P163、面试题29：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。

思路：

解法一：基于partition函数的O(n)算法。

        先用partition函数对数组进行交换修改，然后对数组里的无效情况进行判断，还有计算通过partition计算出来的数字出现的次数是否超过一半。

解法二：数组中有一个数字出现的次数超过数组长度的一半，也就是说它出现的次数比其他所有数字出现次数的和还要多。因此我们可以考虑在遍历数组的时候保存两个值：一个是数组中的一个数字，一个是次数。当我们遍历到下一个数字的时候，如果下一个数字和我们之前保存的数字相同，则次数加1,；如果下一个数字和我们之前保存的数字不同，则次数减1,。如果次数为0，我们需要保存下一个数字，并把次数设为1.由于我们要找的数字出现的次数比其他所有数字出现的次数之和还要多，那么要找的数字肯定是最后一次把次数设为1时对应的数字。

 

测试用例：

1）功能测试（输入的数组中存在一个出现次数超过数组长度一半的数字，输入的数组中不存在一个出现次数超过数组长度一半的数字）；

2）特殊输入测试（输入的数组中只有一个数字、输入null指针）。

 

实现代码：

package com.yyq;
/**
 * Created by gao on 15-10-23.
 */
public class MoreThanHalfNumber {
    public static boolean g_bInputInvalid = false;
    public static boolean checkInvalidArray(int[] numbers, int length) {
        g_bInputInvalid = false;
        if (numbers == null || length <= 0) {
            System.out.printf("Numbers is null! Invalid Parameters.");
            g_bInputInvalid = true;
        }
        return g_bInputInvalid;
    }
    public static boolean checkMoreThanHalf(int[] numbers, int length, int number) {
        int times = 0;
        for (int i = 0; i < length; i++) {
            if (number == numbers[i])
                times++;
        }
        boolean isMoreThanHalf = true;
        if (times * 2 <= length) {
            System.out.println("the number you find is not more than half.");
            isMoreThanHalf = false;
            g_bInputInvalid = true;
        }
        return isMoreThanHalf;
    }
    public static int Partition(int[] numbers, int length, int start, int end) {
        if (numbers == null || length <= 0 || start < 0 || end >= length) {
            System.out.printf("Invalid Parameters!");
            return -1;
        }
        int index = numbers[start];
        while (start < end) {
            while (start < end && numbers[end] >= index) end--;
            numbers[start] = numbers[end];
            while (start < end && numbers[start] <= index) start++;
            numbers[end] = numbers[start];
        }
        numbers[start] = index;
        return start;
    }
    //==================方法一:partition========================
    public static 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) {
            if (index > middle) {
                end = index - 1;
                index = Partition(numbers, length, start, end);
            } else {
                start = index + 1;
                index = Partition(numbers, length, start, end);
            }
        }
        int result = numbers[middle];
        if (!checkMoreThanHalf(numbers, length, result)) {
            result = 0;
        }
        return result;
    }
    public static int moreThanHalfNum_solution2(int[] numbers, int length) {
        if (checkInvalidArray(numbers, length)) {
            return 0;
        }
        int result = numbers[0];
        int times = 1;
        for(int i = 1; i < length; i++){
            if (times == 0){
                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====================
    public static void Test(String testName, int[] numbers, int length, int expectedValue, boolean expectedFlag)
    {
        if(testName != null)
            System.out.println("\n"+testName+" begins: ");
        int[] copy = new int[length];
        for(int i = 0; i < length; ++i)
            copy[i] = numbers[i];
        System.out.printf("Test for solution1: ");
        int result = moreThanHalfNum_solution1(numbers, length);
        if(result == expectedValue && g_bInputInvalid == expectedFlag)
            System.out.println("Passed.");
        else
            System.out.println("Failed.");
        System.out.printf("Test for solution2: ");
        result = moreThanHalfNum_solution2(copy, length);
        if(result == expectedValue && g_bInputInvalid == expectedFlag)
            System.out.println("Passed.");
        else
            System.out.println("Failed.");
         copy = null;
    }
    // 存在出现次数超过数组长度一半的数字
    public static void Test1()
    {
        int numbers[] = {1, 2, 3, 2, 2, 2, 5, 4, 2};
        Test("Test1", numbers, numbers.length, 2, false);
    }
    // 不存在出现次数超过数组长度一半的数字
    public static void Test2()
    {
        int numbers[] = {1, 2, 3, 2, 4, 2, 5, 2, 3};
        Test("Test2", numbers, numbers.length, 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
    public static void Test3()
    {
        int numbers[] = {2, 2, 2, 2, 2, 1, 3, 4, 5};
        Test("Test3", numbers, numbers.length, 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
    public static void Test4()
    {
        int numbers[] = {1, 3, 4, 5, 2, 2, 2, 2, 2};
        Test("Test4", numbers, numbers.length, 2, false);
    }
    // 数组为1个元素
    public static void Test5()
    {
        int numbers[] = {1};
        Test("Test5", numbers, 1, 1, false);
    }
    // 输入空指针
    public static void Test6()
    {
        Test("Test6", null, 0, 0, true);
    }
    public static void main(String[] args)
    {
        Test1();
        Test2();
        Test3();
        Test4();
        Test5();
        Test6();
    }
}

 

输出结果：

 

Test1 begins:

Test for solution1: Passed.

Test for solution2: Passed.

 

Test2 begins:

Test for solution1: the number you find is not more than half.

Passed.

Test for solution2: the number you find is not more than half.

Passed.

 

Test3 begins:

Test for solution1: Passed.

Test for solution2: Passed.

 

Test4 begins:

Test for solution1: Passed.

Test for solution2: Passed.

 

Test5 begins:

Test for solution1: Passed.

Test for solution2: Passed.

 

Test6 begins:

Test for solution1: Numbers is null! Invalid Parameters.Passed.

Test for solution2: Numbers is null! Invalid Parameters.Passed.

 

Process finished with exit code 0