refer to: https://www.algoexpert.io/questions/Largest%20Range

Problem Statement

 

 

 

 Analysis

The most naive way, sort the array, then check the largest range, need O(nlogn) time complexity

 

 Code

# step 1: store all the values in hashmap
# step 2: iterate all the values in the array, for each value, check the range related to this value, how to check? check if the left/right number contains in the hashmap or not.
# if in the hashmap, set the value of that key in the hashmap to False(visited), then we don't need to recheck those False values
def largestRange(array):
    # Write your code here.
    bestRange = []
    longestLength = 0
    nums = {} # create a hashmap to store all the values, 
    
    for num in array:
        nums[num] = True # initialize all to True(all values do not have been touched at first
    for num in array:
        if not nums[num]:
            continue # if set to false, the value has been explored, do nothing
        nums[num] = False  # now, the current value is being explored
        currentLength = 1 # the currentLength is itself
        left = num - 1
        right = num + 1
        while left in nums:
            nums[left] = False
            currentLength += 1
            left -= 1 # continue to explore the range from right to left
        while right in nums:
            nums[right] = False
            currentLength += 1
            right += 1 # continue to expolre the range from left to right
            
        if currentLength > longestLength:
            longestLength = currentLength
            bestRange = [left + 1, right - 1] # at the end of the two while loops, right has been plus 1, left has been minus 1, need to restore the real values of left and right
    return bestRange

Time complexity: O(n) one pass for creating a hashmap, another pass for traversing each value in the array

Space complexity: O(n) store the hashmap

n is the length of the input array