62. Unique Paths

Given the two integers m and n, return the number of possible unique paths that the robot can take to go from top left to the bottom-right.

Example

Input: m = 3, n = 7   Output: 28

Note: The most beautiful DP problem.
Initializing with 1, avoids additional loops and
it's ok because we overwrite the elements anyway.

There is also a math approach (m-1 + n-1)! / (m-1)! (n-1)!


def uniquePaths(self, m: int, n: int):
       
    dp = [[1]*n for _ in range(m)]
           
    for r in range(1, m):
        for c in range(1, n):
            dp[r][c] = dp[r-1][c] + dp[r][c-1]
           
    return dp[m-1][n-1]

Comments

Post a Comment

Popular posts from this blog

849. Maximize Distance to Closest Person

You are given an array representing a row of  seats  where  seats[i] = 1  represents a person sitting in the  i th  seat, and  seats[i] = 0  represents that the  i th  seat is empty  (0-indexed) . There is at least one empty seat, and at least one person sitting. Alex wants to sit in the seat such that the distance between him and the closest person to him is maximized.  Return  that maximum distance to the closest person . def maxDistToClosest ( self , seats : List [ int ]):                     taken = []         for i , occupied in enumerate ( seats ):         if occupied :             taken . append ( i )         S = len ( seats )     T = len ( taken )                 maxDist = max ( taken [ 0 ], S - taken [- 1 ] - 1 ) ...
Read more

347. Top K Frequent Elements

Given an integer array  nums  and an integer  k , return  the   k   most frequent elements . You may return the answer in  any order .   Example: Input: nums = [1,1,1,2,2,3], k = 2 Output: [1,2] def topKFrequent ( self , nums : List [ int ], k : int ):             freq = Counter ( nums )         return heapq . nlargest ( k , freq . keys (), key = freq . get )    
Read more

139. Word Break

Given a string  s  and a dictionary of strings  wordDict , return  true  if  s  can be segmented into a space-separated sequence of one or more dictionary words. Note  that the same word in the dictionary may be reused multiple times in the segmentation.   Example: Input: s = "leetcode", wordDict = ["leet","code"] Output: true Explanation: Return true because "leetcode" can be segmented as "leet code".   def wordBreak ( s : str , wordDict : List [ str ]):             word_set = set ( wordDict )     dp = [ False ] * ( len ( s ) + 1 )     dp [ 0 ] = True     for i in range ( 1 , len ( s ) + 1 ):         for j in range ( i ):             if dp [ j ] and s [ j : i ] in word_set :                 dp [ i ] = True                 break   ...
Read more