You need to find the minimum number of perfect square numbers that sum to a given integer n. Which algorithmic approach guarantees an optimal solution for this problem?
easy🔍 Pattern Recognition Q11 of Q15
Dynamic Programming: Knapsack - Perfect Squares
You need to find the minimum number of perfect square numbers that sum to a given integer n. Which algorithmic approach guarantees an optimal solution for this problem?
ADynamic programming using unbounded knapsack pattern with bottom-up tabulation
BGreedy approach picking the largest square first until the sum is reached
CSimple recursion without memoization exploring all combinations
DSorting all squares and using binary search to find the closest sum
Step-by-Step Solution
Solution:
Step 1: Understand problem constraints
The problem requires the minimum count of perfect squares summing to n, which is a classic unbounded knapsack variant where items (squares) can be reused.
Step 2: Identify algorithm that guarantees optimality
Greedy fails because picking largest squares first can be suboptimal (e.g., n=12). Simple recursion is correct but inefficient. Binary search does not solve the combinatorial optimization. Bottom-up DP with unbounded knapsack pattern systematically explores all combinations and ensures optimality.
