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Posts tagged as “prefix”

花花酱 LeetCode 1442. Count Triplets That Can Form Two Arrays of Equal XOR

Given an array of integers arr.

We want to select three indices ij and k where (0 <= i < j <= k < arr.length).

Let’s define a and b as follows:

  • a = arr[i] ^ arr[i + 1] ^ ... ^ arr[j - 1]
  • b = arr[j] ^ arr[j + 1] ^ ... ^ arr[k]

Note that ^ denotes the bitwise-xor operation.

Return the number of triplets (ij and k) Where a == b.

Example 1:

Input: arr = [2,3,1,6,7]
Output: 4
Explanation: The triplets are (0,1,2), (0,2,2), (2,3,4) and (2,4,4)

Example 2:

Input: arr = [1,1,1,1,1]
Output: 10

Example 3:

Input: arr = [2,3]
Output: 0

Example 4:

Input: arr = [1,3,5,7,9]
Output: 3

Example 5:

Input: arr = [7,11,12,9,5,2,7,17,22]
Output: 8

Constraints:

  • 1 <= arr.length <= 300
  • 1 <= arr[i] <= 10^8

Solution 1: Brute Force (TLE)

Time complexity: O(n^4)
Space complexity: O(1)

C++

Solution 2: Prefix XORs

Let xors[i] = arr[0] ^ arr[1] ^ … ^ arr[i-1]
arr[i] ^ arr[i + 1] ^ … ^ arr[j – 1] = (arr[0] ^ … ^ arr[j – 1]) ^ (arr[0] ^ … ^ arr[i-1]) = xors[j] ^ xors[i]

We then can compute a and b in O(1) time.

Time complexity: O(n^3)
Space complexity: O(n)

C++

Solution 3: Prefix XORs II

a = arr[i] ^ arr[i + 1] ^ … ^ arr[j – 1]
b = arr[j] ^ arr[j + 1] ^ … ^ arr[k]
a == b => a ^ b == 0
XORs(i ~ k) == 0
XORS(0 ~ k) ^ XORs(0 ~ i – 1) = 0

Problem => find all pairs of (i – 1, k) such that xors[k+1] == xors[i]
For each pair (i – 1, k), there are k – i positions we can insert j.

Time complexity: O(n^2)
Space complexity: O(1)

C++

Solution 3: HashTable

Similar to target sum, use a hashtable to store the frequency of each prefix xors.

Time complexity: O(n)
Space complexity: O(n)

C++

KMP Algorithm SP19

KMP Algorithm, KMP 字符串搜索算法

Time complexity: O(m+n)
Space complexity: O(m)

Implementation

C++

Python3

Applications

LeetCode 28. strStr()

C++

LeetCode 459. Repeated Substring Pattern

C++

1392. Longest Happy Prefix

C++

花花酱 LeetCode 1395. Count Number of Teams

There are n soldiers standing in a line. Each soldier is assigned a unique rating value.

You have to form a team of 3 soldiers amongst them under the following rules:

  • Choose 3 soldiers with index (ijk) with rating (rating[i]rating[j]rating[k]).
  • A team is valid if:  (rating[i] < rating[j] < rating[k]) or (rating[i] > rating[j] > rating[k]) where (0 <= i < j < k < n).

Return the number of teams you can form given the conditions. (soldiers can be part of multiple teams).

Example 1:

Input: rating = [2,5,3,4,1]
Output: 3
Explanation: We can form three teams given the conditions. (2,3,4), (5,4,1), (5,3,1). 

Example 2:

Input: rating = [2,1,3]
Output: 0
Explanation: We can't form any team given the conditions.

Example 3:

Input: rating = [1,2,3,4]
Output: 4

Constraints:

  • n == rating.length
  • 1 <= n <= 200
  • 1 <= rating[i] <= 10^5

Solution 1: Brute Force

Time complexity: O(n^3)
Space complexity: O(1)

C++

Solution 2: Math

For each soldier j, count how many soldiers on his left has smaller ratings as left[j], count how many soldiers his right side has larger ratings as right[j]

ans = sum(left[j] * right[j] + (j – left[j]) * (n – j – 1 * right[j])

Time complexity: O(n^2)
Space complexity: O(1)

C++

花花酱 LeetCode 1352. Product of the Last K Numbers

Implement the class ProductOfNumbers that supports two methods:

1. add(int num)

  • Adds the number num to the back of the current list of numbers.

