Problem
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Perfect Squares
Certification: Advanced Level
Accuracy: 0%
Submissions: 0
Points: 15
Write a C# program to implement the NumSquares(int n) function that calculates the least number of perfect square numbers that sum to n. A perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 1, 4, 9, and 16 are perfect squares while 3 and 11 are not.
Example 1
- Input: n = 12
- Output: 3
- Explanation:
- Step 1: Identify all perfect squares less than or equal to n (1, 4, 9).
- Step 2: Find the minimum number of these perfect squares needed to sum to n.
- 12 = 4 + 4 + 4 (three perfect squares)
- Step 3: Return the minimum count, which is 3.
Example 2
- Input: n = 13
- Output: 2
- Explanation:
- Step 1: Identify all perfect squares less than or equal to n (1, 4, 9).
- Step 2: Find the minimum number of these perfect squares needed to sum to n.
- 13 = 4 + 9 (two perfect squares)
- Step 3: Return the minimum count, which is 2.
Constraints
- 1 ≤ n ≤ 10^4
- Time Complexity: O(n * sqrt(n)) where n is the input integer
- Space Complexity: O(n) for the dynamic programming array
- Your solution should work efficiently for all valid inputs
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Solution Hints
- Consider this as a shortest path problem and use BFS to solve it
- Alternatively, use dynamic programming to build up the solution
- For each number from 1 to n, find the minimum number of perfect squares needed
- Use previously calculated results to compute the current number
- Consider all possible perfect squares less than or equal to the current number