Compute distinct sums from limited coins
Problem Statement
You are provided with two integer arrays, denom and count, both of length n. denom[i] represents a coin denomination (where denom[i] > 0), and count[i] indicates the number of available coins of that denomination (where count[i] >= 0).
Your task is to return the total number of distinct positive sums that can be formed. When forming these sums, you can use at most count[i] coins of value denom[i]. Each coin of a given denomination is identical and can be used at most once within a specific sum.
Describe your algorithm, analyze its time and space complexity, and discuss how you would handle scenarios where the maximum reachable sum is large (e.g., up to 10^6).
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Core dilemma
Efficiently computing and storing all distinct reachable sums given limited quantities of each coin denomination, especially when the maximum possible sum is large.
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Compute distinct sums from limited coins
Problem Statement
You are provided with two integer arrays, denom and count, both of length n. denom[i] represents a coin denomination (where denom[i] > 0), and count[i] indicates the number of available coins of that denomination (where count[i] >= 0).
Your task is to return the total number of distinct positive sums that can be formed. When forming these sums, you can use at most count[i] coins of value denom[i]. Each coin of a given denomination is identical and can be used at most once within a specific sum.
Describe your algorithm, analyze its time and space complexity, and discuss how you would handle scenarios where the maximum reachable sum is large (e.g., up to 10^6).