Number of Ways to Wear Different Hats to Each Other

arraydynamic programmingbit manipulation

Problem Statement

There are n people and 40 types of hats labeled from 1 to 40 .

Given a 2D integer array hats , where hats[i] is a list of all hats preferred by the i ^th person.

Return the number of ways that n people can wear different hats from each other.

Since the answer may be too large, return it modulo 10 ^9 + 7 .

Examples

Example 1

Input: hats = [[3,4],[4,5],[5]]
Output: 1
There is only one way to choose hats given the conditions. 
First person chooses hat 3, Second person chooses hat 4 and last one hat 5.

Example 2

Input: hats = [[3,5,1],[3,5]]
Output: 4
There are 4 ways to choose hats:
(3,5), (5,3), (1,3) and (1,5)

Example 3

Input: hats = [[1,2,3,4],[1,2,3,4],[1,2,3,4],[1,2,3,4]]
Output: 24
Each person can choose hats labeled from 1 to 4.
Number of Permutations of (1,2,3,4) = 24.

Constraints

n == hats.length

1 <= n <= 10

1 <= hats[i].length <= 40

1 <= hats[i][j] <= 40

hats[i] contains a list of unique integers.

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming