"content":"<p>Given a rectangular pizza represented as a <code>rows x cols</code> matrix containing the following characters: <code>'A'</code> (an apple) and <code>'.'</code> (empty cell) and given the integer <code>k</code>. You have to cut the pizza into <code>k</code> pieces using <code>k-1</code> cuts. </p>\n\n<p>For each cut you choose the direction: vertical or horizontal, then you choose a cut position at the cell boundary and cut the pizza into two pieces. If you cut the pizza vertically, give the left part of the pizza to a person. If you cut the pizza horizontally, give the upper part of the pizza to a person. Give the last piece of pizza to the last person.</p>\n\n<p><em>Return the number of ways of cutting the pizza such that each piece contains <strong>at least</strong> one apple. </em>Since the answer can be a huge number, return this modulo 10^9 + 7.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/04/23/ways_to_cut_apple_1.png\" style=\"width: 500px; height: 378px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> pizza = ["A..","AAA","..."], k = 3\n<strong>Output:</strong> 3 \n<strong>Explanation:</strong> The figure above shows the three ways to cut the pizza. Note that pieces must contain at least one apple.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> pizza = ["A..","AA.","..."], k = 3\n<strong>Output:</strong> 1\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> pizza = ["A..","A..","..."], k = 1\n<strong>Output:</strong> 1\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= rows, cols <= 50</code></li>\n\t<li><code>rows == pizza.length</code></li>\n\t<li><code>cols == pizza[i].length</code></li>\n\t<li><code>1 <= k <= 10</code></li>\n\t<li><code>pizza</code> consists of characters <code>'A'</code> and <code>'.'</code> only.</li>\n</ul>\n",
"Note that after each cut the remaining piece of pizza always has the lower right coordinate at (rows-1,cols-1).",
"Use dynamic programming approach with states (row1, col1, c) which computes the number of ways of cutting the pizza using \"c\" cuts where the current piece of pizza has upper left coordinate at (row1,col1) and lower right coordinate at (rows-1,cols-1).",
"For the transitions try all vertical and horizontal cuts such that the piece of pizza you have to give a person must contain at least one apple. The base case is when c=k-1.",
"Additionally use a 2D dynamic programming to respond in O(1) if a piece of pizza contains at least one apple."
"envInfo":"{\"cpp\": [\"C++\", \"<p>Compiled with <code> clang 11 </code> using the latest C++ 20 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level two optimization (<code>-O2</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\"], \"java\": [\"Java\", \"<p><code>OpenJDK 17</code>. Java 8 features such as lambda expressions and stream API can be used. </p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>\"], \"python\": [\"Python\", \"<p><code>Python 2.7.12</code>.</p>\\r\\n\\r\\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\\\"https://docs.python.org/2/library/array.html\\\" target=\\\"_blank\\\">array</a>, <a href=\\\"https://docs.python.org/2/library/bisect.html\\\" target=\\\"_blank\\\">bisect</a>, <a href=\\\"https://docs.python.org/2/library/collections.html\\\" target=\\\"_blank\\\">collections</a>. If you need more libraries, you can import it yourself.</p>\\r\\n\\r\\n<p>For Map/TreeMap data structure, you may use <a href=\\\"http://www.grantjenks.com/docs/sortedcontainers/\\\" target=\\\"_blank\\\">sortedcontainers</a> library.</p>\\r\\n\\r\\n<p>Note that Python 2.7 <a href=\\\"https://www.python.org/dev/peps/pep-0373/\\\" target=\\\"_blank\\\">will not be maintained past 2020</a>. For the latest Python, please choose Python3 instead.</p>\"], \"c\": [\"C\", \"<p>Compiled with <code>gcc 8.2</code> using the gnu11 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level one optimization (<code>-O1</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n\\r\\n<p>For hash table operations, you may use <a href=\\\"https://troydhanson.github.io/uthash/\\\" target=\\\"_blank\\\">uthash</a>. \\\"uthash.h\\\" is included by default. Below are some examples:</p>\\r\\n\\r\\n<p><b>1. Adding an item to a hash.</b>\\r\\n<pre>\\r\\nstruct hash_entry {\\r\\n int id; /* we'll use this field as the key */\\r\\n char name[10];\\r\\n UT_hash_handle hh; /* makes this structure hashable */\\r\\n};\\r\\n\\r\\nstruct hash_entry *users = NULL;\\r\\n\\r\\nvoid add_user(struct hash_entry *s) {\\r\\n HASH_ADD_INT(users, id, s);\\r\\n}\\r\\n</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>2. Looking up an item in a hash:</b>\\r\\n<pre>\\r\\nstruct hash_entry *find_user(int user_id) {\\r\\n struct hash_entry *s;\\r\\n HASH_FIND_INT(users, &user_id, s);\\r\\n return s;\\r\\n}\\r\\n</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>3. Deleting an item in a hash:</b>\\r\\n<pre>\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n HASH_DEL(users, user); \\r\\n}\\r\\n</pre>\\r\\n</p>\"], \"csharp\": [\"C#\", \"<p><a href=\\\"https://learn.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-10\\\" target=\\\"_blank\\\">C# 10 with .NET 6 runtime</a></p>\"], \"javascript\": [\"JavaScript\", \"<p><code>Node.js 16.13.2</code>.</p>\\r\\n\\r\\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\\\"http://node.green/\\\" target=\\\"_blank\\\">new ES6 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\\r\\n\\r\\n<p>For Priority Queue / Queue data structures, you may use 5.3.0 version of <a href=\\\"https://github.com/datastructures-js/priority-queue/tree/fb4fdb984834421279aeb081df7af624d17c2a03\\\" target=\\\"_blank\\\">datastructures-js/priority-queue</a> and 4.2.1 version of <a href=\\\"https://githu
