leetcode-problemset/leetcode/originData/number-of-ways-to-stay-in-the-same-place-after-some-steps.json

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            "title": "Number of Ways to Stay in the Same Place After Some Steps",
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            "content": "<p>You have a pointer at index <code>0</code> in an array of size <code>arrLen</code>. At each step, you can move 1 position to the left, 1 position to the right in the array, or stay in the same place (The pointer should not be placed outside the array at any time).</p>\n\n<p>Given two integers <code>steps</code> and <code>arrLen</code>, return the number of ways such that your pointer is still at index <code>0</code> after <strong>exactly</strong> <code>steps</code> steps. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> steps = 3, arrLen = 2\n<strong>Output:</strong> 4\n<strong>Explanation: </strong>There are 4 differents ways to stay at index 0 after 3 steps.\nRight, Left, Stay\nStay, Right, Left\nRight, Stay, Left\nStay, Stay, Stay\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> steps = 2, arrLen = 4\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> There are 2 differents ways to stay at index 0 after 2 steps\nRight, Left\nStay, Stay\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> steps = 4, arrLen = 2\n<strong>Output:</strong> 8\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= steps &lt;= 500</code></li>\n\t<li><code>1 &lt;= arrLen &lt;= 10<sup>6</sup></code></li>\n</ul>\n",
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                    "code": "# @param {Integer} steps\n# @param {Integer} arr_len\n# @return {Integer}\ndef num_ways(steps, arr_len)\n    \nend",
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            "hints": [
                "Try with Dynamic programming, dp(pos,steps): number of ways to back pos = 0 using exactly \"steps\" moves.",
                "Notice that the computational complexity does not depend of \"arrlen\"."
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