Package g3001_3100.s3082_find_the_sum_of_the_power_of_all_subsequences

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    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 <code>10<sup>9</sup> + 7</code>.

    Example 1:

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

    Output: 6

    Explanation:

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

    • The subsequence <code><ins> **1** </ins>,<ins> **2** </ins>,<ins> **3** </ins></code> has 2 subsequences with sum == 3: <code>1,2,<ins>3</ins></code> and <code><ins>1</ins>,<ins>2</ins>,3</code>.

    • The subsequence <code><ins> **1** </ins>,2,<ins> **3** </ins></code> has 1 subsequence with sum == 3: <code>1,2,<ins>3</ins></code>.

    • The subsequence <code>1,<ins> **2** </ins>,<ins> **3** </ins></code> has 1 subsequence with sum == 3: <code>1,2,<ins>3</ins></code>.

    • The subsequence <code><ins> **1** </ins>,<ins> **2** </ins>,3</code> has 1 subsequence with sum == 3: <code><ins>1</ins>,<ins>2</ins>,3</code>.

    • The subsequence <code>1,2,<ins> **3** </ins></code> has 1 subsequence with sum == 3: <code>1,2,<ins>3</ins></code>.

    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 <code><ins> **2** </ins>,<ins> **3** </ins>,<ins> **3** </ins></code> has 2 subsequences with sum == 5: <code><ins>2</ins>,3,<ins>3</ins></code> and <code><ins>2</ins>,<ins>3</ins>,3</code>.

    • The subsequence <code><ins> **2** </ins>,3,<ins> **3** </ins></code> has 1 subsequence with sum == 5: <code><ins>2</ins>,3,<ins>3</ins></code>.

    • The subsequence <code><ins> **2** </ins>,<ins> **3** </ins>,3</code> has 1 subsequence with sum == 5: <code><ins>2</ins>,<ins>3</ins>,3</code>.

    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 &lt;= n &lt;= 100

    • <code>1 <= numsi<= 10<sup>4</sup></code>

    • 1 &lt;= k &lt;= 100

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Integer sumOfPower(IntArray nums, Integer k)

      • Methods inherited from class java.lang.Object

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