[DP] add Solution to Perfect Squares

Author: Yi Gu

DP/PerfectSquares.swift

@@ -0,0 +1,28 @@
+/**
+ * Question Link: https://leetcode.com/problems/perfect-squares/
+ * Primary idea: Dynamic Programming, transition function is 
+ *               nums[i] = min(nums[i], nums[i - j * j] + 1)
+ * Time Complexity: O(n^2), Space Complexity: O(n)
+ */
+
+class PerfectSquares {
+    func numSquares(n: Int) -> Int {
+        guard n > 0 else {
+            return 0
+        }
+        
+        var leastNums = [Int](count: n + 1, repeatedValue: Int.max)
+        leastNums[0] = 0
+        
+        for i in 1 ... n {
+            for j in 1 ... i  {
+                if j * j > i {
+                    break
+                }
+                leastNums[i] = min(leastNums[i], leastNums[i - j * j] + 1)
+            }
+        }
+        
+        return leastNums[n]
+    }
+}