归并排序流程
1. 归并排序递归实现
代码实现：
public class Mine_MergeSort {// 归并排序 递归实现方式public static void mergeSort(int[] arr) {if (arr == null || arr.length < 2) {return;}process(arr, 0, arr.length - 1);}// 归并排序的递归过程// 递归含义，数组L-R范围上实现有序public static void process(int[] arr, int L, int R) {if (L == R) {return;}// 分治思想 L-mid 左边有序， mid+1 - R右侧有序，然后两个有序数组进行merge整体有序int mid = L + ((R - L) >> 1);process(arr, L, mid);process(arr, mid + 1, R);merge(arr, L, mid, R);}// merge过程，合并两个有序数组public static void merge(int[] arr, int L, int M, int R) {//双指针 + 辅助数组int[] help = new int[R - L + 1];int i = 0;int p1 = L;int p2 = M + 1;//mergewhile (p1 <= M && p2 <= R) {// 谁小拷贝谁，相等先拷贝左边help[i++] = arr[p1] <= arr[p2] ? arr[p1++] : arr[p2++];}while (p1 <= M) {help[i++] = arr[p1++];}while (p2 <= R) {help[i++] = arr[p2++];}//将辅助数组中的值拷贝到arr数组中for (int j = 0; j < help.length; j++) {arr[L + j] = help[j];}}// 测试public static void main(String[] args) {int[] arr = {3, 4, 2, 6, 5, 3, 1, 9, 6, 5, 0};mergeSort(arr);for (int each : arr) {System.out.print(each + " ");}}}
2. 递归排序相关的题目
2.1 小和问题
2.2. 逆序对问题
逆序对
package class04;
/**
* 查找一个数组中有多少个逆序对
* 就是相当于求每一个数右边有多少个数比它小
*/
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 < r
int 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 test
public 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 test
public 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 test
public 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 test
public 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 test
public 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 test
public 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");
}
}
2.3. 右侧大于二倍问题
package class04;
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 < r
int 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 test
public 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 test
public 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 test
public 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 test
public 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 test
public 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 test
public 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");
}
}
2.4 区间和个数
给你一个整数数组 nums 以及两个整数 lower 和 upper 。
求数组中，值位于范围 [lower, upper] （包含 lower 和 upper）之内的 区间和的个数 。
方式一： 暴力解决， 复杂度 O(n2)
public static int countRangeSum(int[] nums, int lower, int upper) {
int countSize = 0;
// 统计给定数组的子数组数
for(int i = 0; i < nums.length; i++){
long sum = 0;
for (int j = i; j < nums.length; j++){
//num[i,j]上求和
sum += nums[j];
if (sum >= lower && sum <= upper){
countSize++;
}
}
}
return countSize;
}
方式二： 归并排序 时间复杂度 O(N * logN)
public static int countRangeSum(int[] nums, int lower, int upper) {
if (nums == null || nums.length == 0) {
return 0;
}
long[] sum = new long[nums.length];
sum[0] = nums[0];
for (int i = 1; i < nums.length; i++) {
sum[i] = sum[i - 1] + nums[i];
}
return process(sum, 0, sum.length - 1, lower, upper);
}
public static int process(long[] sum, int L, int R, int lower, int upper) {
if (L == R) {
return sum[L] >= lower && sum[L] <= upper ? 1 : 0;
}
int M = L + ((R - L) >> 1);
return process(sum, L, M, lower, upper) + process(sum, M + 1, R, lower, upper)
+ merge(sum, L, M, R, lower, upper);
}
public static int merge(long[] arr, int L, int M, int R, int lower, int upper) {
int ans = 0;
int windowL = L;
int windowR = L;
// [windowL, windowR)
for (int i = M + 1; i <= R; i++) {
long min = arr[i] - upper;
long max = arr[i] - lower;
while (windowR <= M && arr[windowR] <= max) {
windowR++;
}
while (windowL <= M && arr[windowL] < min) {
windowL++;
}
ans += windowR - windowL;
}
long[] help = new long[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;
}
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