Add 923. 3Sum With Multiplicity (Counting)

README.md

@@ -27,6 +27,18 @@
     <th>Solution</th>
     <th>Topics</th>
   </tr>
+  <tr>
+    <td align="center">September 2nd</td>
+    <td>923. <a href="https://leetcode.com/problems/3sum-with-multiplicity/">3Sum With Multiplicity</a></td>
+    <td align="center">$\text{\color{Dandelion}Medium}$</td>
+    <td align="center">
+      <a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Counting.java">Counting</a>
+    </td>
+    <td align="center">
+      <a href="#array">Array</a>,
+      <a href="#counting">Counting</a>
+    </td>
+  </tr>
   <tr>
     <td align="center">September 1st</td>
     <td>16. <a href="https://leetcode.com/problems/3sum-closest/">3Sum Closest</a></td>
@@ -76,19 +88,6 @@
       <a href="#array">Array</a>
     </td>
   </tr>
-  <tr>
-    <td align="center">August 28th</td>
-    <td>3. <a href="https://leetcode.com/problems/longest-substring-without-repeating-characters/">Longest Substring Without Repeating Characters</a></td>
-    <td align="center">$\text{\color{Dandelion}Medium}$</td>
-    <td align="center">
-      <a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/3.%20Longest%20Substring%20Without%20Repeating%20Characters/LongestSubstringWithoutRepeatingCharacters_HashTable.java">Hash Table & Sliding Window</a>
-    </td>
-    <td align="center">
-      <a href="#hash-table">Hash Table</a>,
-      <a href="#sliding-window">Sliding Window</a>,
-      <a href="#string">String</a>
-    </td>
-  </tr>
 </table>
 </br>
 <hr>
@@ -952,6 +951,19 @@
     </td>
     <td></td>
   </tr>
+  <tr>
+    <td align="center">923</td>
+    <td><a href="https://leetcode.com/problems/3sum-with-multiplicity/">3Sum With Multiplicity</a></td>
+    <td align="center">
+      <a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Counting.java">Java</a>
+    </td>
+    <td align="center">$\text{\color{Dandelion}Medium}$</td>
+    <td align="center">
+      <a href="#array">Array</a>,
+      <a href="#counting">Counting</a>
+    </td>
+    <td></td>
+  </tr>
   <tr>
     <td align="center">929</td>
     <td><a href="https://leetcode.com/problems/unique-email-addresses/">Unique Email Addresses</a></td>
@@ -3270,6 +3282,19 @@
       <a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/383.%20Ransom%20Note/RansomNote_HashTable.java"><em>Hash Table</em></a>
     </td>
   </tr>
+  <tr>
+    <td align="center">923</td>
+    <td><a href="https://leetcode.com/problems/3sum-with-multiplicity/">3Sum With Multiplicity</a></td>
+    <td align="center">
+      <a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Counting.java">Java</a>
+    </td>
+    <td align="center">$\text{\color{Dandelion}Medium}$</td>
+    <td align="center">
+      <a href="#array">Array</a>,
+      <a href="#counting">Counting</a>
+    </td>
+    <td></td>
+  </tr>
   <tr>
     <td align="center">1497</td>
     <td><a href="https://leetcode.com/problems/check-if-array-pairs-are-divisible-by-k/">Check If Array Pairs Are Divisible by k</a></td>

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

@@ -0,0 +1,53 @@
+package com.cheehwatang.leetcode;
+
+// Time Complexity  : O(n),
+// where 'n' is the length of 'arr'.
+// We traverse 'arr' once to count the frequency of the elements.
+//
+// Space Complexity : O(1),
+// as the auxiliary space used is independent of the input 'arr',
+// with the counting array with size of 101 regardless of the input 'arr'.
+
+public class ThreeSumWithMultiplicity_Counting {
+
+    // Approach:
+    // Using a counting array, get the frequency of all the integers,
+    // then check all the possible combinations to get the sum.
+    // Note that, i < j < k and arr[i] + arr[j] + arr[k] == target,
+    // do not require the index as the sum is not dependent on the index.
+
+    public int threeSumMulti(int[] arr, int target) {
+
+        // With the constraint of 0 <= arr[i] <= 100, count the frequency of all the integers/
+        int[] counting = new int[101];
+        for (int integer : arr) counting[integer]++;
+
+        // Keep the count as long type, so as only need to perform the modulo once at the end.
+        long count = 0;
+
+        // Traverse the counting array in two for-loops to get the value for 'i' and 'j'.
+        for (int i = 0; i <= 100; i++) {
+            for (int j = i; j <= 100; j++) {
+                // Get the k integer to check if it is in the counting array.
+                int k = target - i - j;
+                if (k < 0 || k > 100) continue;
+                if (counting[k] > 0) {
+                    // If the triplet is of the same integers (eg. [1,1,1], target = 3),
+                    // then perform geometric sum for 3 elements.
+                    if (i == k && j == k)
+                        count += (long) counting[i] * (counting[i] - 1) * (counting[i] - 2) / 6;
+                    // If i and j is identical, but different from k (eg. [1,1,2], target = 4),
+                    // then perform geometric sum for i & j, then multiply with k.
+                    else if (i == j)
+                        count += (long) counting[i] * (counting[i] - 1) / 2 * counting[k];
+                    // If both i and j is smaller than k, then get the multiples of all the frequency.
+                    // This is to make sure no duplicates of results
+                    // (eg, [1,2,3], target = 6), only [1,2,3] is counted, but not [2,1,3] or [3,2,1], etc.)
+                    else if (i < k && j < k)
+                        count += (long) counting[i] * counting[j] * counting[k];
+                }
+            }
+        }
+        return (int) (count % (1e9 + 7));
+    }
+}