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leetcode-problemset/leetcode/originData/maximum-total-reward-using-operations-i.json
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"title": "Maximum Total Reward Using Operations I",
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"content": "<p>You are given an integer array <code>rewardValues</code> of length <code>n</code>, representing the values of rewards.</p>\n\n<p>Initially, your total reward <code>x</code> is 0, and all indices are <strong>unmarked</strong>. You are allowed to perform the following operation <strong>any</strong> number of times:</p>\n\n<ul>\n\t<li>Choose an <strong>unmarked</strong> index <code>i</code> from the range <code>[0, n - 1]</code>.</li>\n\t<li>If <code>rewardValues[i]</code> is <strong>greater</strong> than your current total reward <code>x</code>, then add <code>rewardValues[i]</code> to <code>x</code> (i.e., <code>x = x + rewardValues[i]</code>), and <strong>mark</strong> the index <code>i</code>.</li>\n</ul>\n\n<p>Return an integer denoting the <strong>maximum </strong><em>total reward</em> you can collect by performing the operations optimally.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">rewardValues = [1,1,3,3]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">4</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>During the operations, we can choose to mark the indices 0 and 2 in order, and the total reward will be 4, which is the maximum.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">rewardValues = [1,6,4,3,2]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">11</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>Mark the indices 0, 2, and 1 in order. The total reward will then be 11, which is the maximum.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= rewardValues.length &lt;= 2000</code></li>\n\t<li><code>1 &lt;= rewardValues[i] &lt;= 2000</code></li>\n</ul>\n",
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"hints": [
"Sort the rewards array first.",
"If we decide to apply some rewards, it's always optimal to apply them in order.",
"Let <code>dp[i][j]</code> (true/false) be the state after the first <code>i</code> rewards, indicating whether we can get exactly <code>j</code> points.",
"The transition is given by: <code>dp[i][j] = dp[i - 1][j rewardValues[i]]</code> if <code>j rewardValues[i] < rewardValues[i]</code>."
],
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