一、题目描述

二、解题思路

• 既然所有数字都在$[0,n-1)$范围内，那么一个下标一定对应着一个值，且该值与下标最终一定相等，一个萝呗占一个坑。
• 如果比较过程中，下标和值不等，那么就交换理论上与值唯一匹配的那个下标的值（$a[a[i]]$）和当前的值（$a[i]$），不停地交换，直到它们相等。
• 如果在这一过程中（下标和值此时仍然不匹配），理论上与值唯一匹配的那个下标的值$a[a[i]]$）和当前的值（$a[i]$）相等，那说明遇到了两个相等的值，于是直接返回
• 默认返回$-1$

三、解题代码

class Solution {
   
public:
    int findRepeatNumber(vector<int>& a) {
   
        auto len = a.size();
        for(size_t i = 0; i < len; i++){
   
            while(a[i] != i){
   
            //if(a[i] != i){ //由第二点，不能为if
                if(a[i] == a[a[i]])
                    return a[i];
                swap(a[i], a[a[i]]);
            }
        }
        return -1;
    }
};

四、测试程序

/******************************************************************* Copyright(c) 2016, Harry He All rights reserved. Distributed under the BSD license. (See accompanying file LICENSE.txt at https://github.com/zhedahht/CodingInterviewChinese2/blob/master/LICENSE.txt) *******************************************************************/

//==================================================================
// 《剑指Offer——名企面试官精讲典型编程题》代码
// 作者：何海涛
//==================================================================

// 面试题3（一）：找出数组中重复的数字
// 题目：在一个长度为n的数组里的所有数字都在0到n-1的范围内。数组中某些数字是重复的，但不知道有几个数字重复了，
// 也不知道每个数字重复了几次。请找出数组中任意一个重复的数字。例如，如果输入长度为7的数组{2, 3, 1, 0, 2, 5, 3}，
// 那么对应的输出是重复的数字2或者3。

#include <cstdio>
// 参数:
// numbers: 一个整数数组
// length: 数组的长度
// duplication: (输出) 数组中的一个重复的数字
// 返回值:
// true - 输入有效，并且数组中存在重复的数字
// false - 输入无效，或者数组中没有重复的数字
bool duplicate(int numbers[], int length, int *duplication)
{
   
    if (length <= 0 || numbers == nullptr)
        return false;
    for (int i = 0; i < length; i++)
    {
   
        if (numbers[i] < 0 || numbers[i] > length - 1)
            return false;
    }
    for (int i = 0; i < length; ++i)
    {
   
        while (numbers[i] != i)
        {
   
            if (numbers[i] == numbers[numbers[i]])
            {
   
                *duplication = numbers[i];
                return true;
            }
            auto tmp = numbers[i];
            numbers[i] = numbers[tmp];
            numbers[tmp] = tmp;
        }
    }
    return false;
}
// ====================测试代码====================
bool contains(int array[], int length, int number)
{
   
    for (int i = 0; i < length; ++i)
    {
   
        if (array[i] == number)
            return true;
    }

    return false;
}

void test(char *testName, int numbers[], int lengthNumbers, int expected[], int expectedExpected, bool validArgument)
{
   
    printf("%s begins: ", testName);

    int duplication;
    bool validInput = duplicate(numbers, lengthNumbers, &duplication);

    if (validArgument == validInput)
    {
   
        if (validArgument)
        {
   
            if (contains(expected, expectedExpected, duplication))
                printf("Passed.\n");
            else
                printf("FAILED.\n");
        }
        else
            printf("Passed.\n");
    }
    else
        printf("FAILED.\n");
}

// 重复的数字是数组中最小的数字
void test1()
{
   
    int numbers[] = {
   2, 1, 3, 1, 4};
    int duplications[] = {
   1};
    test("Test1", numbers, sizeof(numbers) / sizeof(int), duplications, sizeof(duplications) / sizeof(int), true);
}

// 重复的数字是数组中最大的数字
void test2()
{
   
    int numbers[] = {
   2, 4, 3, 1, 4};
    int duplications[] = {
   4};
    test("Test2", numbers, sizeof(numbers) / sizeof(int), duplications, sizeof(duplications) / sizeof(int), true);
}

// 数组中存在多个重复的数字
void test3()
{
   
    int numbers[] = {
   2, 4, 2, 1, 4};
    int duplications[] = {
   2, 4};
    test("Test3", numbers, sizeof(numbers) / sizeof(int), duplications, sizeof(duplications) / sizeof(int), true);
}

// 没有重复的数字
void test4()
{
   
    int numbers[] = {
   2, 1, 3, 0, 4};
    int duplications[] = {
   -1}; // not in use in the test function
    test("Test4", numbers, sizeof(numbers) / sizeof(int), duplications, sizeof(duplications) / sizeof(int), false);
}

// 没有重复的数字
void test5()
{
   
    int numbers[] = {
   2, 1, 3, 5, 4};
    int duplications[] = {
   -1}; // not in use in the test function
    test("Test5", numbers, sizeof(numbers) / sizeof(int), duplications, sizeof(duplications) / sizeof(int), false);
}

// 无效的输入
void test6()
{
   
    int *numbers = nullptr;
    int duplications[] = {
   -1}; // not in use in the test function
    test("Test6", numbers, 0, duplications, sizeof(duplications) / sizeof(int), false);
}

int main()
{
   
    test1();
    test2();
    test3();
    test4();
    test5();
    test6();
    return 0;
}

五、运行结果

main.cpp: In function 'void test1()':
main.cpp:126:113: warning: ISO C++ forbids converting a string constant to 'char*' [-Wwrite-strings]
     test("Test1", numbers, sizeof(numbers) / sizeof(int), duplications, sizeof(duplications) / sizeof(int), true);
                                                                                                                 ^
main.cpp: In function 'void test2()':
main.cpp:134:113: warning: ISO C++ forbids converting a string constant to 'char*' [-Wwrite-strings]
     test("Test2", numbers, sizeof(numbers) / sizeof(int), duplications, sizeof(duplications) / sizeof(int), true);
                                                                                                                 ^
main.cpp: In function 'void test3()':
main.cpp:142:113: warning: ISO C++ forbids converting a string constant to 'char*' [-Wwrite-strings]
     test("Test3", numbers, sizeof(numbers) / sizeof(int), duplications, sizeof(duplications) / sizeof(int), true);
                                                                                                                 ^
main.cpp: In function 'void test4()':
main.cpp:150:114: warning: ISO C++ forbids converting a string constant to 'char*' [-Wwrite-strings]
     test("Test4", numbers, sizeof(numbers) / sizeof(int), duplications, sizeof(duplications) / sizeof(int), false);
                                                                                                                  ^
main.cpp: In function 'void test5()':
main.cpp:158:114: warning: ISO C++ forbids converting a string constant to 'char*' [-Wwrite-strings]
     test("Test5", numbers, sizeof(numbers) / sizeof(int), duplications, sizeof(duplications) / sizeof(int), false);
                                                                                                                  ^
main.cpp: In function 'void test6()':
main.cpp:166:86: warning: ISO C++ forbids converting a string constant to 'char*' [-Wwrite-strings]
     test("Test6", numbers, 0, duplications, sizeof(duplications) / sizeof(int), false);
                                                                                      ^
Test1 begins: Passed.
Test2 begins: Passed.
Test3 begins: Passed.
Test4 begins: Passed.
Test5 begins: Passed.
Test6 begins: Passed.