Q229

Author: nishant0708

dsa-solutions/lc-solutions/0200-0299/0229-Majority-Element.md

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+---
+id: majority-element-II
+title: Majority Element II
+sidebar_label: 0229-Majority-Element-II
+tags:
+- Arrays
+- Counting
+- C++
+- Java
+- Python
+description: "This document provides a solution to the Majority Element II problem, where we need to find all elements that appear more than ⌊ n/3 ⌋ times."
+---
+
+## Problem
+
+Given an integer array of size n, find all elements that appear more than ⌊ n/3 ⌋ times.
+
+### Examples
+
+**Example 1:**
+
+Input: nums = [3,2,3]  
+Output: [3]
+
+**Example 2:**
+
+Input: nums = [1]  
+Output: [1]
+
+**Example 3:**
+
+Input: nums = [1,2]  
+Output: [1,2]
+
+### Constraints
+
+- $1 \leq nums.length \leq 5 \times 10^4$
+- $-10^9 \leq nums[i] \leq 10^9$
+
+### Approach
+
+To solve this problem, we can use the Boyer-Moore Voting Algorithm, which efficiently finds the majority elements in linear time and constant space. The algorithm can be summarized in the following steps:
+
+1. **First Pass**:
+   - Use two counters and two candidate variables to identify the potential majority elements.
+   - Iterate through the array, updating the candidates and their counts accordingly.
+
+2. **Second Pass**:
+   - Verify the candidates by counting their occurrences in the array.
+
+### Solution
+
+#### Code in Different Languages
+
+<Tabs>
+<TabItem value="cpp" label="C++">
+<SolutionAuthor name="@Vipullakum007"/>
+```cpp
+#include <vector>
+#include <iostream>
+
+using namespace std;
+
+vector<int> majorityElement(vector<int>& nums) {
+    int n = nums.size();
+    if (n == 0) return {};
+    
+    int candidate1 = 0, candidate2 = 1, count1 = 0, count2 = 0;
+    
+    // First pass to find potential candidates
+    for (int num : nums) {
+        if (num == candidate1) {
+            count1++;
+        } else if (num == candidate2) {
+            count2++;
+        } else if (count1 == 0) {
+            candidate1 = num;
+            count1 = 1;
+        } else if (count2 == 0) {
+            candidate2 = num;
+            count2 = 1;
+        } else {
+            count1--;
+            count2--;
+        }
+    }
+    
+    // Second pass to confirm the candidates
+    count1 = count2 = 0;
+    for (int num : nums) {
+        if (num == candidate1) count1++;
+        if (num == candidate2) count2++;
+    }
+    
+    vector<int> result;
+    if (count1 > n / 3) result.push_back(candidate1);
+    if (count2 > n / 3) result.push_back(candidate2);
+    
+    return result;
+}
+
+int main() {
+    vector<int> nums = {3,2,3};
+    vector<int> result = majorityElement(nums);
+    for (int num : result) {
+        cout << num << " ";
+    }
+}
+</TabItem>
+<TabItem value="java" label="Java">
+<SolutionAuthor name="@Vipullakum007"/>
+import java.util.*;
+
+public class MajorityElementII {
+    public static List<Integer> majorityElement(int[] nums) {
+        int n = nums.length;
+        if (n == 0) return Collections.emptyList();
+        
+        int candidate1 = 0, candidate2 = 1, count1 = 0, count2 = 0;
+        
+        // First pass to find potential candidates
+        for (int num : nums) {
+            if (num == candidate1) {
+                count1++;
+            } else if (num == candidate2) {
+                count2++;
+            } else if (count1 == 0) {
+                candidate1 = num;
+                count1 = 1;
+            } else if (count2 == 0) {
+                candidate2 = num;
+                count2 = 1;
+            } else {
+                count1--;
+                count2--;
+            }
+        }
+        
+        // Second pass to confirm the candidates
+        count1 = count2 = 0;
+        for (int num : nums) {
+            if (num == candidate1) count1++;
+            if (num == candidate2) count2++;
+        }
+        
+        List<Integer> result = new ArrayList<>();
+        if (count1 > n / 3) result.add(candidate1);
+        if (count2 > n / 3) result.add(candidate2);
+        
+        return result;
+    }
+
+    public static void main(String[] args) {
+        int[] nums = {3, 2, 3};
+        List<Integer> result = majorityElement(nums);
+        System.out.println(result);
+    }
+}
+</TabItem>
+<TabItem value="python" label="Python">
+<SolutionAuthor name="@Vipullakum007"/>
+def majorityElement(nums):
+    n = len(nums)
+    if n == 0:
+        return []
+    
+    candidate1, candidate2, count1, count2 = 0, 1, 0, 0
+    
+    # First pass to find potential candidates
+    for num in nums:
+        if num == candidate1:
+            count1 += 1
+        elif num == candidate2:
+            count2 += 1
+        elif count1 == 0:
+            candidate1 = num
+            count1 = 1
+        elif count2 == 0:
+            candidate2 = num
+            count2 = 1
+        else:
+            count1 -= 1
+            count2 -= 1
+    
+    # Second pass to confirm the candidates
+    count1, count2 = 0, 0
+    for num in nums:
+        if num == candidate1:
+            count1 += 1
+        elif num == candidate2:
+            count2 += 1
+    
+    result = []
+    if count1 > n / 3:
+        result.append(candidate1)
+    if count2 > n / 3:
+        result.append(candidate2)
+    
+    return result
+
+nums = [3, 2, 3]
+print(majorityElement(nums))
+</TabItem>
+</Tabs>
+
+Complexity Analysis
+
+Time Complexity: O(N)
+Reason: We perform two passes through the array, each requiring linear time.
+
+Space Complexity: O(1)
+Reason: We use a constant amount of extra space for counters and candidates.
+
+This solution efficiently finds all elements that appear more than ⌊ n/3 ⌋ times using the Boyer-Moore Voting Algorithm. The time complexity is linear, and the space complexity is constant, making it suitable for large input sizes.
+
+References
+LeetCode Problem: Majority Element II
+Authors GeeksforGeeks Profile: Vipul lakum