{"id":909,"date":"2020-06-30T21:52:10","date_gmt":"2020-06-30T13:52:10","guid":{"rendered":"https:\/\/www.changxuan.top\/?p=909"},"modified":"2020-10-12T20:05:55","modified_gmt":"2020-10-12T12:05:55","slug":"unique-path","status":"publish","type":"post","link":"https:\/\/www.changxuan.top\/?p=909","title":{"rendered":"Unique Path"},"content":{"rendered":"\n<p>A robot is located at the top-left corner of a&nbsp;<em>m<\/em>&nbsp;x&nbsp;<em>n<\/em>&nbsp;grid (marked &#8216;Start&#8217; in the diagram below).<\/p>\n\n\n\n<p>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 &#8216;Finish&#8217; in the diagram below).<\/p>\n\n\n\n<p>How many possible unique paths are there?<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/assets.leetcode.com\/uploads\/2018\/10\/22\/robot_maze.png\" alt=\"\"\/><\/figure>\n\n\n\n<p><br>Above is a 7 x 3 grid. How many possible unique paths are there?<\/p>\n\n\n\n<p><strong>Example 1:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><strong>Input:<\/strong> m = 3, n = 2\n<strong>Output:<\/strong> 3\n<strong>Explanation:<\/strong>\nFrom the top-left corner, there are a total of 3 ways to reach the bottom-right corner:\n1. Right -&gt; Right -&gt; Down\n2. Right -&gt; Down -&gt; Right\n3. Down -&gt; Right -&gt; Right\n<\/pre>\n\n\n\n<p><strong>Example 2:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><strong>Input:<\/strong> m = 7, n = 3\n<strong>Output:<\/strong> 28\n<\/pre>\n\n\n\n<p><strong>Constraints:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><code>1 &lt;= m, n &lt;= 100<\/code><\/li><li>It&#8217;s guaranteed that the answer will be less than or equal to&nbsp;<code>2 * 10 ^ 9<\/code>.<\/li><\/ul>\n\n\n\n<p><strong>Solution<\/strong><\/p>\n\n\n<p><!-- wp:code \n\n\n<pre class=\"wp-block-code\"><code>class Solution {\n    public int uniquePaths(int m, int n) {\n        int[] temp = new int[m];\n        for (int i = 0; i &lt; m; i++)\n            temp[i] = 1;\n        for (int j = 0; j &lt; n-1; j++){\n            for (int c = 1; c &lt; m; c++){\n                temp[c] = temp[c-1] + temp[c];\n            }\n        }\n        return temp[m-1];\n    }\n}<\/code><\/pre>\n\n\n\/wp:code --><\/p>\n<section id=\"nice\" data-tool=\"mdnice\u7f16\u8f91\u5668\" data-website=\"https:\/\/www.mdnice.com\" style=\"font-size: 16px; color: black; padding: 0 10px; line-height: 1.6; word-spacing: 0px; letter-spacing: 0px; word-break: break-word; word-wrap: break-word; text-align: left; font-family: Optima-Regular, Optima, PingFangSC-light, PingFangTC-light, 'PingFang SC', Cambria, Cochin, Georgia, Times, 'Times New Roman', serif;\">\n<pre class=\"custom\" data-tool=\"mdnice\u7f16\u8f91\u5668\" style=\"margin-top: 10px; margin-bottom: 10px; border-radius: 5px; box-shadow: rgba(0, 0, 0, 0.55) 0px 2px 10px;\"><span style=\"display: block; background: url(https:\/\/my-wechat.mdnice.com\/point.png); height: 30px; width: 100%; background-size: 40px; background-repeat: no-repeat; background-color: #282c34; margin-bottom: -7px; border-radius: 5px; background-position: 10px 10px;\"><\/span><code class=\"hljs\" style=\"overflow-x: auto; padding: 16px; color: #abb2bf; display: -webkit-box; font-family: Operator Mono, Consolas, Monaco, Menlo, monospace; font-size: 12px; -webkit-overflow-scrolling: touch; padding-top: 15px; background: #282c34; border-radius: 5px;\"><span class=\"hljs-class\" style=\"line-height: 26px;\"><span class=\"hljs-keyword\" style=\"color: #c678dd; line-height: 26px;\">class<\/span>&nbsp;<span class=\"hljs-title\" style=\"color: #e6c07b; line-height: 26px;\">Solution<\/span>&nbsp;<\/span>{<br>&nbsp;&nbsp;&nbsp;&nbsp;<span