{"id":6975,"date":"2020-06-27T13:35:09","date_gmt":"2020-06-27T20:35:09","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=6975"},"modified":"2020-06-29T09:22:29","modified_gmt":"2020-06-29T16:22:29","slug":"leetcode-1493-longest-subarray-of-1s-after-deleting-one-element","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/dynamic-programming\/leetcode-1493-longest-subarray-of-1s-after-deleting-one-element\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 1493. Longest Subarray of 1&#8217;s After Deleting One Element"},"content":{"rendered":"\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"\u82b1\u82b1\u9171 LeetCode 1493. Longest Subarray of 1&#039;s After Deleting One Element - \u5237\u9898\u627e\u5de5\u4f5c EP339\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/lgN5zT6EYqs?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p>Given a binary array&nbsp;<code>nums<\/code>, you should delete one element from it.<\/p>\n\n\n\n<p>Return the size of the longest non-empty subarray containing only 1&#8217;s&nbsp;in the resulting array.<\/p>\n\n\n\n<p>Return 0 if there is no such subarray.<\/p>\n\n\n\n<p><strong>Example 1:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted;crayon:false\"><strong>Input:<\/strong> nums = [1,1,0,1]\n<strong>Output:<\/strong> 3\n<strong>Explanation: <\/strong>After deleting the number in position 2, [1,1,1] contains 3 numbers with value of 1's.<\/pre>\n\n\n\n<p><strong>Example 2:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted;crayon:false\"><strong>Input:<\/strong> nums = [0,1,1,1,0,1,1,0,1]\n<strong>Output:<\/strong> 5\n<strong>Explanation: <\/strong>After deleting the number in position 4, [0,1,1,1,1,1,0,1] longest subarray with value of 1's is [1,1,1,1,1].<\/pre>\n\n\n\n<p><strong>Example 3:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted;crayon:false\"><strong>Input:<\/strong> nums = [1,1,1]\n<strong>Output:<\/strong> 2\n<strong>Explanation: <\/strong>You must delete one element.<\/pre>\n\n\n\n<p><strong>Example 4:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted;crayon:false\"><strong>Input:<\/strong> nums = [1,1,0,0,1,1,1,0,1]\n<strong>Output:<\/strong> 4\n<\/pre>\n\n\n\n<p><strong>Example 5:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted;crayon:false\"><strong>Input:<\/strong> nums = [0,0,0]\n<strong>Output:<\/strong> 0\n<\/pre>\n\n\n\n<p><strong>Constraints:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><code>1 &lt;= nums.length &lt;= 10^5<\/code><\/li><li><code>nums[i]<\/code>&nbsp;is either&nbsp;<code>0<\/code>&nbsp;or&nbsp;<code>1<\/code>.<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Solution 1: DP<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"540\" src=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2020\/06\/1493-ep339-1.png\" alt=\"\" class=\"wp-image-7006\" srcset=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2020\/06\/1493-ep339-1.png 960w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2020\/06\/1493-ep339-1-300x169.png 300w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2020\/06\/1493-ep339-1-768x432.png 768w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><\/figure>\n\n\n\n<p>Preprocess:<br>l[i] := longest 1s from left side ends with nums[i], l[i] = nums[i] + nums[i] * l[i &#8211; 1]<br>r[i] := longest 1s from right side ends with nums[i], r[i] = nums[i] + nums[i] * r[i + 1]<br><br>Use each node as a bridge (ignored), the total number of consecutive 1s = l[i &#8211; 1] + r[i + 1].<\/p>\n\n\n\n<p>ans = max{l[i-1] + r[i +1]}<br>Time complexity: O(n)<br>Space complexity: O(n)<\/p>\n\n\n\n<div class=\"responsive-tabs\">\n<h2 class=\"tabtitle\">C++<\/h2>\n<div class=\"tabcontent\">\n\n<pre lang=\"C++\">\n\/\/ Author: Huahua\nclass Solution {\npublic:\n  int longestSubarray(vector<int>& nums) {\n    const int n = nums.size();\n    vector<int> l(n);\n    vector<int> r(n);\n    for (int i = 0; i < n; ++i)\n      l[i] = (i > 0 ? l[i - 1] * nums[i] : 0) + nums[i];\n    for (int i = n - 1; i >= 0; --i)\n      r[i] = (i < n - 1 ? r[i + 1] * nums[i] : 0) + nums[i];\n    int ans = 0;\n    for (int i = 0; i < n; ++i)\n      ans = max(ans, (i > 0 ? l[i - 1] : 0) + \n                     (i < n - 1 ? r[i + 1] : 0));\n    return ans;\n  }\n};\n<\/pre>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Solution 2: DP<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"540\" src=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2020\/06\/1493-ep339-2.png\" alt=\"\" class=\"wp-image-7007\" srcset=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2020\/06\/1493-ep339-2.png 960w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2020\/06\/1493-ep339-2-300x169.png 300w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2020\/06\/1493-ep339-2-768x432.png 768w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><\/figure>\n\n\n\n<p>dp[i][0] := longest subarray ends with nums[i] has no ones.<br>dp[i][0] := longest subarray ends with nums[i] has 1 one.<br>if nums[i] == 1: <br>  dp[i][0] = dp[i - 1][0] + 1<br>  dp[i][1] = dp[i - 1][1] + 1<br>if nums[i] == 0:<br>  dp[i][0] = 0<br>  dp[i][1] = dp[i - 1][0] + 1<br>Time complexity: O(n)<br>Space complexity: O(n) -&gt; O(1)<\/p>\n\n\n\n<div class=\"responsive-tabs\">\n<h2 class=\"tabtitle\">C++<\/h2>\n<div class=\"tabcontent\">\n\n<pre lang=\"C++\">\n\/\/ Author: Huahua\nclass Solution {\npublic:\n  int longestSubarray(vector<int>& nums) {\n    const int n = nums.size();\n    \/\/ dp[i][0] := longest subarray ends with nums[i-1] has no zeros.\n    \/\/ dp[i][0] := longest subarray ends with nums[i-1] has 1 zero.\n    vector<vector<int>> dp(n + 1, vector<int>(2));\n    int ans = 0;\n    for (int i = 1; i <= n; ++i) {\n      if (nums[i - 1] == 1) {\n        dp[i][0] = dp[i - 1][0] + 1;\n        dp[i][1] = dp[i - 1][1] + 1;\n      } else {\n        dp[i][0] = 0;\n        dp[i][1] = dp[i - 1][0] + 1;\n      }\n      ans = max({ans, dp[i][0] - 1, dp[i][1] - 1});\n    }\n    return ans;\n  }\n};\n<\/pre>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Solution 3: Sliding Window<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"540\" src=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2020\/06\/1493-ep339-3.png\" alt=\"\" class=\"wp-image-7008\" srcset=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2020\/06\/1493-ep339-3.png 960w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2020\/06\/1493-ep339-3-300x169.png 300w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2020\/06\/1493-ep339-3-768x432.png 768w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><\/figure>\n\n\n\n<p>Maintain a sliding window l ~ r s.t sum(num[l~r]) &gt;= r - l. There can be <strong>at most<\/strong> one 0 in the window.<br>ans = max{r - l} for all valid windows.<\/p>\n\n\n\n<p>Time complexity: O(n)<br>Space complexity: O(1)<\/p>\n\n\n\n<div class=\"responsive-tabs\">\n<h2 class=\"tabtitle\">C++<\/h2>\n<div class=\"tabcontent\">\n\n<pre lang=\"C++\">\n\/\/ Author: Huahua\nclass Solution {\npublic:\n  int longestSubarray(vector<int>& nums) {\n    const int n = nums.size();\n    int ans = 0;\n    int sum = 0; \/\/ sum of nums[l~r].\n    for (int l = 0, r = 0; r < n; ++r) {\n      sum += nums[r];\n      \/\/ Maintain sum >= r - l, at most 1 zero.\n      while (l < r &#038;&#038; sum < r - l)\n        sum -= nums[l++];\n      ans = max(ans, r - l);\n    }\n    return ans;\n  }\n};\n<\/pre>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Given a binary array&nbsp;nums, you should delete one element from it. Return the size of the longest non-empty subarray containing only 1&#8217;s&nbsp;in the resulting array.&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[46],"tags":[20,18,117,177,215,41],"class_list":["post-6975","post","type-post","status-publish","format-standard","hentry","category-dynamic-programming","tag-array","tag-dp","tag-longest","tag-medium","tag-sliding-window","tag-subarray","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/6975","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/comments?post=6975"}],"version-history":[{"count":10,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/6975\/revisions"}],"predecessor-version":[{"id":7017,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/6975\/revisions\/7017"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=6975"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=6975"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=6975"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}