dp[i] = min( min_prev, dp[ i - j*j ] + 1 );
j starts from 1, 2, 3...
update every iteration j++.

public class Solution {
    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++) {
            int min_cnt = Integer.MAX_VALUE;
            int j=1;
            while(i - j*j >= 0) {
                min_cnt = Math.min(min_cnt, dp[i-j*j]+1);
                j++;
            }
            dp[i] = min_cnt;
        }
        return dp[n];
    }
}