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Merge pull request #325 from cheehwatang/add-923-3SumWithMultiplicity
Add 923. 3Sum With Multiplicity (Sorting & Two Pointers)
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‎README.md‎

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<th>Solution</th>
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<th>Topics</th>
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</tr>
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<tr>
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<td align="center">September 4th</td>
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<td>923. <a href="https://leetcode.com/problems/3sum-with-multiplicity/">3Sum With Multiplicity</a></td>
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<td align="center">$\text{\color{Dandelion}Medium}$</td>
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<td align="center">
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Sorting_TwoPointers.java">Sorting & Two Pointers</a>
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</td>
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<td align="center">
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<a href="#array">Array</a>,
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<a href="#sorting">Sorting</a>,
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<a href="#two-pointers">Two Pointers</a>
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</td>
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</tr>
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<tr>
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<td align="center">September 3rd</td>
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<td>923. <a href="https://leetcode.com/problems/3sum-with-multiplicity/">3Sum With Multiplicity</a></td>
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<a href="#two-pointers">Two Pointers</a>
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</td>
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</tr>
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<tr>
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<td align="center">August 30th</td>
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<td>121. <a href="https://leetcode.com/problems/best-time-to-buy-and-sell-stock/">Best Time to Buy and Sell Stock</a></td>
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<td align="center">$\text{\color{TealBlue}Easy}$</td>
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<td align="center">
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/121.%20Best%20Time%20to%20Buy%20and%20Sell%20Stock/BestTimeToBuyAndSellStock_DynamicProgramming.java">Dynamic Programming</a>
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</td>
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<td align="center">
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<a href="#array">Array</a>,
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<a href="#dynamic-programming">Dynamic Programming</a>
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</td>
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</tr>
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<tr>
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<td align="center">August 29th</td>
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<td>121. <a href="https://leetcode.com/problems/best-time-to-buy-and-sell-stock/">Best Time to Buy and Sell Stock</a></td>
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<td align="center">$\text{\color{TealBlue}Easy}$</td>
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<td align="center">
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/121.%20Best%20Time%20to%20Buy%20and%20Sell%20Stock/BestTimeToBuyAndSellStock.java">Array</a>
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</td>
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<td align="center">
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<a href="#array">Array</a>
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</td>
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</tr>
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</table>
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</br>
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<hr>
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<td align="center">923</td>
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<td><a href="https://leetcode.com/problems/3sum-with-multiplicity/">3Sum With Multiplicity</a></td>
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<td align="center">Java with
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Counting.java">Counting</a> or
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_HashTable.java">Hash Table</a>
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Counting.java">Counting</a>
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_HashTable.java">Hash Table</a> or
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Sorting_TwoPointers.java">Sorting & Two Pointers</a>
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</td>
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<td align="center">$\text{\color{Dandelion}Medium}$</td>
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<td align="center">
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<a href="#array">Array</a>,
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<a href="#counting">Counting</a>,
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<a href="#hash-table">Hash Table</a>
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<a href="#hash-table">Hash Table</a>,
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<a href="#sorting">Sorting</a>,
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<a href="#two-pointers">Two Pointers</a>
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</td>
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<td></td>
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</tr>
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<td align="center">
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<a href="#array">Array</a>,
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<a href="#counting">Counting</a>,
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<a href="#hash-table">Hash Table</a>
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<a href="#hash-table">Hash Table</a>,
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<a href="#sorting">Sorting</a>,
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<a href="#two-pointers">Two Pointers</a>
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</td>
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<td>Solution Using
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_HashTable.java"><em>Hash Table</em></a>
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_HashTable.java"><em>Hash Table</em></a> or
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Sorting_TwoPointers.java"><em>Sorting & Two Pointers</em></a>
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</td>
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</tr>
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<td align="center">
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<a href="#array">Array</a>,
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<a href="#counting">Counting</a>,
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<a href="#hash-table">Hash Table</a>
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<a href="#hash-table">Hash Table</a>,
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<a href="#sorting">Sorting</a>,
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<a href="#two-pointers">Two Pointers</a>
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</td>
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<td>Solution Using
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Counting.java"><em>Counting</em></a>
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Counting.java"><em>Counting</em></a> or
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Sorting_TwoPointers.java"><em>Sorting & Two Pointers</em></a>
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</td>
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</tr>
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</td>
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<td></td>
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</tr>
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<tr>
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<td align="center">923</td>
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<td><a href="https://leetcode.com/problems/3sum-with-multiplicity/">3Sum With Multiplicity</a></td>
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<td align="center">
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Sorting_TwoPointers.java">Java</a>
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</td>
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<td align="center">$\text{\color{Dandelion}Medium}$</td>
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<td align="center">
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<a href="#array">Array</a>,
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<a href="#counting">Counting</a>,
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<a href="#hash-table">Hash Table</a>,
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<a href="#sorting">Sorting</a>,
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<a href="#two-pointers">Two Pointers</a>
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</td>
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<td>Solution Using
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Counting.java"><em>Counting</em></a>
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_HashTable.java"><em>Hash Table</em></a>
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</td>
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</tr>
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<tr>
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<td align="center">948</td>
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<td><a href="https://leetcode.com/problems/bag-of-tokens/">Bag of Tokens</a></td>
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</td>
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<td></td>
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</tr>
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<tr>
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<td align="center">923</td>
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<td><a href="https://leetcode.com/problems/3sum-with-multiplicity/">3Sum With Multiplicity</a></td>
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<td align="center">
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Sorting_TwoPointers.java">Java</a>
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</td>
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<td align="center">$\text{\color{Dandelion}Medium}$</td>
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<td align="center">
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<a href="#array">Array</a>,
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<a href="#counting">Counting</a>,
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<a href="#hash-table">Hash Table</a>,
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<a href="#sorting">Sorting</a>,
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<a href="#two-pointers">Two Pointers</a>
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</td>
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<td>Solution Using
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Counting.java"><em>Counting</em></a>
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_HashTable.java"><em>Hash Table</em></a>
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</td>
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</tr>
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<td align="center">948</td>
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<td><a href="https://leetcode.com/problems/bag-of-tokens/">Bag of Tokens</a></td>

‎solutions/923. 3Sum With Multiplicity/ThreeSumWithMultiplicity_Sorting_TwoPointers.java‎

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package com.cheehwatang.leetcode;
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import java.util.Arrays;
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// Time Complexity : O(n^2),
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// where 'n' is the length of 'arr'.
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// We traverse 'arr'. With each 'arr[i]', we use two pointers to traverse to find the triplets.
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// Arrays.sort() function has a time complexity of O(n logn).
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//
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// Space Complexity : O(1),
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// as the auxiliary space used is independent of the input 'arr'.
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public class ThreeSumWithMultiplicity_Sorting_TwoPointers {
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// Approach:
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// Using sorting and two pointers to traverse the sorted array and check each number if they sum to 'target'.
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// Note that, i < j < k and arr[i] + arr[j] + arr[k] == target,
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// do not require the index as the sum is not dependent on the index, so sorting is fine.
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public int threeSumMulti(int[] arr, int target) {
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int n = arr.length;
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Arrays.sort(arr);
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long count = 0;
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// With each 'i', use two pointers 'j' and 'k' to traverse the remaining numbers to the right of 'i'.
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for (int i = 0; i < n - 2; i++) {
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// If the smallest number is greater than 'target',
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// then the remaining numbers (which are greater) are impossible to sum to be equal to 'target'.
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if (arr[i] + arr[i + 1] + arr[i + 2] > target) break;
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// If the largest number is less than 'target', meaning we need to increase 'i' to get a larger number.
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if (arr[i] + arr[n - 1] + arr[n - 2] < target) continue;
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// After the check, traverse with 'j' and 'k' from both ends.
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int j = i + 1;
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int k = n - 1;
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while (j < k) {
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int sum = arr[i] + arr[j] + arr[k];
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// Move 'j' to right if sum is less than target.
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if (sum < target) j++;
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// Move 'k' to left if sum is greater than target.
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else if (sum > target) k--;
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// If it is equal, keep track of the frequency for both 'arr[j]' and 'arr[k]'.
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else {
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int countJ = 1;
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while (j < k && arr[j] == arr[j + 1]) {
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j++;
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countJ++;
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}
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int countK = 1;
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while (j < k && arr[k] == arr[k - 1]) {
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k--;
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countK++;
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}
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// If both are same, get the geometric sum for 'countJ' + 'countK' - 1.
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// Example: [1,2,2,2,2], target = 5. With arr[i] = 1, arr[j] == arr[k] = 2.
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// Note that the "j < k" will break with 'j' overlapping with 'k'.
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// Thus, 'countJ' = 4 and 'countK' = 1.
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// 'countJ' + 'countK' - 1 = 4, which results in 4 * 3 / 2 = 6 possible combinations.
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if (arr[j] == arr[k]) {
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int frequency = countJ + countK - 1;
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count += (long) frequency * (frequency - 1) / 2;
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}
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// If they are different, the count increase by the multiplication for both.
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// Example: [1,2,2,3,3], target = 6. With arr[i] = 1, arr[j] = 2 and arr[k] = 3.
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// There are 2 * 2 = 4 possible combinations for the 2 and 3.
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else
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count += (long) countJ * countK;
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// Once done, move both pointers to continue check the other numbers.
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j++;
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k--;
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}
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}
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}
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return (int) (count % (1e9 + 7));
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}
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}

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