Which algorithmic approach guarantees finding the optimal solution efficiently?
easy🔍 Pattern Recognition Q11 of Q15
Dynamic Programming: Knapsack - Integer Break
You need to split a positive integer n into at least two positive integers such that the product of these integers is maximized. Which algorithmic approach guarantees finding the optimal solution efficiently?
APure brute force recursion exploring all partitions without memoization
BA greedy approach that always cuts the integer into 3s and 2s
CDynamic programming using bottom-up tabulation with state representing maximum product for each integer up to n
DDivide and conquer by splitting the integer into two halves recursively without caching results
Step-by-Step Solution
Step 1: Understand problem structure
The problem requires maximizing product by splitting an integer into parts, which naturally fits a DP approach where subproblems represent maximum product for smaller integers.
Step 2: Evaluate options
Greedy (always cutting 3s) fails on some inputs; brute force recursion is correct but inefficient; divide and conquer without memoization repeats work. Bottom-up DP tabulation efficiently computes all subproblems and combines results.
Final Answer:
Option C -> Option C
Quick Check:
DP tabulation ensures optimal substructure and overlapping subproblems [OK]
