesses to sort any array of size N
aux = [None] * len(
arr) # Create aux outside _sort to avoid extensive costs.
_add_history(array_history, arr, aux) # Record initial state of arrays
_sort(arr, aux, low=0, high=len(arr) - 1, array_history=array_history)
assert _isSorted(arr)
def Sort(ARR, array_history=None):
"""Rearranges the array, ARR, in ascending order, using the natural order."""
# param array_history; For visualization. When true prints ASCII Art demonstrating the sort
N = len(ARR)
# Items from i to j-1 are Sorted
# IN the ith iteration, find the smallest remaining Item above i
for i in range(N): # MOVE pointer to the right
min_elem_idx = i # Index of smallest element to the right of pointer i
# Identify index of min Item right of j
for j in range(i+1,N):
if __lt__(ARR[j], ARR[min_elem_idx]): # COMPARE is counted toward cost
min_elem_idx = j
if array_history is not None: array_history.add_history(ARR, {i:'*', min_elem_idx:'*'})
_exch(ARR, i, min_elem_idx) # EXCHANGE is counted toward cost
assert _isSorted(ARR, 0, i)
assert _isSorted(ARR)
if array_history is not None: array_history.add_history(ARR, None)
def Sort(pq):
N = len(pq)
for k in range(N/2, 0, -1):
_sink(pq, k, N)
while (N > 1):
_exch(pq, 1, N)
N -= 1
_sink(pq, 1, N)
assert _isSorted(pq)
def Sort(ARR, array_history=None):
"""Rearranges the array, ARR, in ascending order, using the natural order."""
# param array_history; For visualization. When true prints ASCII Art demonstrating the sort
N = len(ARR)
# Items from i to j-1 are Sorted
# IN the ith iteration, find the smallest remaining Item above i
for i in range(N): # MOVE pointer to the right
min_elem_idx = i # Index of smallest element to the right of pointer i
# Identify index of min Item right of j
for j in range(i + 1, N):
if __lt__(ARR[j],
ARR[min_elem_idx]): # COMPARE is counted toward cost
min_elem_idx = j
if array_history is not None:
array_history.add_history(ARR, {i: '*', min_elem_idx: '*'})
_exch(ARR, i, min_elem_idx) # EXCHANGE is counted toward cost
assert _isSorted(ARR, 0, i)
assert _isSorted(ARR)
if array_history is not None: array_history.add_history(ARR, None)
def Sort(a, array_history=None): # N lg N
"""Rearranges the array, a, in ascending order, using the natural order."""
N = len(a)
aux = [None for i in range(N)]
_add_history(array_history, a, aux) # Record initial state of arrays
sarr_sz = 1
# First nested loop is "Size of the sub-array" executed only lg N times (lg N passes)
while sarr_sz < N: # i.e. for (int sz=1; sz<N; sz=sz+sz)
lo = 0
while lo < N-sarr_sz: # i.e. for (int lo = 0; lo < N-sz; lo += sz+sz)
mid = lo + sarr_sz - 1
hi = min(lo + sarr_sz + sarr_sz - 1, N-1)
merge(a, aux, lo, mid, hi)
_add_history(array_history, a, aux, (lo, hi, mid))
lo += sarr_sz+sarr_sz
sarr_sz = sarr_sz+sarr_sz # Double the size of the sub-array until we get to N
assert _isSorted(a)
def Sort(ARR, array_history=None, sort_seq=None):
"""Rearranges the array, ARR, in ascending order, using the natural order."""
# array_history; Used in tests. When true prints ASCII Art demonstrating the sort
N = len(ARR)
# 3x+1 increment sequence: [1, 4, 13, 40, 121, 364, 1093, ...
ha = get_sort_seq(N, sort_seq)
print ha
for h in reversed(ha):
# h-sort the array (insertion sort)
for i in range(h, N):
j = i
while j >= h and __lt__(ARR[j], ARR[j - h]):
if array_history is not None:
array_history.add_history(ARR, {j: '*', j - h: '*'})
_exch(ARR, j, j - h)
j -= h
assert _isHsorted(ARR, h)
assert _isSorted(ARR)
if array_history is not None:
array_history.add_history(ARR, None)
def Sort(ARR, array_history=None, sort_seq=None):
"""Rearranges the array, ARR, in ascending order, using the natural order."""
# array_history; Used in tests. When true prints ASCII Art demonstrating the sort
N = len(ARR)
# 3x+1 increment sequence: [1, 4, 13, 40, 121, 364, 1093, ...
ha = get_sort_seq(N, sort_seq)
print ha
for h in reversed(ha):
# h-sort the array (insertion sort)
for i in range(h,N):
j = i
while j >= h and __lt__(ARR[j], ARR[j-h]):
if array_history is not None:
array_history.add_history(ARR, {j:'*', j-h:'*'} )
_exch(ARR, j, j-h)
j -= h
assert _isHsorted(ARR, h)
assert _isSorted(ARR)
if array_history is not None:
array_history.add_history(ARR, None)