Count Number of Special Subsequences

arraydynamic programming

Problem Statement

A sequence is special if it consists of a positive number of 0 s, followed by a positive number of 1 s, then a positive number of 2 s.

For example, [0,1,2] and [0,0,1,1,1,2] are special.

In contrast, [2,1,0] , [1] , and [0,1,2,0] are not special.

Given an array nums (consisting of only integers 0 , 1 , and 2 ), return the number of different subsequences that are special . Since the answer may be very large, return it modulo 10 ^9 + 7 .

A subsequence of an array is a sequence that can be derived from the array by deleting some or no elements without changing the order of the remaining elements. Two subsequences are different if the set of indices chosen are different.

Examples

Example 1

Input: nums = [0,1,2,2]
Output: 3
The special subsequences are bolded [ 0 , 1 , 2 ,2], [ 0 , 1 ,2, 2 ], and [ 0 , 1 , 2 , 2 ].

Example 2

Input: nums = [2,2,0,0]
Output: 0
There are no special subsequences in [2,2,0,0].

Example 3

Input: nums = [0,1,2,0,1,2]
Output: 7
The special subsequences are bolded:
- [ 0 , 1 , 2 ,0,1,2]
- [ 0 , 1 ,2,0,1, 2 ]
- [ 0 , 1 , 2 ,0,1, 2 ]
- [ 0 , 1 ,2,0, 1 , 2 ]
- [ 0 ,1,2, 0 , 1 , 2 ]
- [ 0 ,1,2,0, 1 , 2 ]
- [0,1,2, 0 , 1 , 2 ]

Constraints

1 <= nums.length <= 10 ^5

0 <= nums[i] <= 2

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming