279.perfect-squares

Author: luzhipeng

279.perfect-squares.js

@@ -0,0 +1,104 @@
+## 题目地址
+https://leetcode.com/problems/perfect-squares/description/
+
+## 题目描述
+
+
+```
+Given a positive integer n, find the least number of perfect square numbers (for example, 1, 4, 9, 16, ...) which sum to n.
+
+Example 1:
+
+Input: n = 12
+Output: 3 
+Explanation: 12 = 4 + 4 + 4.
+Example 2:
+
+Input: n = 13
+Output: 2
+Explanation: 13 = 4 + 9.
+
+```
+
+## 思路
+
+直接递归处理即可，但是这种暴力的解法很容易超时。如果你把递归的过程化成一棵树的话（其实就是递归树），
+可以看出中间有很多重复的计算。 
+
+如果能将重复的计算缓存下来，说不定能够解决时间复杂度太高的问题。
+
+> 递归对内存的要求也很高， 如果数字非常大，也会面临爆栈的风险，将递归转化为循环可以解决。
+
+如果使用DP，其实本质上和递归 + 缓存 差不多。
+
+## 关键点解析
+
+- 如果用递归 + 缓存， 缓存的设计很重要
+我的做法是key就是n，value是以n为起点，到达底端的深度。
+下次取出缓存的时候用当前的level + 存的深度 就是我们想要的level.
+
+## 代码
+
+```js
+/*
+ * @lc app=leetcode id=279 lang=javascript
+ *
+ * [279] Perfect Squares
+ *
+ * https://leetcode.com/problems/perfect-squares/description/
+ *
+ * algorithms
+ * Medium (40.98%)
+ * Total Accepted:    168.2K
+ * Total Submissions: 408.5K
+ * Testcase Example:  '12'
+ *
+ * Given a positive integer n, find the least number of perfect square numbers
+ * (for example, 1, 4, 9, 16, ...) which sum to n.
+ *
+ * Example 1:
+ *
+ *
+ * Input: n = 12
+ * Output: 3
+ * Explanation: 12 = 4 + 4 + 4.
+ *
+ * Example 2:
+ *
+ *
+ * Input: n = 13
+ * Output: 2
+ * Explanation: 13 = 4 + 9.
+ */
+
+const mapper = {};
+
+function d(n, level) {
+
+  if (n  === 0) return level;
+
+  let i = 1;
+  const arr = [];
+
+  while(n - i * i >= 0) {
+    const hit = mapper[n - i * i];
+    if (hit) {
+      arr.push(hit + level);
+    } else {
+      const depth = d(n - i * i, level + 1) - level;
+      mapper[n - i * i] = depth;
+      arr.push(depth + level);
+    }
+    i++;
+  }
+
+  return Math.min(...arr);
+}
+/**
+ * @param {number} n
+ * @return {number}
+ */
+var numSquares = function(n) {
+  return d(n, 0);
+};
+```

279.perfect-squares.md

@@ -30,6 +30,7 @@ leetcode题解，记录自己的leecode解题之路。
 - [328.odd-even-linked-list](./328.odd-even-linked-list.md)
 - [445.add-two-numbers-ii](./445.add-two-numbers-ii.md)
 - [877.stone-game](./877.stone-game.md)
+- [279.perfect-squares](./279.perfect-squares.md)
 
 ### 困难难度
 - [145.binary-tree-postorder-traversal](./145.binary-tree-postorder-traversal.md)