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 distinct combinations to reach the given score.Example 1:Inputn = 10Output2ExplanationThere are two ways {5,5} and {10}.
Question
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 distinct combinations to reach the given score.Example 1:Inputn = 10Output2ExplanationThere are two ways {5,5} and {10}.
Solution
Sure, I can help with that. This problem can be solved using dynamic programming. Here are the steps:
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Initialize an array dp of size n+1 with all elements as 0. This array will be used to store the number of combinations for all scores from 0 to n. Set dp[0] = 1 because there is exactly one way to score zero points (which is not to score at all).
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For each of the scores, 3, 5, and 10, do the following:
- For every i from score to n, increment dp[i] by dp[i-score]. This is because the number of ways to get to i (dp[i]) is increased by the number of ways to get to (i-score).
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Finally, dp[n] will hold the number of ways to score n points.
Here is a Python code snippet that implements the above steps:
def count_combinations(n):
dp = [0 for i in range(n+1)]
dp[0] = 1
for score in [3, 5, 10]:
for i in range(score, n+1):
dp[i] += dp[i-score]
return dp[n]
For example, if n = 10, the function count_combinations(10) will return 2, which means there are two ways to score 10 points: {5, 5} and {10}.
Similar Questions
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