Number of Ways to Earn Points

arraydynamic programming

Problem Statement

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 types[i] = [count _i , marks _i ] indicates that there are count _i questions of the i ^th type, and each one of them is worth marks _i 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 10 ^9 + 7 .

Note that questions of the same type are indistinguishable.

For example, if there are 3 questions of the same type, then solving the 1 ^st and 2 ^nd questions is the same as solving the 1 ^st and 3 ^rd questions, or the 2 ^nd and 3 ^rd questions.

Examples

Example 1

Input: target = 6, types = [[6,1],[3,2],[2,3]]
Output: 7
You can earn 6 points in one of the seven ways:
- Solve 6 questions of the 0 ^th type: 1 + 1 + 1 + 1 + 1 + 1 = 6
- Solve 4 questions of the 0 ^th type and 1 question of the 1 ^st type: 1 + 1 + 1 + 1 + 2 = 6
- Solve 2 questions of the 0 ^th type and 2 questions of the 1 ^st type: 1 + 1 + 2 + 2 = 6
- Solve 3 questions of the 0 ^th type and 1 question of the 2 ^nd type: 1 + 1 + 1 + 3 = 6
- Solve 1 question of the 0 ^th type, 1 question of the 1 ^st type and 1 question of the 2 ^nd type: 1 + 2 + 3 = 6
- Solve 3 questions of the 1 ^st type: 2 + 2 + 2 = 6
- Solve 2 questions of the 2 ^nd type: 3 + 3 = 6

Example 2

Input: target = 5, types = [[50,1],[50,2],[50,5]]
Output: 4
You can earn 5 points in one of the four ways:
- Solve 5 questions of the 0 ^th type: 1 + 1 + 1 + 1 + 1 = 5
- Solve 3 questions of the 0 ^th type and 1 question of the 1 ^st type: 1 + 1 + 1 + 2 = 5
- Solve 1 questions of the 0 ^th type and 2 questions of the 1 ^st type: 1 + 2 + 2 = 5
- Solve 1 question of the 2 ^nd type: 5

Example 3

Input: target = 18, types = [[6,1],[3,2],[2,3]]
Output: 1
You can only earn 18 points by answering all questions.

Constraints

1 <= target <= 1000

n == types.length

1 <= n <= 50

types[i].length == 2

1 <= count _i , marks _i <= 50

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming