[LeetCode] Problem 279 - Perfect Squares

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Given a positive integer n, find the least number of perfect square numbers (for example, 1, 4, 9, 16, …) which sum to n.

Example

No.1

Input: n = 12

Output: 3

Explanation: 12 = 4 + 4 + 4.

No.2

Input: n = 13

Output: 2

Explanation: 13 = 4 + 9.

Code

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// dp[n] = min{dp[n-i*i] + 1}, n-i*i >= 0, i >= 1
public int numSquares(int n) {
    int[] dp = new int[n + 1];
    Arrays.fill(dp, Integer.MAX_VALUE);
    dp[0] = 0;

    for (int i = 1; i <= n; i++) {
        for (int j = 1; j * j <= i; j++)
            dp[i] = Math.min(dp[i], dp[i - j * j] + 1);
    }

    return dp[n];
}