Max Increase to Keep City Skyline

In a 2 dimensional array grid, each value grid[i][j] represents the height of a building located there. We are allowed to increase the height of any number of buildings, by any amount (the amounts can be different for different buildings). Height 0 is considered to be a building as well. 

At the end, the “skyline” when viewed from all four directions of the grid, i.e. top, bottom, left, and right, must be the same as the skyline of the original grid. A city’s skyline is the outer contour of the rectangles formed by all the buildings when viewed from a distance. See the following example.

What is the maximum total sum that the height of the buildings can be increased?

Input: grid = [[3,0,8,4],[2,4,5,7],[9,2,6,3],[0,3,1,0]]
Output: 35
The grid is:
[ [3, 0, 8, 4], 
  [2, 4, 5, 7],
  [9, 2, 6, 3],
  [0, 3, 1, 0] ]

The skyline viewed from top or bottom is: [9, 4, 8, 7]
The skyline viewed from left or right is: [8, 7, 9, 3]

The grid after increasing the height of buildings without affecting skylines is:

gridNew = [ [8, 4, 8, 7],
            [7, 4, 7, 7],
            [9, 4, 8, 7],
            [3, 3, 3, 3] ]


  • 1 < grid.length = grid[0].length <= 50.
  • All heights grid[i][j] are in the range [0, 100].
  • All buildings in grid[i][j] occupy the entire grid cell: that is, they are a 1 x 1 x grid[i][j] rectangular prism.
class Solution:
    def maxIncreaseKeepingSkyline(self, grid: List[List[int]]) -> int:
        lr_view = [max(line) for line in grid]
        tb_view = [max(line) for line in zip(*grid)]
        result = 0
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                diff = min(tb_view[j], lr_view[i]) - grid[i][j]
                result += max(0, diff)
        return result

My Calendar I

Implement a MyCalendar class to store your events. A new event can be added if adding the event will not cause a double booking.

Your class will have the method, book(int start, int end). Formally, this represents a booking on the half open interval [start, end), the range of real numbers x such that start <= x < end.

double booking happens when two events have some non-empty intersection (ie., there is some time that is common to both events.)

For each call to the method, return true if the event can be added to the calendar successfully without causing a double booking. Otherwise, return false and do not add the event to the calendar.Your class will be called like this: MyCalendar cal = new MyCalendar();, end)

Example 1:
MyCalendar();, 20); // returns true, 25); // returns false, 30); // returns true
The first event can be booked.  The second can't because time 15 is already booked by another event.
The third event can be booked, as the first event takes every time less than 20, but not including 20.


  • The number of calls to per test case will be at most 1000.
  • In calls to, end)start and end are integers in the range [0, 10^9].
import bisect

class MyCalendar:

    def __init__(self):
        self.ints = []

    def book(self, start: int, end: int) -> bool:
        idx = bisect.bisect_left(self.ints, (start, end))

        is_left_valid = idx == 0 or self.ints[idx - 1][1] <= start
        is_right_valid = idx == len(self.ints) or end <= self.ints[idx][0]

        if is_left_valid and is_right_valid:
            self.ints.insert(idx, (start, end))
            return True
        return False

Find the Shortest Superstring

Given an array A of strings, find any smallest string that contains each string in A as a substring.

We may assume that no string in A is substring of another string in A.

Example 1:
Input: ["alex","loves","leetcode"]
Output: "alexlovesleetcode"
Explanation: All permutations of "alex","loves","leetcode" would also be accepted.
Example 2:
Input: ["catg","ctaagt","gcta","ttca","atgcatc"]
Output: "gctaagttcatgcatc"

1 <= A.length <= 12
1 <= A[i].length <= 20

Solution 1 (Naive and TLE):
At the very first, I did this solution that naively using DFS to search each possible solution, and finally we can pick up the shortest one. It works on small test set but got TLE on large sets.

from functools import lru_cache

class Solution:
    def combinateStrings(self, str1, str2):
        for i in range(len(str2), -1, -1):
            if str1.endswith(str2[:i]):
                return str1 + str2[i:]

    def shortestSuperstring(self, A):

        def func(current_list, result, results):
            if not current_list:

            for s in current_list:
                func(current_list, self.combinateStrings(result, s), results)
                func(current_list, self.combinateStrings(s, result), results)

        results = []

        func(A, "", results)

        return min(results, key= lambda x: len(x))

Best Time to Buy and Sell Stock with Transaction Fee

Your are given an array of integers prices, for which the i-th element is the price of a given stock on day i; and a non-negative integer fee representing a transaction fee.

