Problem
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 <= 10^4
Solution (Java)
class Solution {
private boolean validSquare(int n) {
int root = (int) Math.sqrt(n);
return root * root == n;
}
public int numSquares(int n) {
if (n < 4) {
return n;
}
if (validSquare(n)) {
return 1;
}
while ((n & 3) == 0) {
n >>= 2;
}
if ((n & 7) == 7) {
return 4;
}
int x = (int) Math.sqrt(n);
for (int i = 1; i <= x; i++) {
if (validSquare(n - i * i)) {
return 2;
}
}
return 3;
}
}
Solution (Javascript)
/**
* @param {number} n
* @return {number}
*/
var numSquares = function(n) {
// Important: n + 1 length because we use dp[0]
let dp = new Array(n + 1).fill(Number.MAX_VALUE);
dp[0] = 0;
for (let i = 1; i <= n; i++)
for(let j = 1; j * j <= i; j++)
dp[i] = Math.min(dp[i], dp[i - j * j] + 1);
return dp[n];
};
Explain:
nope.
Complexity:
- Time complexity : O(n).
- Space complexity : O(n).