279 Perfect Squares

Problem:

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.

Solutions:

``````public class Solution {
private HashMap<Integer, Integer> data = new HashMap<Integer, Integer>();;
public int numSquares(int n) {
if (data.containsKey(n)) {
return data.get(n);
}
int up = (int)(Math.sqrt(n));
if (up * up == n) {
data.put(n, 1);
return 1;
}
int min = Integer.MAX_VALUE;
for (int i = up; i > 0; i --) {
int tmp = 1 + numSquares(n - i * i);
min = Math.min(min, tmp);
}
data.put(n, min);
return min;

}
}
``````
``````public class Solution {
public int numSquares(int n) {
int[] nums = new int[n + 1];
for (int i = 1; i < n + 1; i ++) {
nums[i] = Integer.MAX_VALUE;
}
int up = (int) Math.sqrt(n);
for (int i = 1; i < n + 1; i ++) {
for (int j = 1; j <= up && j * j <= i; j ++) {
if (j * j == i) {
nums[i] = 1;
}
else {
nums[i] = Math.min(nums[i], nums[i - j * j] + 1);
}
}
}
return nums[n];
}
}
``````