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leetcode/originData/minimum-sum-of-mountain-triplets-i.json
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leetcode/originData/minimum-sum-of-mountain-triplets-i.json
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leetcode/originData/minimum-sum-of-mountain-triplets-ii.json
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leetcode/originData/minimum-sum-of-mountain-triplets-ii.json
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<p>Given a string <code>s</code> and an integer <code>k</code>, partition <code>s</code> into <code>k</code> <strong>substrings</strong> such that the sum of the number of letter changes required to turn each <strong>substring</strong> into a <strong>semi-palindrome</strong> is minimized.</p>
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<p>Return <em>an integer denoting the <strong>minimum</strong> number of letter changes required.</em></p>
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<p><strong>Notes</strong></p>
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<ul>
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<li>A string is a <strong>palindrome</strong> if it can be read the same way from left to right and right to left.</li>
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<li>A string with a length of <code>len</code> is considered a <strong>semi-palindrome</strong> if there exists a positive integer <code>d</code> such that <code>1 <= d < len</code> and <code>len % d == 0</code>, and if we take indices that have the same modulo by <code>d</code>, they form a <strong>palindrome</strong>. For example, <code>"aa"</code>, <code>"aba"</code>, <code>"adbgad"</code>, and, <code>"abab"</code> are <strong>semi-palindrome</strong> and <code>"a"</code>, <code>"ab"</code>, and, <code>"abca"</code> are not.</li>
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<li>A <strong>substring</strong> is a contiguous sequence of characters within a string.</li>
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</ul>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> s = "abcac", k = 2
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<strong>Output:</strong> 1
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<strong>Explanation:</strong> We can divide s into substrings "ab" and "cac". The string "cac" is already a semi-palindrome. If we change "ab" to "aa", it becomes a semi-palindrome with d = 1.
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It can be shown that there is no way to divide the string "abcac" into two semi-palindrome substrings. Therefore, the answer would be at least 1.</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> s = "abcdef", k = 2
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<strong>Output:</strong> 2
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<strong>Explanation:</strong> We can divide it into substrings "abc" and "def". Each of the substrings "abc" and "def" requires one change to become a semi-palindrome, so we need 2 changes in total to make all substrings semi-palindrome.
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It can be shown that we cannot divide the given string into two substrings in a way that it would require less than 2 changes.</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> s = "aabbaa", k = 3
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<strong>Output:</strong> 0
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<strong>Explanation:</strong> We can divide it into substrings "aa", "bb" and "aa".
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The strings "aa" and "bb" are already semi-palindromes. Thus, the answer is zero.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>2 <= s.length <= 200</code></li>
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<li><code>1 <= k <= s.length / 2</code></li>
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<li><code>s</code> consists only of lowercase English letters.</li>
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</ul>
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<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code>.</p>
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<p>We want to group the indices so for each index <code>i</code> in the range <code>[0, n - 1]</code>, it is assigned to <strong>exactly one</strong> group.</p>
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<p>A group<strong> </strong>assignment is <strong>valid</strong> if the following conditions hold:</p>
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<ul>
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<li>For every group <code>g</code>, all indices <code>i</code> assigned to group <code>g</code> have the same value in <code>nums</code>.</li>
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<li>For any two groups <code>g<sub>1</sub></code> and <code>g<sub>2</sub></code>, the <strong>difference</strong> between the <strong>number of indices</strong> assigned to <code>g<sub>1</sub></code> and <code>g<sub>2</sub></code> should <strong>not exceed</strong> <code>1</code>.</li>
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</ul>
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<p>Return <em>an integer denoting </em><em>the <strong>minimum</strong> number of groups needed to create a valid group assignment.</em></p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [3,2,3,2,3]
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<strong>Output:</strong> 2
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<strong>Explanation:</strong> One way the indices can be assigned to 2 groups is as follows, where the values in square brackets are indices:
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group 1 -> [0,2,4]
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group 2 -> [1,3]
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All indices are assigned to one group.
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In group 1, nums[0] == nums[2] == nums[4], so all indices have the same value.
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In group 2, nums[1] == nums[3], so all indices have the same value.
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The number of indices assigned to group 1 is 3, and the number of indices assigned to group 2 is 2.
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Their difference doesn't exceed 1.
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It is not possible to use fewer than 2 groups because, in order to use just 1 group, all indices assigned to that group must have the same value.