class=\"hljs-function\" style=\"line-height: 26px;\"><span class=\"hljs-keyword\" style=\"color: #c678dd; line-height: 26px;\">public<\/span>&nbsp;<span class=\"hljs-keyword\" style=\"color: #c678dd; line-height: 26px;\">int<\/span>&nbsp;<span class=\"hljs-title\" style=\"color: #61aeee; line-height: 26px;\">uniquePaths<\/span><span class=\"hljs-params\" style=\"line-height: 26px;\">(<span class=\"hljs-keyword\" style=\"color: #c678dd; line-height: 26px;\">int<\/span>&nbsp;m,&nbsp;<span class=\"hljs-keyword\" style=\"color: #c678dd; line-height: 26px;\">int<\/span>&nbsp;n)<\/span>&nbsp;<\/span>{<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=\"hljs-keyword\" style=\"color: #c678dd; line-height: 26px;\">int<\/span>[]&nbsp;temp&nbsp;=&nbsp;<span class=\"hljs-keyword\" style=\"color: #c678dd; line-height: 26px;\">new<\/span>&nbsp;<span class=\"hljs-keyword\" style=\"color: #c678dd; line-height: 26px;\">int<\/span>[m];<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=\"hljs-keyword\" style=\"color: #c678dd; line-height: 26px;\">for<\/span>&nbsp;(<span class=\"hljs-keyword\" style=\"color: #c678dd; line-height: 26px;\">int<\/span>&nbsp;i&nbsp;=&nbsp;<span class=\"hljs-number\" style=\"color: #d19a66; line-height: 26px;\">0<\/span>;&nbsp;i&nbsp;&lt;&nbsp;m;&nbsp;i++)<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;temp[i]&nbsp;=&nbsp;<span class=\"hljs-number\" style=\"color: #d19a66; line-height: 26px;\">1<\/span>;<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=\"hljs-keyword\" style=\"color: #c678dd; line-height: 26px;\">for<\/span>&nbsp;(<span class=\"hljs-keyword\" style=\"color: #c678dd; line-height: 26px;\">int<\/span>&nbsp;j&nbsp;=&nbsp;<span class=\"hljs-number\" style=\"color: #d19a66; line-height: 26px;\">0<\/span>;&nbsp;j&nbsp;&lt;&nbsp;n-<span class=\"hljs-number\" style=\"color: #d19a66; line-height: 26px;\">1<\/span>;&nbsp;j++){<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=\"hljs-keyword\" style=\"color: #c678dd; line-height: 26px;\">for<\/span>&nbsp;(<span class=\"hljs-keyword\" style=\"color: #c678dd; line-height: 26px;\">int<\/span>&nbsp;c&nbsp;=&nbsp;<span class=\"hljs-number\" style=\"color: #d19a66; line-height: 26px;\">1<\/span>;&nbsp;c&nbsp;&lt;&nbsp;m;&nbsp;c++){<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;temp&nbsp;=&nbsp;temp[c-<span class=\"hljs-number\" style=\"color: #d19a66; line-height: 26px;\">1<\/span>]&nbsp;+&nbsp;temp;<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;}<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;}<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=\"hljs-keyword\" style=\"color: #c678dd; line-height: 26px;\">return<\/span>&nbsp;temp[m-<span class=\"hljs-number\" style=\"color: #d19a66; line-height: 26px;\">1<\/span>];<br>&nbsp;&nbsp;&nbsp;&nbsp;}<br>}<\/code><\/pre>\n<\/section>","protected":false},"excerpt":{"rendered":"<p>A robot is located at the top-left corner of a&nbsp;m&#038;n &hellip; <a href=\"https:\/\/www.changxuan.top\/?p=909\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">Unique Path<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[37],"tags":[82],"class_list":["post-909","post","type-post","status-publish","format-standard","hentry","category-tech","tag-dynamic-programming"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Unique Path - \u5e38\u8f69<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.changxuan.top\/?p=909\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Unique Path - \u5e38\u8f69\" \/>\n<meta property=\"og:description\" content=\"A robot is located at the top-left corner of a&nbsp;m&amp;n 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