This is a premium problem. We're working on making it available for free soon.
Explore Free ProblemsUse these hints if you're stuck. Try solving on your own first.
Consider using dynamic programming.
Define <code>dp[i][x]</code> as the number of ways to make the sum <code>x</code> using only the first <code>i</code> coins; and define <code>coin[i]</code> as the value of coin <code>i</code>.
We can calculate <code>dp[i][x]</code> as the sum of <code>dp[i - 1][x]</code> and <code>dp[i][x - coin[i]]</code>.
Remember that 4 can at most be multiplied twice, so we calculate the <code>dp</code> for our infinite coins and then manually handle the existence of 4.
Solutions for this premium problem will be available for free soon.
Browse Free ProblemsWatch expert explanations and walkthroughs
Jot down your thoughts, approach, and key learnings
Dynamic programming helps avoid recomputing the same subproblems repeatedly. By storing results for smaller sums, the algorithm can build solutions for larger sums efficiently while keeping time complexity manageable.
Yes, variations of this problem are commonly asked in technical interviews, especially those focusing on dynamic programming. It is closely related to the classic coin change and combination counting problems.
A one-dimensional array is typically the best data structure for this problem. The array stores the number of ways to form each sum from 0 to the target, enabling efficient updates during iteration.
The optimal approach uses dynamic programming to count the number of ways to form each intermediate sum. A DP array stores the number of combinations for every value up to the target, allowing previously solved subproblems to be reused efficiently.