From e6306ba2c0669bb2ea1b32f8b025d873bf93a1f3 Mon Sep 17 00:00:00 2001
From: Ishita Mukherjee <ishitam299@gmail.com>
Date: Sun, 21 Jul 2024 23:18:21 +0530
Subject: [PATCH] Solution of Common in 3 Sorted Arrays from gfg is added

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+---
+id: common-in-3-sorted-arrays
+title: Common In 3 Sorted Arrays
+sidebar_label: Common-In-3-Sorted-Arrays
+tags:
+  - Searching
+  - Algorithms
+description: "This tutorial covers the solution to the Common in 3 sorted arrays problem from the GeeksforGeeks."
+---
+## Problem Description
+
+You are given three arrays sorted in increasing order. Find the elements that are common in all three arrays.
+If there are no such elements return an empty array. In this case, the output will be -1.
+
+## Examples
+
+**Example 1:**
+
+```
+Input: arr1 = [1, 5, 10, 20, 40, 80] , arr2 = [6, 7, 20, 80, 100] , arr3 = [3, 4, 15, 20, 30, 70, 80, 120]
+Output: [20, 80]
+Explanation: 20 and 80 are the only common elements in arr, brr and crr.
+```
+
+**Example 2:**
+
+```
+Input: arr1 = [1, 2, 3, 4, 5] , arr2 = [6, 7] , arr3 = [8,9,10]
+Output: [-1]
+Explanation: There are no common elements in arr, brr and crr.
+```
+
+
+Expected Time Complexity: O(n)
+
+Expected Auxiliary Space: O(n)
+
+## Constraints
+
+* `-10^5 <= arr1i , arr2i , 1arr3i <= 10^5`
+
+## Problem Explanation
+
+The task is to traverse the arrays and find the common element.
+
+## Code Implementation
+
+### C++ Solution
+
+```cpp
+
+#include <vector>
+#include <algorithm>
+
+std::vector<int> commonElements(std::vector<int> arr1, std::vector<int> arr2, std::vector<int> arr3) {
+  std::vector<int> result;
+  int i = 0, j = 0, k = 0;
+  while (i < arr1.size() && j < arr2.size() && k < arr3.size()) {
+    if (arr1[i] == arr2[j] && arr2[j] == arr3[k]) {
+      result.push_back(arr1[i]);
+      i++;
+      j++;
+      k++;
+    } else {
+      if (arr1[i] <= arr2[j] && arr1[i] <= arr3[k]) {
+        i++;
+      } else if (arr2[j] <= arr1[i] && arr2[j] <= arr3[k]) {
+        j++;
+      } else {
+        k++;
+      }
+    }
+  }
+
+  return result;
+}
+
+
+```
+
+```java
+import java.util.ArrayList;
+import java.util.List;
+
+public class Main {
+  public static List<Integer> commonElements(List<Integer> arr1, List<Integer> arr2, List<Integer> arr3) {
+    List<Integer> result = new ArrayList<>();
+    int i = 0, j = 0, k = 0;
+    while (i < arr1.size() && j < arr2.size() && k < arr3.size()) {
+      if (arr1.get(i) == arr2.get(j) && arr2.get(j) == arr3.get(k)) {
+        result.add(arr1.get(i));
+        i++;
+        j++;
+        k++;
+      } else {
+        if (arr1.get(i) <= arr2.get(j) && arr1.get(i) <= arr3.get(k)) {
+          i++;
+        } else if (arr2.get(j) <= arr1.get(i) && arr2.get(j) <= arr3.get(k)) {
+          j++;
+        } else {
+          k++;
+        }
+      }
+    }
+
+    return result;
+  }
+}
+
+
+
+
+```
+
+```python
+
+def commonElements(arr1, arr2, arr3):
+  result = []
+  i = j = k = 0
+
+  while i < len(arr1) and j < len(arr2) and k < len(arr3):
+    if arr1[i] == arr2[j] == arr3[k]:
+      result.append(arr1[i])
+      i += 1
+      j += 1
+      k += 1
+    else:
+      if arr1[i] <= arr2[j] and arr1[i] <= arr3[k]:
+        i += 1
+      elif arr2[j] <= arr1[i] and arr2[j] <= arr3[k]:
+        j += 1
+      else:
+        k += 1
+
+  return result
+
+
+```
+
+```javascript
+function commonElements(arr1, arr2, arr3) {
+  const result = [];
+  const i = j = k = 0;
+
+  while (i < arr1.length && j < arr2.length && k < arr3.length) {
+    if (arr1[i] === arr2[j] && arr2[j] === arr3[k]) {
+      result.push(arr1[i]);
+      i++;
+      j++;
+      k++;
+    } else {
+      if (arr1[i] <= arr2[j] && arr1[i] <= arr3[k]) {
+        i++;
+      } else if (arr2[j] <= arr1[i] && arr2[j] <= arr3[k]) {
+        j++;
+      } else {
+        k++;
+      }
+    }
+  }
+
+  return result.length ? result : [-1];
+}
+
+
+```
+
+## Solution Logic:
+
+1. Initialize three pointers, one for each array, at the beginning of the arrays.
+2. Compare the elements at the current pointers. If they are equal, add the element to the result array and increment all three pointers.
+3. If the elements are not equal, increment the pointer of the array with the smallest current element.
+4. Repeat steps 2-3 until one of the arrays is exhausted.
+5. Return the result array.
+
+
+
+## Time Complexity
+
+* The time complexity is $O(N^2)$ where n is the length of the shortest array. This is because in the worst case, we need to iterate through all elements of the shortest array.
+
+
+## Space Complexity
+
+* The auxiliary space complexity is $O(m)$ where m is the number of common elements found. This is because we store the common elements in the result array.
+