《剑指offer》第三十九题（数组中出现次数超过一半的数字）

// 面试题39：数组中出现次数超过一半的数字
// 题目：数组中有一个数字出现的次数超过数组长度的一半，请找出这个数字。例
// 如输入一个长度为9的数组{1, 2, 3, 2, 2, 2, 5, 4, 2}。由于数字2在数组中
// 出现了5次，超过数组长度的一半，因此输出2。

#include <iostream>
using namespace std;

/*Random Partition*/
int RandomInRange(int min, int max)
{
    int random = rand() % (max - min + 1) + min;
    return random;
}

void Swap(int* num1, int* num2)
{
    int temp = *num1;
    *num1 = *num2;
    *num2 = temp;
}

int Partition(int data[], int length, int start, int end)//快排
{
    if (data == nullptr || length <= 0 || start < 0 || end >= length)
        throw new exception("Invalid Parameters");

    int index = RandomInRange(start, end);//生成随机点
    Swap(&data[index], &data[end]);//放到最后

    int small = start - 1;
    for (index = start; index < end; ++index)//把数列中小于随机点的值放到前面
    {
        if (data[index] < data[end])
        {
            ++small;
            if (small != index)
                Swap(&data[index], &data[small]);
        }
    }

    ++small;
    Swap(&data[small], &data[end]);//然后把随机点放入小于它的值的后面

    return small;
}

bool g_bInputInvalid = false;//使用全局变量处理错误方式

bool CheckInvalidArray(int* numbers, int length)//核对是否是有效函数
{
    g_bInputInvalid = false;
    if (numbers == nullptr && length <= 0)
        g_bInputInvalid = true;

    return g_bInputInvalid;
}

bool CheckMoreThanHalf(int* numbers, int length, int number)//检查number在数列中是否超过一半
{
    int times = 0;
    for (int i = 0; i < length; ++i)
    {
        if (numbers[i] == number)
            times++;
    }

    bool isMoreThanHalf = true;
    if (times * 2 <= length)
    {
        g_bInputInvalid = true;
        isMoreThanHalf = false;
    }

    return isMoreThanHalf;
}

// ====================方法1====================
//受快排启发，进行一轮快排，看本轮的中点是在数组的哪部分，具体分三种情况
int MoreThanHalfNum_Solution1(int* numbers, int length)
{
    if (CheckInvalidArray(numbers, length))
        return 0;

    int middle = length >> 1;
    int start = 0;
    int end = length - 1;
    int index = Partition(numbers, length, start, end);
    while (index != middle)//如果index == middle，那么说明numbers[middle]超过一半，注意这个判断条件中，index和middle不随迭代而改变
    {
        if (index > middle)//如果index != middle，且index > middle，则在index左边
        {
            end = index - 1;
            index = Partition(numbers, length, start, end);
        }
        else//如果index != middle，且index < middle，则在index右边
        {
            start = index + 1;
            index = Partition(numbers, length, start, end);
        }
    }

    int result = numbers[middle];
    if (!CheckMoreThanHalf(numbers, length, result))//必须检查，有可能不是
        result = 0;

    return result;
}

// ====================方法2====================
//这个比较复杂，就是下一值如果和当前值一致，count就+1,否则-1，如果为0，则舍弃记录当前值，改下一值，最后+1的值可能会超过一半
int MoreThanHalfNum_Solution2(int* numbers, int length)
{
    if (CheckInvalidArray(numbers, length))
        return 0;

    int result = numbers[0];//初试为第一个值
    int times = 1;//初试为1
    for (int i = 1; i < length; ++i)
    {
        if (times == 0)//改记录下一值
        {
            result = numbers[i];
            times = 1;
        }
        else if (numbers[i] == result)
            times++;
        else
            times--;
    }

    if (!CheckMoreThanHalf(numbers, length, result))
        result = 0;

    return result;
}

// ====================测试代码====================
void Test(const char* testName, int* numbers, int length, int expectedValue, bool expectedFlag)
{
    if (testName != nullptr)
        printf("%s begins: 
", testName);

    int* copy = new int[length];
    for (int i = 0; i < length; ++i)
        copy[i] = numbers[i];

    printf("Test for solution1: ");
    int result = MoreThanHalfNum_Solution1(numbers, length);
    if (result == expectedValue && g_bInputInvalid == expectedFlag)
        printf("Passed.
");
    else
        printf("Failed.
");

    printf("Test for solution2: ");
    result = MoreThanHalfNum_Solution2(copy, length);
    if (result == expectedValue && g_bInputInvalid == expectedFlag)
        printf("Passed.
");
    else
        printf("Failed.
");

    delete[] copy;
}

// 存在出现次数超过数组长度一半的数字
void Test1()
{
    int numbers[] = { 1, 2, 3, 2, 2, 2, 5, 4, 2 };
    Test("Test1", numbers, sizeof(numbers) / sizeof(int), 2, false);
}

// 不存在出现次数超过数组长度一半的数字
void Test2()
{
    int numbers[] = { 1, 2, 3, 2, 4, 2, 5, 2, 3 };
    Test("Test2", numbers, sizeof(numbers) / sizeof(int), 0, true);
}

// 出现次数超过数组长度一半的数字都出现在数组的前半部分
void Test3()
{
    int numbers[] = { 2, 2, 2, 2, 2, 1, 3, 4, 5 };
    Test("Test3", numbers, sizeof(numbers) / sizeof(int), 2, false);
}

// 出现次数超过数组长度一半的数字都出现在数组的后半部分
void Test4()
{
    int numbers[] = { 1, 3, 4, 5, 2, 2, 2, 2, 2 };
    Test("Test4", numbers, sizeof(numbers) / sizeof(int), 2, false);
}

// 输入空指针
void Test5()
{
    int numbers[] = { 1 };
    Test("Test5", numbers, 1, 1, false);
}

// 输入空指针
void Test6()
{
    Test("Test6", nullptr, 0, 0, true);
}

int main(int argc, char* argv[])
{
    Test1();
    Test2();
    Test3();
    Test4();
    Test5();
    Test6();
    system("pause");
    return 0;
}