279. Perfect Squares

题目：

Given a positive integer n, find the least number of perfect square numbers (for example,

1, 4, 9, 16, ...

) which sum to n.

For example, given n =

12

, return

3

because

12 = 4 + 4 + 4

; given n =

13

, return

2

because

13 = 4 + 9

.

链接： http://leetcode.com/problems/perfect-squares/

题解：

又是数学题，每次一看jianchao.li.fighter添加的题目，就知道跟数字有关系。数学不好的我，做起来真的很头大....这道题看了discuss以后发现有好多种方法，有dp, BFS，还有纯数学解法。下面是最简单的dp，核心的递推公式是对于j= 1 , j * j <= i来说， tmp = Math.min(tmp, tmp[i - j * j] + 1);

Time Complexity - O(nlogn)， Space Complexity - O(n)

public class Solution {
public int numSquares(int n) {
if(n < 1) {
return 0;
}
int[] min = new int[n + 1];

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

return min
;
}
}

题外话：

最近似乎丧失了独立思考的能力，每次做题想了5分钟就不耐烦去看Discuss的答案了。这样可不行，需要锻炼的不是记题背题，而是自己的思维。真是懒惰到家了。

Reference:
https://leetcode.com/discuss/58056/summary-of-different-solutions-bfs-static-and-mathematics https://leetcode.com/discuss/56982/o-sqrt-n-in-ruby-c-c https://leetcode.com/discuss/62526/an-easy-understanding-dp-solution-in-java https://leetcode.com/discuss/56983/simple-java-dp-solution https://leetcode.com/discuss/57021/simple-java-solution https://leetcode.com/discuss/57850/explanation-of-the-dp-solution https://leetcode.com/discuss/68295/beautiful-9-lines-java-solution https://leetcode.com/discuss/57020/java-solution-o-n-1-2-time-and-o-1-space https://leetcode.com/discuss/57477/sqrt-applying-fermats-theorm-brahmagupta-fibonacci-identity https://leetcode.com/discuss/63750/concise-java-dp-solution https://en.wikipedia.org/wiki/Fermat%27s_theorem_on_sums_of_two_squares