Consider a game where a player can score 3 or 5 or 10 points in a move. Given a total score n, find number of ways to reach the given score.
Input: n = 20 Output: 4 There are following 4 ways to reach 20 (10, 10) (5, 5, 10) (5, 5, 5, 5) (3, 3, 3, 3, 3, 5) Input: n = 13 Output: 2 There are following 2 ways to reach 13 (3, 5, 5) (3, 10)
This problem is a variation of coin change problem and can be solved in O(n) time and O(n) auxiliary space.
The idea is to create a table of size n+1 to store counts of all scores from 0 to n. For every possible move (3, 5 and 10), increment values in table.
Count for 20 is 4 Count for 13 is 2
Exercise: How to count score when (10, 5, 5), (5, 5, 10) and (5, 10, 5) are considered as different sequences of moves. Similarly, (5, 3, 3), (3, 5, 3) and (3, 3, 5) are considered different.
This article is contributed by Rajeev Arora. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
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