You may complete as many transactions as you like, but you need to pay the transaction fee for each transaction. You may not buy more than 1 share of a stock at a time (ie. you must sell the stock share before you buy again.)

Return the maximum profit you can make.

Example 1:

Input: prices = [1, 3, 2, 8, 4, 9], fee = 2
Output: 8
Explanation: The maximum profit can be achieved by:
Buying at prices[0] = 1Selling at prices[3] = 8Buying at prices[4] = 4Selling at prices[5] = 9The total profit is ((8 - 1) - 2) + ((9 - 4) - 2) = 8.

0 < prices.length <= 50000.
0 < prices[i] < 50000.
0 <= fee < 50000.

class Solution:
    def maxProfit(self, prices: List[int], fee: int) -> int:
        sell = 0
        buy = -0x7777777
        for price in prices:
            # Not buy or pay current price and fee
            buy = max(buy, sell - price - fee)
            # Not sell or get current price
            sell = max(sell, buy + price)
        return sell

Reverse Pairs

Given an array nums, we call (i, j) an important reverse pair if i < j and nums[i] > 2*nums[j].

You need to return the number of important reverse pairs in the given array.


Input: [1,3,2,3,1]
Output: 2


Input: [2,4,3,5,1]
Output: 3


  1. The length of the given array will not exceed 50,000.
  2. All the numbers in the input array are in the range of 32-bit integer.
# Solution 1: Using Binary Index Tree, which has O(nlogn) time complexity.

class BIT():
    def __init__(self, n):
        self.n = n + 1
        self.sums = [0] * self.n

    def update(self, i, delta):
        while i < self.n:
            self.sums[i] += delta
            i += i & (-i)

    def query(self, i):
        res = 0
        while i > 0:
            res += self.sums[i]
            i -= i & (-i)
        return res
class Solution:
    def reversePairs(self, nums: List[int]) -> int:
        sorted_nums = sorted(list(set(nums + [x * 2 for x in nums])))
        tree = BIT(len(sorted_nums))

        res = 0
        ranks = {}

        for i, n in enumerate(sorted_nums):
            ranks[n] = i + 1

        for n in nums[::-1]:
            res += tree.query(ranks[n] - 1)
            tree.update(ranks[n * 2], 1)

        return res
# Solution 2: At this time, we are going to use bisect. Got inspiration from Merge Sort (Divide and Conquer).

class Solution:
    def reversePairs(self, nums: List[int]) -> int:
        ranks = list()
        ans = 0

        for n in reverse(nums):
            ans += bisect.bisect_left(ranks, n)
            bisect.insort_left(ranks, n * 2)

        return ans

Largest Rectangle in Histogram

Given n non-negative integers representing the histogram’s bar height where the width of each bar is 1, find the area of largest rectangle in the histogram.

Above is a histogram where width of each bar is 1, given height = [2,1,5,6,2,3].

The largest rectangle is shown in the shaded area, which has area = 10 unit.


Input: [2,1,5,6,2,3]
Output: 10

Actually, I have met this problem on the online assessment of Amazon a few days ago.


class Solution:
    def largestRectangleArea(self, heights: List[int]) -> int:
        stack = [-1]
        ans = 0
        for i in range(len(heights)):
            while heights[i] < heights[stack[-1]]:
                h = heights[stack.pop()]
                w = i - stack[-1] - 1
                ans = max(ans, h * w)

        return ans

Is Graph Bipartite?

Given an undirected graph, return true if and only if it is bipartite.

Recall that a graph is bipartite if we can split it’s set of nodes into two independent subsets A and B such that every edge in the graph has one node in A and another node in B.

The graph is given in the following form: graph[i] is a list of indexes j for which the edge between nodes i and j exists.  Each node is an integer between 0 and graph.length - 1.  There are no self edges or parallel edges: graph[i] does not contain i, and it doesn’t contain any element twice.

Example 1:
Input: [[1,3], [0,2], [1,3], [0,2]]
Output: true
The graph looks like this:
|    |
|    |
We can divide the vertices into two groups: {0, 2} and {1, 3}.
Example 2:
Input: [[1,2,3], [0,2], [0,1,3], [0,2]]
Output: false
The graph looks like this:
| \  |
|  \ |
We cannot find a way to divide the set of nodes into two independent subsets.


  • graph will have length in range [1, 100].
  • graph[i] will contain integers in range [0, graph.length - 1].
  • graph[i] will not contain i or duplicate values.
  • The graph is undirected: if any element j is in graph[i], then i will be in graph[j].
class Solution:
    def isBipartite(self, graph: List[List[int]]) -> bool:
        color = collections.defaultdict(lambda: -1)
        def dfs(v, cur_color):
            if color[v] != -1: return color[v] == cur_color
            color[v] = cur_color
            return all(dfs(e, cur_color ^ 1) for e in graph[v])
        return all(dfs(v, 0) for v in range(len(graph)) if color[v] == -1)

Word Break

Given a non-empty string s and a dictionary wordDict containing a list of non-empty words, determine if s can be segmented into a space-separated sequence of one or more dictionary words.


  • The same word in the dictionary may be reused multiple times in the segmentation.
  • You may assume the dictionary does not contain duplicate words.

Example 1:

Input: s = "leetcode", wordDict = ["leet", "code"]
Output: true
Explanation: Return true because "leetcode" can be segmented as "leet code".

Example 2:

Input: s = "applepenapple", wordDict = ["apple", "pen"]
Output: true
Explanation: Return true because "applepenapple" can be segmented as "apple pen apple".
Note that you are allowed to reuse a dictionary word.

Example 3:

Input: s = "catsandog", wordDict = ["cats", "dog", "sand", "and", "cat"]
Output: false
# TLE solution
class Solution:
    def helper(self, s):
        if not s: return True
        return any(self.helper(s[len(word):]) for word in self.wordDict if s.startswith(word))
    def wordBreak(self, s: str, wordDict: List[str]) -> bool:
        self.wordDict = wordDict
        return self.helper(s)
# Basic DP
class Solution:
    def wordBreak(self, s: str, wordDict: List[str]) -> bool:
        dp = [False] * len(s)    
        for i in range(len(s)):
            for word in wordDict:
                if s[:i+1].endswith(word) and (dp[i-len(word)] or i-len(word) == -1):
                    dp[i] = True
        return dp[-1]
# Advanced DP
class Solution:
    def wordBreak(self, s: str, wordDict: List[str]) -> bool:
        dp = [True]
        for i in range(1, len(s)+1):
            dp += any(dp[j] and s[j:i] in wordDict for j in range(i)),
        return dp[-1]

Increasing Triplet Subsequence

Given an unsorted array return whether an increasing subsequence of length 3 exists or not in the array.

Formally the function should:

Return true if there exists i, j, k
such that arr[i] < arr[j] < arr[k] given 0 ≤ i < j < k ≤ n-1 else return false.

Note: Your algorithm should run in O(n) time complexity and O(1) space complexity.

Example 1:

Input: [1,2,3,4,5]
Output: true

Example 2:

Input: [5,4,3,2,1]
Output: false

History is always recurrent.

At the very first, I thought it is a typical dp question, and then I wrote a classical dp solution, and then I got a TLE…

This AC solution I actually checked it out from discuss board, that is really smart.

class Solution:
    def increasingTriplet(self, nums: List[int]) -> bool:
        N = len(nums)
        first = float("inf")
        second = float("inf")

        for i in range(N):
            if nums[i] < first:
                first = nums[i]
            elif first < nums[i] < second:
                second = nums[i]
            if nums[i] > second:
                return True

        return False