55 lines
1.1 KiB
Ruby
55 lines
1.1 KiB
Ruby
|
# Given a sorted array of n unique integers where each integer is in the range from 0 to m-1 and m > n.
|
||
|
|
# Find the smallest number that is missing from the array.
|
||
|
|
|
||
|
|
#Algorithm: Binary Search (Compare elements with indexes and then decide)
|
||
|
|
#Time-complexity: O(logn), Auxiliary-space: O(1)
|
||
|
|
|
||
|
|
|
||
|
|
# Iterative
|
||
|
|
def smallest_missing(a)
|
||
|
|
lo=0
|
||
|
|
hi=a.length-1
|
||
|
|
while hi>lo
|
||
|
|
mid=lo+(hi-lo)/2
|
||
|
|
if a[mid]>mid
|
||
|
|
hi=mid
|
||
|
|
else
|
||
|
|
lo=mid+1
|
||
|
|
end
|
||
|
|
end
|
||
|
|
if a[lo]==lo # if lo == end of array
|
||
|
|
print lo+1
|
||
|
|
else
|
||
|
|
print lo
|
||
|
|
end
|
||
|
|
end
|
||
|
|
smallest_missing([0, 1, 2, 3]) #=> 4
|
||
|
|
smallest_missing([0, 1, 2, 5]) #=> 3
|
||
|
|
|
||
|
|
#recursive
|
||
|
|
|
||
|
|
#Driver function
|
||
|
|
def driver_func(a)
|
||
|
|
lo=0
|
||
|
|
hi=a.length-1
|
||
|
|
print smallest_missing(a,lo,hi)
|
||
|
|
end
|
||
|
|
|
||
|
|
#Algorithm
|
||
|
|
def smallest_missing(a,lo,hi)
|
||
|
|
if lo>hi
|
||
|
|
return hi+1
|
||
|
|
end
|
||
|
|
if a[lo] != lo
|
||
|
|
return lo
|
||
|
|
end
|
||
|
|
mid= lo+(hi-lo)/2
|
||
|
|
if a[mid]>mid
|
||
|
|
return smallest_missing(a,lo,mid)
|
||
|
|
else
|
||
|
|
return smallest_missing(a,mid+1,hi)
|
||
|
|
end
|
||
|
|
end
|
||
|
|
driver_func([0, 1, 2, 3]) #=> 4
|
||
|
|
driver_func([0, 1, 2, 5]) #=> 3
|