LeetCode169 Majority Element, LintCode47 Majority Number II, LeetCode229 Majority Element II, LintCode48 Majority Number III

LeetCode169. Majority Element

Given an array of size n, find the majority element. The majority element is the element that appears more than ⌊ n/2 ⌋ times. （Easy）

You may assume that the array is non-empty and the majority element always exist in the array.

分析：

抵消的思想，维护一个result和count,与result相同则count++，否则count--，到0时更新result的值，由于主元素个数较多，所有最后一定能留下。

代码：

class Solution {
public:
    int majorityElement(vector<int>& nums) {
        int result = 0;
        int count = 0;
        for (int i = 0; i < nums.size(); ++i) {
            if (nums[i] == result && count != 0) {
                count++;
            }
            else if (count == 0) {
                result = nums[i];
                count = 1;
            }
            else {
                count--;
            }
        }
        return result;
    }
};

LintCode47. Majority NumberII

Given an array of integers, the majority number is the number that occurs more than 1/3 of the size of the array. （Medium）

Find it.

Notice : There is only one majority number in the array. 

分析：

同majority number1的思路相似，维护两个result和count，相同则对相应count操作，不同则均减一；

注意最后剩下两个元素，并不一定count值大的就一定是出现次数多的（可能另一个参与抵消过多），所以需要重新遍历一遍，对这个两个数比较出现次数大小。

代码：

class Solution {
public:
    /**
     * @param nums: A list of integers
     * @return: The majority number occurs more than 1/3.
     */
    int majorityNumber(vector<int> nums) {
        // write your code here
        int candidate1 = 0, candidate2 = 0;
        int count1 = 0, count2 = 0;
        for (int i = 0; i < nums.size(); ++i) {
            if (nums[i] == candidate1 && count1 != 0) {
                count1++;
            } 
            else if (nums[i] == candidate2 && count2 != 0) {
                count2++;
            }
            else if (count1 == 0) {
                candidate1 = nums[i];
                count1 = 1;
            }
            else if (count2 == 0) {
                candidate2 = nums[i];
                count2 = 1;
            }
            else {
                count1--;
                count2--;
            }
        }
        count1 = 0;
        count2 = 0;
        for (int i = 0; i < nums.size(); ++i) {
            if (nums[i] == candidate1) {
                count1++;
            }
            else if (nums[i] == candidate2) {
                count2++;
            }
        }
        return count1 > count2 ? candidate1 : candidate2;
    }
};

LeetCode229. Majority Element II

Given an integer array of size n, find all elements that appear more than ⌊ n/3 ⌋ times. The algorithm should run in linear time and in O(1) space.（Medium）

分析：

这个与lintcode中的majority number2基本相似，只是要求找到所有的大于n / 3次的元素（至多也就是两个）；

所以最后一步从比较两个canditate的count大小，变成将这两个count与 size() / 3比较。

代码：

class Solution {
public:
    vector<int> majorityElement(vector<int>& nums) {
        int candidate1 = 0, candidate2 = 0;
        int count1 = 0, count2 = 0;
        for (int i = 0; i < nums.size(); ++i) {
            if (nums[i] == candidate1 && count1 != 0) {
                count1++;
            } 
            else if (nums[i] == candidate2 && count2 != 0) {
                count2++;
            }
            else if (count1 == 0) {
                candidate1 = nums[i];
                count1 = 1;
            }
            else if (count2 == 0) {
                candidate2 = nums[i];
                count2 = 1;
            }
            else {
                count1--;
                count2--;
            }
        }
        count1 = 0;
        count2 = 0;
        for (int i = 0; i < nums.size(); ++i) {
            if (nums[i] == candidate1) {
                count1++;
            }
            else if (nums[i] == candidate2) {
                count2++;
            }
        }
        vector<int> result;
        if (count1 > nums.size() / 3) {
            result.push_back(candidate1);
        }
        if (count2 > nums.size() / 3) {
            result.push_back(candidate2);
        }
        return result;

    }
};

LintCode48. Majority Number III

Given an array of integers and a number k, the majority number is the number that occurs more than 1/k of the size of the array. （Medium）

Find it.

Notice：There is only one majority number in the array.

分析：

从前一题的1/3变为1/k，道理还是一样，不过这次需要用一个hashmap来维护出现的次数，注意unordered_map插入删除相关操作的写法即可。

尤其hashmap元素个数等于k需要删除的时候，需要维护一个vector存key，如果用iterator边走边删除可能出现位置变化。

代码：

class Solution {
public:
    /**
     * @param nums: A list of integers
     * @param k: As described
     * @return: The majority number
     */
    int majorityNumber(vector<int> nums, int k) {
        // write your code here
        unordered_map<int, int> hash;
        for (int i = 0; i < nums.size(); ++i) {
            if (hash.size() < k) {
                hash[nums[i]]++;
            }
            else {
                vector<int> eraseVec;
                for (auto itr = hash.begin(); itr != hash.end(); ++itr) {
                    (itr -> second)--;
                    if (itr -> second == 0) {
                        eraseVec.push_back(itr -> first);
                    }
                }
                for (int i = 0; i < eraseVec.size(); ++i) {
                    hash.erase(eraseVec[i]);
                }
                hash[nums[i]]++;
            }
        }
        for (auto& n : hash) {
            n.second = 0;
        }
        for (int i = 0; i < nums.size(); ++i) {
            if (hash.find(nums[i]) != hash.end()) {
                hash[nums[i]]++;
                if (hash[nums[i]] > nums.size() / k) {
                    return nums[i];
                }
            }
        }
        return -1;
    }
};