Package g2501_2600.s2585_number_of_ways_to_earn_points

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    2585 - Number of Ways to Earn Points.

    Hard

    There is a test that has n types of questions. You are given an integer target and a 0-indexed 2D integer array types where <code>typesi = count<sub>i</sub>, marks<sub>i</sub></code> indicates that there are <code>count<sub>i</sub></code> questions of the <code>i<sup>th</sup></code> type, and each one of them is worth <code>marks<sub>i</sub></code> points.

    Return the number of ways you can earn exactly target points in the exam. Since the answer may be too large, return it modulo <code>10<sup>9</sup> + 7</code>.

    Note that questions of the same type are indistinguishable.

    • For example, if there are 3 questions of the same type, then solving the <code>1<sup>st</sup></code> and <code>2<sup>nd</sup></code> questions is the same as solving the <code>1<sup>st</sup></code> and <code>3<sup>rd</sup></code> questions, or the <code>2<sup>nd</sup></code> and <code>3<sup>rd</sup></code> questions.

    Example 1:

    Input: target = 6, types = [6,1,3,2,2,3]

    Output: 7

    Explanation: You can earn 6 points in one of the seven ways:

    • Solve 6 questions of the 0<sup>th</sup> type: 1 + 1 + 1 + 1 + 1 + 1 = 6

    • Solve 4 questions of the 0<sup>th</sup> type and 1 question of the 1<sup>st</sup> type: 1 + 1 + 1 + 1 + 2 = 6

    • Solve 2 questions of the 0<sup>th</sup> type and 2 questions of the 1<sup>st</sup> type: 1 + 1 + 2 + 2 = 6

    • Solve 3 questions of the 0<sup>th</sup> type and 1 question of the 2<sup>nd</sup> type: 1 + 1 + 1 + 3 = 6

    • Solve 1 question of the 0<sup>th</sup> type, 1 question of the 1<sup>st</sup> type and 1 question of the 2<sup>nd</sup> type: 1 + 2 + 3 = 6

    • Solve 3 questions of the 1<sup>st</sup> type: 2 + 2 + 2 = 6 - Solve 2 questions of the 2<sup>nd</sup> type: 3 + 3 = 6

    Example 2:

    Input: target = 5, types = [50,1,50,2,50,5]

    Output: 4

    Explanation: You can earn 5 points in one of the four ways:

    • Solve 5 questions of the 0<sup>th</sup> type: 1 + 1 + 1 + 1 + 1 = 5

    • Solve 3 questions of the 0<sup>th</sup> type and 1 question of the 1<sup>st</sup> type: 1 + 1 + 1 + 2 = 5

    • Solve 1 questions of the 0<sup>th</sup> type and 2 questions of the 1<sup>st</sup> type: 1 + 2 + 2 = 5

    • Solve 1 question of the 2<sup>nd</sup> type: 5

    Example 3:

    Input: target = 18, types = [6,1,3,2,2,3]

    Output: 1

    Explanation: You can only earn 18 points by answering all questions.

    Constraints:

    • 1 &lt;= target &lt;= 1000

    • n == types.length

    • 1 &lt;= n &lt;= 50

    • types[i].length == 2

    • <code>1 <= count<sub>i</sub>, marks<sub>i</sub><= 50</code>

    • 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 waysToReachTarget(Integer target, Array<IntArray> types)

      • Methods inherited from class java.lang.Object

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