三大排序算法&对数器
1.选择排序
Java版
package class01;import java.util.Arrays;public class Code01_SelectionSort {public static void selectionSort(int[] arr) {if (arr == null || arr.length < 2) {return;}// 0 ~ N-1 找到最小值,在哪,放到0位置上// 1 ~ n-1 找到最小值,在哪,放到1 位置上// 2 ~ n-1 找到最小值,在哪,放到2 位置上for (int i = 0; i < arr.length - 1; i++) {int minIndex = i;for (int j = i + 1; j < arr.length; j++) { // i ~ N-1 上找最小值的下标 minIndex = arr[j] < arr[minIndex] ? j : minIndex;}swap(arr, i, minIndex);}}public static void swap(int[] arr, int i, int j) {int tmp = arr[i];arr[i] = arr[j];arr[j] = tmp;}// for testpublic static void comparator(int[] arr) {Arrays.sort(arr);}// for testpublic static int[] generateRandomArray(int maxSize, int maxValue) {// Math.random() [0,1) // Math.random() * N [0,N)// (int)(Math.random() * N) [0, N-1]int[] arr = new int[(int) ((maxSize + 1) * Math.random())];for (int i = 0; i < arr.length; i++) {// [-? , +?]arr[i] = (int) ((maxValue + 1) * Math.random()) - (int) (maxValue * Math.random());}return arr;}// for testpublic static int[] copyArray(int[] arr) {if (arr == null) {return null;}int[] res = new int[arr.length];for (int i = 0; i < arr.length; i++) {res[i] = arr[i];}return res;}// for testpublic static boolean isEqual(int[] arr1, int[] arr2) {if ((arr1 == null && arr2 != null) || (arr1 != null && arr2 == null)) {return false;}if (arr1 == null && arr2 == null) {return true;}if (arr1.length != arr2.length) {return false;}for (int i = 0; i < arr1.length; i++) {if (arr1[i] != arr2[i]) {return false;}}return true;}// for testpublic static void printArray(int[] arr) {if (arr == null) {return;}for (int i = 0; i < arr.length; i++) {System.out.print(arr[i] + " ");}System.out.println();}// for testpublic static void main(String[] args) {int testTime = 500000;int maxSize = 100;int maxValue = 100;boolean succeed = true;for (int i = 0; i < testTime; i++) {int[] arr1 = generateRandomArray(maxSize, maxValue);int[] arr2 = copyArray(arr1);selectionSort(arr1);comparator(arr2);if (!isEqual(arr1, arr2)) {succeed = false;printArray(arr1);printArray(arr2);break;}}System.out.println(succeed ? "Nice!" : "Wrong!");int[] arr = generateRandomArray(maxSize, maxValue);printArray(arr);selectionSort(arr);printArray(arr);}}
C++
#include <iostream>
#include <algorithm>
#include <vector>using namespace std;void selectionSort(vector<int>& arr) {if (arr.size() < 2) {return;}for (int i = 0; i < arr.size() - 1; i++) {int minIndex = i;for (int j = i + 1; j < arr.size(); j++) { // i ~ N-1 上找最小值的下标 minIndex = arr[j] < arr[minIndex] ? j : minIndex;}swap(arr[i], arr[minIndex]);}
}// for test
void comparator(vector<int>& arr) {sort(arr.begin(), arr.end());
}// for test
vector<int> generateRandomArray(int maxSize, int maxValue) {vector<int> arr((size_t)((maxSize + 1) * (double)rand() / RAND_MAX));for (int i = 0; i < arr.size(); i++) {arr[i] = (int)((maxValue + 1) * (double)rand() / RAND_MAX) - (int)(maxValue * (double)rand() / RAND_MAX);}return arr;
}// for test
vector<int> copyArray(const vector<int>& arr) {if (arr.empty()) {return {};}vector<int> res(arr.size());for (size_t i = 0; i < arr.size(); i++) {res[i] = arr[i];}return res;
}// for test
bool isEqual(const vector<int>& arr1, const vector<int>& arr2) {if ((arr1.empty() && !arr2.empty()) || (!arr1.empty() && arr2.empty())) {return false;}if (arr1.empty() && arr2.empty()) {return true;}if (arr1.size() != arr2.size()) {return false;}for (size_t i = 0; i < arr1.size(); i++) {if (arr1[i] != arr2[i]) {return false;}}return true;
}// for test
void printArray(const vector<int>& arr) {if (arr.empty()) {return;}for (const auto& val : arr) {cout << val << " ";}cout << endl;
}// for test
int main() {srand(time(nullptr));int testTime = 500000;int maxSize = 100;int maxValue = 100;bool succeed = true;for (int i = 0; i < testTime; i++) {vector<int> arr1 = generateRandomArray(maxSize, maxValue);vector<int> arr2 = copyArray(arr1);selectionSort(arr1);comparator(arr2);if (!isEqual(arr1, arr2)) {succeed = false;printArray(arr1);printArray(arr2);break;}}cout << (succeed ? "Nice!" : "Wrong!") << endl;vector<int> arr = generateRandomArray(maxSize, maxValue);printArray(arr);selectionSort(arr);printArray(arr);return 0;
}
对数器
1,你想要测的方法a(最优解)
2,实现复杂度不好但是容易实现的方法b(暴力解)
3,实现一个随机样本产生器(长度也随机、值也随机)
4,把方法a和方法b跑相同的输入样本,看看得到的结果是否一样
5,如果有一个随机样本使得比对结果不一致,打印这个出错的样本进行人工干预,改对方法a和方法b
6,当样本数量很多时比对测试依然正确,可以确定方法a(最优解)已经正确。
关键是第5步,找到一个数据量小的错误样本,便于你去带入debug
然后把错误例子带入代码一步一步排查
Print大法、断点技术都可以
对数器的门槛其实是比较高的,因为往往需要在两种不同思路下实现功能相同的两个方法,暴力一个、想象中的最优解是另一个。
以后的很多题目都会用到对数器,几乎可以验证任何方法,尤其在验证贪心、观察规律方面很有用
到时候会丰富很多对数器的实战用法,这里只是一个简单易懂的示例
2.冒泡排序
public class Code02_BubbleSort {public static void bubbleSort(int[] arr) {if (arr == null || arr.length < 2) {return;}// 0 ~ N-1// 0 ~ N-2// 0 ~ N-3for (int e = arr.length - 1; e > 0; e--) { // 0 ~ efor (int i = 0; i < e; i++) {if (arr[i] > arr[i + 1]) {swap(arr, i, i + 1);}}}}// 交换arr的i和j位置上的值public static void swap(int[] arr, int i, int j) {arr[i] = arr[i] ^ arr[j];arr[j] = arr[i] ^ arr[j];arr[i] = arr[i] ^ arr[j];}
3.插入排序(类似打扑克时摸到牌插牌的感觉)
public static void insertionSort(int[] arr) {if (arr == null || arr.length < 2) {return;}// 不只1个数for (int i = 1; i < arr.length; i++) { // 0 ~ i 做到有序for (int j = i - 1; j >= 0 && arr[j] > arr[j + 1]; j--) {swap(arr, j, j + 1);}}}// i和j是一个位置的话,会出错public static void swap(int[] arr, int i, int j) {arr[i] = arr[i] ^ arr[j];arr[j] = arr[i] ^ arr[j];arr[i] = arr[i] ^ arr[j];}
二分
1.在有序数组中确定num存在还是不存在
指针来到中间位置,中间值比n大意味着n-n-1位置都不可能,右指针来到mid-1,在左右之间再次取中间值递归
package class01;import java.util.Arrays;public class Code04_BSExist {public static boolean exist(int[] sortedArr, int num) {if (sortedArr == null || sortedArr.length == 0) {return false;}int L = 0;int R = sortedArr.length - 1;int mid = 0;// L..Rwhile (L < R) { // L..R 至少两个数的时候mid = L + ((R - L) >> 1);if (sortedArr[mid] == num) {return true;} else if (sortedArr[mid] > num) {R = mid - 1;} else {L = mid + 1;}}return sortedArr[L] == num;}// for testpublic static boolean test(int[] sortedArr, int num) {for(int cur : sortedArr) {if(cur == num) {return true;}}return false;}// for testpublic static int[] generateRandomArray(int maxSize, int maxValue) {int[] arr = new int[(int) ((maxSize + 1) * Math.random())];for (int i = 0; i < arr.length; i++) {arr[i] = (int) ((maxValue + 1) * Math.random()) - (int) (maxValue * Math.random());}return arr;}public static void main(String[] args) {int testTime = 500000;int maxSize = 10;int maxValue = 100;boolean succeed = true;for (int i = 0; i < testTime; i++) {int[] arr = generateRandomArray(maxSize, maxValue);Arrays.sort(arr);int value = (int) ((maxValue + 1) * Math.random()) - (int) (maxValue * Math.random());if (test(arr, value) != exist(arr, value)) {succeed = false;break;}}System.out.println(succeed ? "Nice!" : "fuck!");}}
2.在有序数组中找>=num的最左位置
/ 在arr上,找满足>=value的最左位置public static int nearestIndex(int[] arr, int value) {int L = 0;int R = arr.length - 1;int index = -1; // 记录最左的对号while (L <= R) { // 至少一个数的时候int mid = L + ((R - L) >> 1);if (arr[mid] >= value) {index = mid;R = mid - 1;} else {L = mid + 1;}}return index;}
3.最右
// 在arr上,找满足<=value的最右位置public static int nearestIndex(int[] arr, int value) {int L = 0;int R = arr.length - 1;int index = -1; // 记录最右的对号while (L <= R) {int mid = L + ((R - L) >> 1);if (arr[mid] <= value) {index = mid;L = mid + 1;} else {R = mid - 1;}}return index;}
4.寻找最小值,二分搜索不一定发生在有序数组上,
package class01;public class Code06_BSAwesome {public static int getLessIndex(int[] arr) {if (arr == null || arr.length == 0) {return -1; // no exist}if (arr.length == 1 || arr[0] < arr[1]) {return 0;}if (arr[arr.length - 1] < arr[arr.length - 2]) {return arr.length - 1;}int left = 1;int right = arr.length - 2;int mid = 0;while (left < right) {mid = (left + right) / 2;if (arr[mid] > arr[mid - 1]) {right = mid - 1;} else if (arr[mid] > arr[mid + 1]) {left = mid + 1;} else {return mid;}}return left;}}