feat: azl397985856#62

README.md

@@ -98,7 +98,8 @@ leetcode 题解，记录自己的 leetcode 解题之路。
 - [11.container-with-most-water](./problems/11.container-with-most-water.md)
 - [19. Remove Nth Node From End of List](./problems/removeNthNodeFromEndofList.md)
 - [24. Swap Nodes In Pairs](./problems/swapNodesInPairs.md)
-- 🆕 [55.jump-game.md](./problems/55.jump-game.md.md)
+- 🆕 [55.jump-game.md](./problems/55.jump-game.md)
+- 🆕 [62.unique-paths](./problems/62.unique-paths.md)
 - [75.sort-colors.md](./problems/75.sort-colors.md)
 - [86.partition-list](./problems/86.partition-list.md)
 - [92.reverse-linked-list-ii](./problems/92.reverse-linked-list-ii.md)

assets/drawio/208.implement-trie-prefix-tree.drawio

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assets/drawio/62.unique-paths.drawio

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problems/62.unique-paths.md

@@ -0,0 +1,143 @@
+
+## 题目地址
+https://leetcode.com/problems/unique-paths/description/
+
+## 题目描述
+```
+
+A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).
+
+The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).
+
+How many possible unique paths are there?
+```
+![62.unique-paths-1](../assets/problems/62.unique-paths-1.png)
+
+```
+Above is a 7 x 3 grid. How many possible unique paths are there?
+
+Note: m and n will be at most 100.
+
+Example 1:
+
+Input: m = 3, n = 2
+Output: 3
+Explanation:
+From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
+1. Right -> Right -> Down
+2. Right -> Down -> Right
+3. Down -> Right -> Right
+Example 2:
+
+Input: m = 7, n = 3
+Output: 28
+```
+
+## 思路
+这是一道典型的适合使用动态规划解决的题目，它和爬楼梯等都属于动态规划中最简单的题目，
+因此也经常会被用于面试之中。
+
+读完题目你就能想到动态规划的话，建立模型并解决恐怕不是难事。其实我们很容易看出，由于机器人只能右移动和下移动，
+因此第[i, j]个格子的总数应该等于[i - 1, j] + [i, j -1]， 因为第[i,j]个格子一定是从左边或者上面移动过来的。
+
+![62.unique-paths-2](../assets/problems/62.unique-paths-2.png)
+
+代码大概是：
+
+```js
+ const dp = [];
+  for (let i = 0; i < m + 1; i++) {
+    dp[i] = [];
+    dp[i][0] = 0;
+  }
+  for (let i = 0; i < n + 1; i++) {
+    dp[0][i] = 0;
+  }
+  for (let i = 1; i < m + 1; i++) {
+    for(let j = 1; j < n + 1; j++) {
+        dp[i][j] = j === 1 ? 1 : dp[i - 1][j] + dp[i][j - 1]; // 转移方程
+    }
+  }
+
+  return dp[m][n];
+
+```
+
+由于dp[i][j] 只依赖于左边的元素和上面的元素，因此空间复杂度可以进一步优化， 优化到O(n).
+
+![62.unique-paths-3](../assets/problems/62.unique-paths-3.png)
+
+具体代码请查看代码区。
+
+## 关键点
+
+- 空间复杂度可以进一步优化到O(n), 这会是一个考点
+- 基本动态规划问题
+## 代码
+
+```js
+/*
+ * @lc app=leetcode id=62 lang=javascript
+ *
+ * [62] Unique Paths
+ *
+ * https://leetcode.com/problems/unique-paths/description/
+ *
+ * algorithms
+ * Medium (46.53%)
+ * Total Accepted:    277K
+ * Total Submissions: 587.7K
+ * Testcase Example:  '3\n2'
+ *
+ * A robot is located at the top-left corner of a m x n grid (marked 'Start' in
+ * the diagram below).
+ *
+ * The robot can only move either down or right at any point in time. The robot
+ * is trying to reach the bottom-right corner of the grid (marked 'Finish' in
+ * the diagram below).
+ *
+ * How many possible unique paths are there?
+ *
+ *
+ * Above is a 7 x 3 grid. How many possible unique paths are there?
+ *
+ * Note: m and n will be at most 100.
+ *
+ * Example 1:
+ *
+ *
+ * Input: m = 3, n = 2
+ * Output: 3
+ * Explanation:
+ * From the top-left corner, there are a total of 3 ways to reach the
+ * bottom-right corner:
+ * 1. Right -> Right -> Down
+ * 2. Right -> Down -> Right
+ * 3. Down -> Right -> Right
+ *
+ *
+ * Example 2:
+ *
+ *
+ * Input: m = 7, n = 3
+ * Output: 28
+ *
+ *   START
+ */
+/**
+ * @param {number} m
+ * @param {number} n
+ * @return {number}
+ */
+var uniquePaths = function(m, n) {
+  const dp = Array(n).fill(1);
+
+  for(let i = 1; i < m; i++) {
+    for(let j = 1; j < n; j++) {
+      dp[j] = dp[j] + dp[j - 1];
+    } 
+  }
+
+  return dp[n - 1];
+};
+```