279. Perfect Squares

Medium (Trung bình) C++ 🔗 Xem trên LeetCode

📋 Đề Bài

Given an integer n, return 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: 12 = 4 + 4 + 4.

Example 2:

Input: n = 13
Output: 2
Explanation: 13 = 4 + 9.

 

Constraints:

  • 1 <= n <= 104

🧠 Thuật Toán & Kỹ Thuật

Dynamic Programming (Quy hoạch động)
⏱️ Thời gian O(n²)
💾 Không gian O(n)

💻 Lời Giải

C++ 0279-perfect-squares.cpp 
class Solution {
public:
    int numSquares(int n) {
        vector<int> dp(n + 1, INT_MAX);
        dp[0] = 0;
        int per = sqrt(n);
        for (int i = 1; i <= per; ++i) {
            for (int j = i * i; j <= n; ++j) {
                dp[j] = min(dp[j], dp[j - i * i] + 1);
            }
        }
        return dp[n];
    }
};