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Program to find maximum width ramp in Python
Suppose we have an array nums, a ramp is a tuple (i, j) for which i < j and nums[i] <= nums[j]. The width of such a ramp is (j-i). We have to find the maximum width of a ramp in nums. If we cannot find such, then return 0.
So, if the input is like nums = [6,0,8,2,1,5], then the output will be 4 because the maximum width ramp is achieved at (i, j) = (1, 5) and nums[1] = 0 and nums[5] = 5.
To solve this, we will follow these steps −
B := a new map
for i in range 0 to size of nums, do
x := nums[i]
if x is in B, then
insert i at the end of B[x]
otherwise,
B[x] := [i]
mini := a list initially store one inf into it
maxi := a list initially store one -inf into it
for each x in sort the list list of all keys of B, do
insert minimum of last element of mini and minimum of B[x] at the end of mini
for each x in reversely sorted list of all keys of B, do
insert minimum of last element of mini and minimum of B[x] at the end of mini
maxi := reverse maxi then take subarray from start to second last element
mini := subarray of mini[from index 1 to end]
p := 0
res := -inf
while p < size of mini, do
res := maximum of res and (maxi[p] - mini[p])
p := p + 1
return res
Example
Let us see the following implementation to get better understanding −
def solve(nums):
B = {}
for i in range(len(nums)):
x = nums[i]
if x in B:
B[x].append(i)
else:
B[x] = [i]
mini = [float('inf')]
maxi = [float('-inf')]
for x in sorted(B.keys()):
mini.append(min(mini[-1], min(B[x])))
for x in sorted(B.keys(), reverse = True):
maxi.append(max(maxi[-1], max(B[x])))
maxi = maxi[::-1][:-1]
mini = mini[1:]
p = 0
res = float('-inf')
while p < len(mini):
res = max(res, maxi[p] - mini[p])
p += 1
return res
nums = [6,0,8,2,1,5]
print(solve(nums))
Input
[6,0,8,2,1,5]
Output
4
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