# 279. Perfect Squares

### Description

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.

### Constraints

* `1 <= n <= 104`

### Approach

### Links

* Binarysearch
* GeeksforGeeks
* [Leetcode](https://leetcode.com/problems/perfect-squares/)
* ProgramCreek
* YouTube

### **Examples**

{% tabs %}
{% tab title="Example 1" %}
**Input:** n = 12

**Output:** 3

**Explanation:** 12 = 4 + 4 + 4.
{% endtab %}

{% tab title="Example 2" %}
**Input:** n = 13

**Output:** 2

**Explanation:** 13 = 4 + 9.
{% endtab %}
{% endtabs %}

### **Solutions**

{% tabs %}
{% tab title="Solution 1" %}

```java
/**
 * Time complexity : 
 * Space complexity : 
 */

class Solution {
    public int numSquares(int n) {
        if(n < 1) {
            return 0;
        }
        
        int noOfSquares = (int)Math.sqrt(n) + 1;
        int[] squareNumbers = new int[noOfSquares];
        
        for(int i = 1; i < noOfSquares; i++) {
            squareNumbers[i] = i*i;
        }
        
        int[] dp = new int[n+1];
        Arrays.fill(dp, Integer.MAX_VALUE);
        dp[0] = 0;
        
        for(int i = 1; i <= n; i++) {
            for(int s = 1; s < noOfSquares; s++) {
                int squareNumber = squareNumbers[s];
                if(i < squareNumber) {
                    break;
                }
                dp[i] = Math.min(dp[i], dp[i-squareNumber]+1);
            }
        }
        
        return dp[n];
    }
}
```

{% endtab %}
{% endtabs %}

### **Follow up**

*