2. getProduct(int k)

  • Returns the product of the last k numbers in the current list.
  • You can assume that always the current list has at least k numbers.

At any time, the product of any contiguous sequence of numbers will fit into a single 32-bit integer without overflowing.

Example:

Input
["ProductOfNumbers","add","add","add","add","add","getProduct","getProduct","getProduct","add","getProduct"]
[[],[3],[0],[2],[5],[4],[2],[3],[4],[8],[2]]

Output: [null,null,null,null,null,null,20,40,0,null,32]
Explanation:
ProductOfNumbers productOfNumbers = new ProductOfNumbers();
productOfNumbers.add(3);        // [3] 
productOfNumbers.add(0);        // [3,0] 
productOfNumbers.add(2);        // [3,0,2]
productOfNumbers.add(5);        // [3,0,2,5]
productOfNumbers.add(4);        // [3,0,2,5,4]
productOfNumbers.getProduct(2); // return 20.
The product of the last 2 numbers is 5 * 4 = 20
productOfNumbers.getProduct(3); // return 40. The product of the last 3 numbers is 2 * 5 * 4 = 40 
productOfNumbers.getProduct(4); // return 0. The product of the last 4 numbers is 0 * 2 * 5 * 4 = 0
productOfNumbers.add(8);        // [3,0,2,5,4,8]
productOfNumbers.getProduct(2); // return 32. The product of the last 2 numbers is 4 * 8 = 32  

Constraints:

  • There will be at most 40000 operations considering both add and getProduct.
  • 0 <= num <= 100
  • 1 <= k <= 40000

Solution: Prefix product

Use p[i] to store the prod of a1*a2*…ai
p[i] = ai*p[i-1]
If ai is 0, reset p = [1].
Compare k with the len(p), if k is greater than len(p) which means there is 0 recently, return 0.
otherwise return p[n] / p[n – k – 1]

Time complexity: Add: O(1), getProduct: O(1)
Space complexity: O(n)

C++

花花酱 LeetCode 1268. Search Suggestions System

Given an array of strings products and a string searchWord. We want to design a system that suggests at most three product names from products after each character of searchWord is typed. Suggested products should have common prefix with the searchWord. If there are more than three products with a common prefix return the three lexicographically minimums products.

Return list of lists of the suggested products after each character of searchWord is typed. 

Example 1:

Input: products = ["mobile","mouse","moneypot","monitor","mousepad"], searchWord = "mouse"
Output: [
["mobile","moneypot","monitor"],
["mobile","moneypot","monitor"],
["mouse","mousepad"],
["mouse","mousepad"],
["mouse","mousepad"]
]
Explanation: products sorted lexicographically = ["mobile","moneypot","monitor","mouse","mousepad"]
After typing m and mo all products match and we show user ["mobile","moneypot","monitor"]
After typing mou, mous and mouse the system suggests ["mouse","mousepad"]

Example 2:

Input: products = ["havana"], searchWord = "havana"
Output: [["havana"],["havana"],["havana"],["havana"],["havana"],["havana"]]

Example 3:

Input: products = ["bags","baggage","banner","box","cloths"], searchWord = "bags"
Output: [["baggage","bags","banner"],["baggage","bags","banner"],["baggage","bags"],["bags"]]

Example 4:

Input: products = ["havana"], searchWord = "tatiana"
Output: [[],[],[],[],[],[],[]]

Constraints:

  • 1 <= products.length <= 1000
  • 1 <= Σ products[i].length <= 2 * 10^4
  • All characters of products[i] are lower-case English letters.
  • 1 <= searchWord.length <= 1000
  • All characters of searchWord are lower-case English letters.

Solution 1: Binary Search

Sort the input array and do two binary searches.
One for prefix of the search word as lower bound, another for prefix + ‘~’ as upper bound.
‘~’ > ‘z’

Time complexity: O(nlogn + l * logn)
Space complexity: O(1)

C++

Solution 2: Trie

Initialization: Sum(len(products[i]))
Query: O(len(searchWord))

C++