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Hence, the answer is 2.</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [10,10,10,3,1,1]
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<strong>Output:</strong> 4
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<strong>Explanation:</strong> One way the indices can be assigned to 4 groups is as follows, where the values in square brackets are indices:
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group 1 -> [0]
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group 2 -> [1,2]
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group 3 -> [3]
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group 4 -> [4,5]
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The group assignment above satisfies both conditions.
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It can be shown that it is not possible to create a valid assignment using fewer than 4 groups.
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Hence, the answer is 4.</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>
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<li><code>1 <= nums[i] <= 10<sup>9</sup></code></li>
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</ul>
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leetcode/problem/minimum-sum-of-mountain-triplets-i.html
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leetcode/problem/minimum-sum-of-mountain-triplets-i.html
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<p>You are given a <strong>0-indexed</strong> array <code>nums</code> of integers.</p>
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<p>A triplet of indices <code>(i, j, k)</code> is a <strong>mountain</strong> if:</p>
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<ul>
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<li><code>i < j < k</code></li>
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<li><code>nums[i] < nums[j]</code> and <code>nums[k] < nums[j]</code></li>
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</ul>
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<p>Return <em>the <strong>minimum possible sum</strong> of a mountain triplet of</em> <code>nums</code>. <em>If no such triplet exists, return</em> <code>-1</code>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [8,6,1,5,3]
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<strong>Output:</strong> 9
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<strong>Explanation:</strong> Triplet (2, 3, 4) is a mountain triplet of sum 9 since:
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- 2 < 3 < 4
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- nums[2] < nums[3] and nums[4] < nums[3]
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And the sum of this triplet is nums[2] + nums[3] + nums[4] = 9. It can be shown that there are no mountain triplets with a sum of less than 9.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [5,4,8,7,10,2]
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<strong>Output:</strong> 13
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<strong>Explanation:</strong> Triplet (1, 3, 5) is a mountain triplet of sum 13 since:
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- 1 < 3 < 5
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- nums[1] < nums[3] and nums[5] < nums[3]
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And the sum of this triplet is nums[1] + nums[3] + nums[5] = 13. It can be shown that there are no mountain triplets with a sum of less than 13.
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</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [6,5,4,3,4,5]
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<strong>Output:</strong> -1
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<strong>Explanation:</strong> It can be shown that there are no mountain triplets in nums.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>3 <= nums.length <= 50</code></li>
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<li><code>1 <= nums[i] <= 50</code></li>
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</ul>
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49
leetcode/problem/minimum-sum-of-mountain-triplets-ii.html
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leetcode/problem/minimum-sum-of-mountain-triplets-ii.html
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<p>You are given a <strong>0-indexed</strong> array <code>nums</code> of integers.</p>
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<p>A triplet of indices <code>(i, j, k)</code> is a <strong>mountain</strong> if:</p>
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<ul>
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<li><code>i < j < k</code></li>
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<li><code>nums[i] < nums[j]</code> and <code>nums[k] < nums[j]</code></li>
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</ul>
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<p>Return <em>the <strong>minimum possible sum</strong> of a mountain triplet of</em> <code>nums</code>. <em>If no such triplet exists, return</em> <code>-1</code>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [8,6,1,5,3]
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<strong>Output:</strong> 9
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<strong>Explanation:</strong> Triplet (2, 3, 4) is a mountain triplet of sum 9 since:
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- 2 < 3 < 4
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- nums[2] < nums[3] and nums[4] < nums[3]
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And the sum of this triplet is nums[2] + nums[3] + nums[4] = 9. It can be shown that there are no mountain triplets with a sum of less than 9.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [5,4,8,7,10,2]
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<strong>Output:</strong> 13
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<strong>Explanation:</strong> Triplet (1, 3, 5) is a mountain triplet of sum 13 since:
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- 1 < 3 < 5
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- nums[1] < nums[3] and nums[5] < nums[3]
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And the sum of this triplet is nums[1] + nums[3] + nums[5] = 13. It can be shown that there are no mountain triplets with a sum of less than 13.
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</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [6,5,4,3,4,5]
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<strong>Output:</strong> -1
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<strong>Explanation:</strong> It can be shown that there are no mountain triplets in nums.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>3 <= nums.length <= 10<sup>5</sup></code></li>
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<li><code>1 <= nums[i] <= 10<sup>8</sup></code></li>
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</ul>
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