leetcode-problemset/leetcode/originData/all-divisions-with-the-highest-score-of-a-binary-array.json

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            "title": "All Divisions With the Highest Score of a Binary Array",
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            "content": "<p>You are given a <strong>0-indexed</strong> binary array <code>nums</code> of length <code>n</code>. <code>nums</code> can be divided at index <code>i</code> (where <code>0 &lt;= i &lt;= n)</code> into two arrays (possibly empty) <code>nums<sub>left</sub></code> and <code>nums<sub>right</sub></code>:</p>\n\n<ul>\n\t<li><code>nums<sub>left</sub></code> has all the elements of <code>nums</code> between index <code>0</code> and <code>i - 1</code> <strong>(inclusive)</strong>, while <code>nums<sub>right</sub></code> has all the elements of nums between index <code>i</code> and <code>n - 1</code> <strong>(inclusive)</strong>.</li>\n\t<li>If <code>i == 0</code>, <code>nums<sub>left</sub></code> is <strong>empty</strong>, while <code>nums<sub>right</sub></code> has all the elements of <code>nums</code>.</li>\n\t<li>If <code>i == n</code>, <code>nums<sub>left</sub></code> has all the elements of nums, while <code>nums<sub>right</sub></code> is <strong>empty</strong>.</li>\n</ul>\n\n<p>The <strong>division score</strong> of an index <code>i</code> is the <strong>sum</strong> of the number of <code>0</code>&#39;s in <code>nums<sub>left</sub></code> and the number of <code>1</code>&#39;s in <code>nums<sub>right</sub></code>.</p>\n\n<p>Return <em><strong>all distinct indices</strong> that have the <strong>highest</strong> possible <strong>division score</strong></em>. You may return the answer in <strong>any order</strong>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [0,0,1,0]\n<strong>Output:</strong> [2,4]\n<strong>Explanation:</strong> Division at index\n- 0: nums<sub>left</sub> is []. nums<sub>right</sub> is [0,0,<u><strong>1</strong></u>,0]. The score is 0 + 1 = 1.\n- 1: nums<sub>left</sub> is [<u><strong>0</strong></u>]. nums<sub>right</sub> is [0,<u><strong>1</strong></u>,0]. The score is 1 + 1 = 2.\n- 2: nums<sub>left</sub> is [<u><strong>0</strong></u>,<u><strong>0</strong></u>]. nums<sub>right</sub> is [<u><strong>1</strong></u>,0]. The score is 2 + 1 = 3.\n- 3: nums<sub>left</sub> is [<u><strong>0</strong></u>,<u><strong>0</strong></u>,1]. nums<sub>right</sub> is [0]. The score is 2 + 0 = 2.\n- 4: nums<sub>left</sub> is [<u><strong>0</strong></u>,<u><strong>0</strong></u>,1,<u><strong>0</strong></u>]. nums<sub>right</sub> is []. The score is 3 + 0 = 3.\nIndices 2 and 4 both have the highest possible division score 3.\nNote the answer [4,2] would also be accepted.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [0,0,0]\n<strong>Output:</strong> [3]\n<strong>Explanation:</strong> Division at index\n- 0: nums<sub>left</sub> is []. nums<sub>right</sub> is [0,0,0]. The score is 0 + 0 = 0.\n- 1: nums<sub>left</sub> is [<u><strong>0</strong></u>]. nums<sub>right</sub> is [0,0]. The score is 1 + 0 = 1.\n- 2: nums<sub>left</sub> is [<u><strong>0</strong></u>,<u><strong>0</strong></u>]. nums<sub>right</sub> is [0]. The score is 2 + 0 = 2.\n- 3: nums<sub>left</sub> is [<u><strong>0</strong></u>,<u><strong>0</strong></u>,<u><strong>0</strong></u>]. nums<sub>right</sub> is []. The score is 3 + 0 = 3.\nOnly index 3 has the highest possible division score 3.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,1]\n<strong>Output:</strong> [0]\n<strong>Explanation:</strong> Division at index\n- 0: nums<sub>left</sub> is []. nums<sub>right</sub> is [<u><strong>1</strong></u>,<u><strong>1</strong></u>]. The score is 0 + 2 = 2.\n- 1: nums<sub>left</sub> is [1]. nums<sub>right</sub> is [<u><strong>1</strong></u>]. The score is 0 + 1 = 1.\n- 2: nums<sub>left</sub> is [1,1]. nums<sub>right</sub> is []. The score is 0 + 0 = 0.\nOnly index 0 has the highest possible division score 2.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == nums.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>nums[i]</code> is either <code>0</code> or <code>1</code>.</li>\n</ul>\n",
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                "When you iterate the array, maintain the number of zeros and ones on the left side. Can you quickly calculate the number of ones on the right side?",
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                "Alternatively, you can quickly calculate it by using a prefix sum array."
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