Package g3001_3100.s3082_find_the_sum_of_the_power_of_all_subsequences

Class Solution

java.lang.Object

g3001_3100.s3082_find_the_sum_of_the_power_of_all_subsequences.Solution

public class Solution
extends java.lang.Object

3082 - Find the Sum of the Power of All Subsequences.

Hard

You are given an integer array nums of length n and a positive integer k.

The power of an array of integers is defined as the number of subsequences with their sum equal to k.

Return the sum of power of all subsequences of nums.

Since the answer may be very large, return it modulo 109 + 7.

Example 1:

Input: nums = [1,2,3], k = 3

Output: 6

Explanation:

There are 5 subsequences of nums with non-zero power:

• The subsequence [ 1 , 2 , 3 ] has 2 subsequences with sum == 3: [1,2,3] and [1,2,3].
• The subsequence [ 1 ,2, 3 ] has 1 subsequence with sum == 3: [1,2,3].
• The subsequence [1, 2 , 3 ] has 1 subsequence with sum == 3: [1,2,3].
• The subsequence [ 1 , 2 ,3] has 1 subsequence with sum == 3: [1,2,3].
• The subsequence [1,2, 3 ] has 1 subsequence with sum == 3: [1,2,3].

Hence the answer is 2 + 1 + 1 + 1 + 1 = 6.

Example 2:

Input: nums = [2,3,3], k = 5

Output: 4

Explanation:

There are 3 subsequences of nums with non-zero power:

• The subsequence [ 2 , 3 , 3 ] has 2 subsequences with sum == 5: [2,3,3] and [2,3,3].
• The subsequence [ 2 ,3, 3 ] has 1 subsequence with sum == 5: [2,3,3].
• The subsequence [ 2 , 3 ,3] has 1 subsequence with sum == 5: [2,3,3].

Hence the answer is 2 + 1 + 1 = 4.

Example 3:

Input: nums = [1,2,3], k = 7

Output: 0

**Explanation: **There exists no subsequence with sum 7. Hence all subsequences of nums have power = 0.

Constraints:

• 1 <= n <= 100
• 1 <= nums[i] <= 104
• 1 <= k <= 100

Constructor Summary

Constructors

Constructor	Description
Solution()

Method Summary

Modifier and Type	Method	Description
int	sumOfPower(int[] nums, int k)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

Solution

public Solution()

Method Details

sumOfPower

public int sumOfPower(int[] nums,
 int k)