算法-4-归并排序-编程知识

归并排序

public class Code01_MergeSort {// 递归方法实现public static void mergeSort1(int[] arr) {if (arr == null || arr.length < 2) {return;}process(arr, 0, arr.length - 1);}// 请把arr[L..R]排有序// l...r N// T(N) = 2 * T(N / 2) + O(N)// O(N * logN)public static void process(int[] arr, int L, int R) {if (L == R) { // base casereturn;}int mid = L + ((R - L) >> 1);process(arr, L, mid);process(arr, mid + 1, R);merge(arr, L, mid, R);}public static void merge(int[] arr, int L, int M, int R) {int[] help = new int[R - L + 1];int i = 0;int p1 = L;int p2 = M + 1;while (p1 <= M && p2 <= R) {help[i++] = arr[p1] <= arr[p2] ? arr[p1++] : arr[p2++];}// 要么p1越界了，要么p2越界了while (p1 <= M) {help[i++] = arr[p1++];}while (p2 <= R) {help[i++] = arr[p2++];}for (i = 0; i < help.length; i++) {arr[L + i] = help[i];}}// 非递归方法实现public static void mergeSort2(int[] arr) {if (arr == null || arr.length < 2) {return;}int N = arr.length;// 步长int mergeSize = 1;while (mergeSize < N) { // log N// 当前左组的，第一个位置int L = 0;while (L < N) {if (mergeSize >= N - L) {//左边都凑不够步长直接退出break;}int M = L + mergeSize - 1;int R = M + Math.min(mergeSize, N - M - 1);//如果没超那就是r=m+步长merge(arr, L, M, R);L = R + 1;}// 防止溢出，N可能很大，步长每次要*2，如果步长大于N/2再成二就溢出if (mergeSize > N / 2) {break;}mergeSize <<= 1;}}// 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;}// 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;System.out.println("测试开始");for (int i = 0; i < testTime; i++) {int[] arr1 = generateRandomArray(maxSize, maxValue);int[] arr2 = copyArray(arr1);mergeSort1(arr1);mergeSort2(arr2);if (!isEqual(arr1, arr2)) {System.out.println("出错了！");printArray(arr1);printArray(arr2);break;}}System.out.println("测试结束");}}

求小和

public class Code02_SmallSum {public static int smallSum(int[] arr) {if (arr == null || arr.length < 2) {return 0;}return process(arr, 0, arr.length - 1);}// arr[L..R]既要排好序，也要求小和返回// 所有merge时，产生的小和，累加// 左 排序   merge// 右 排序  merge// mergepublic static int process(int[] arr, int l, int r) {if (l == r) {return 0;}// l < rint mid = l + ((r - l) >> 1);return process(arr, l, mid) + process(arr, mid + 1, r) + merge(arr, l, mid, r);}public static int merge(int[] arr, int L, int m, int r) {int[] help = new int[r - L + 1];int i = 0;int p1 = L;int p2 = m + 1;int res = 0;while (p1 <= m && p2 <= r) {res += arr[p1] < arr[p2] ? (r - p2 + 1) * arr[p1] : 0;help[i++] = arr[p1] < arr[p2] ? arr[p1++] : arr[p2++];}while (p1 <= m) {help[i++] = arr[p1++];}while (p2 <= r) {help[i++] = arr[p2++];}for (i = 0; i < help.length; i++) {arr[L + i] = help[i];}return res;}// for testpublic static int comparator(int[] arr) {if (arr == null || arr.length < 2) {return 0;}int res = 0;for (int i = 1; i < arr.length; i++) {for (int j = 0; j < i; j++) {res += arr[j] < arr[i] ? arr[j] : 0;}}return res;}// 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;}// 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);if (smallSum(arr1) != comparator(arr2)) {succeed = false;printArray(arr1);printArray(arr2);break;}}System.out.println(succeed ? "Nice!" : "Fucking fucked!");}}

求逆序对

public class Code03_ReversePair {public static int reverPairNumber(int[] arr) {if (arr == null || arr.length < 2) {return 0;}return process(arr, 0, arr.length - 1);}// arr[L..R]既要排好序，也要求逆序对数量返回// 所有merge时，产生的逆序对数量，累加，返回// 左 排序 merge并产生逆序对数量// 右 排序 merge并产生逆序对数量public static int process(int[] arr, int l, int r) {if (l == r) {return 0;}// l < rint mid = l + ((r - l) >> 1);return process(arr, l, mid) + process(arr, mid + 1, r) + merge(arr, l, mid, r);}public static int merge(int[] arr, int L, int m, int r) {int[] help = new int[r - L + 1];int i = help.length - 1;int p1 = m;int p2 = r;int res = 0;while (p1 >= L && p2 > m) {res += arr[p1] > arr[p2] ? (p2 - m) : 0;help[i--] = arr[p1] > arr[p2] ? arr[p1--] : arr[p2--];}while (p1 >= L) {help[i--] = arr[p1--];}while (p2 > m) {help[i--] = arr[p2--];}for (i = 0; i < help.length; i++) {arr[L + i] = help[i];}return res;}// for testpublic static int comparator(int[] arr) {int ans = 0;for (int i = 0; i < arr.length; i++) {for (int j = i + 1; j < arr.length; j++) {if (arr[i] > arr[j]) {ans++;}}}return ans;}// 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;}// 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;System.out.println("测试开始");for (int i = 0; i < testTime; i++) {int[] arr1 = generateRandomArray(maxSize, maxValue);int[] arr2 = copyArray(arr1);if (reverPairNumber(arr1) != comparator(arr2)) {System.out.println("Oops!");printArray(arr1);printArray(arr2);break;}}System.out.println("测试结束");}}

num的右边有多少个数*2后依然小于num，求个数

总思路不变左面求+右边求+总merge


public class Code04_BiggerThanRightTwice {public static int biggerTwice(int[] arr) {if (arr == null || arr.length < 2) {return 0;}return process(arr, 0, arr.length - 1);}public static int process(int[] arr, int l, int r) {if (l == r) {return 0;}// l < rint mid = l + ((r - l) >> 1);return process(arr, l, mid) + process(arr, mid + 1, r) + merge(arr, l, mid, r);}public static int merge(int[] arr, int L, int m, int r) {// [L....M]   [M+1....R]int ans = 0;// 目前囊括进来的数，是从[M+1, windowR)int windowR = m + 1;for (int i = L; i <= m; i++) {while (windowR <= r && arr[i] > (arr[windowR] * 2)) {windowR++;}ans += windowR - m - 1;}int[] help = new int[r - L + 1];int i = 0;int p1 = L;int p2 = m + 1;while (p1 <= m && p2 <= r) {help[i++] = arr[p1] <= arr[p2] ? arr[p1++] : arr[p2++];}while (p1 <= m) {help[i++] = arr[p1++];}while (p2 <= r) {help[i++] = arr[p2++];}for (i = 0; i < help.length; i++) {arr[L + i] = help[i];}return ans;}// for testpublic static int comparator(int[] arr) {int ans = 0;for (int i = 0; i < arr.length; i++) {for (int j = i + 1; j < arr.length; j++) {if (arr[i] > (arr[j] << 1)) {ans++;}}}return ans;}// 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 + 1) * 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;System.out.println("测试开始");for (int i = 0; i < testTime; i++) {int[] arr1 = generateRandomArray(maxSize, maxValue);int[] arr2 = copyArray(arr1);if (biggerTwice(arr1) != comparator(arr2)) {System.out.println("Oops!");printArray(arr1);printArray(arr2);break;}}System.out.println("测试结束");}}