归并排序与随机快排

Code01_MergeSort

package class03;

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);
    }

    // arr[L...R]范围上，变成有序的
    // L...R    N    T(N) = 2*T(N/2) + O(N)  ->
    public static void process(int[] arr, int L, int R) {
        if (L == R) { // base case
            return;
        }
        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;
        int mergeSize = 1;// 当前有序的，左组长度
        while (mergeSize < N) { // log N
            int L = 0;
            // 0.... 
            while (L < N) {
                // L...M  左组（mergeSize）
                int M = L + mergeSize - 1;
                if (M >= N) {
                    break;
                }
                //  L...M   M+1...R(mergeSize)
                int R = Math.min(M + mergeSize, N - 1);
                merge(arr, L, M, R);
                L = R + 1;
            }
            if (mergeSize > N / 2) {
                break;
            }
            mergeSize <<= 1;
        }
    }

    // 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;
        boolean succeed = true;
        for (int i = 0; i < testTime; i++) {
            int[] arr1 = generateRandomArray(maxSize, maxValue);
            int[] arr2 = copyArray(arr1);
            mergeSort1(arr1);
            mergeSort2(arr2);
            if (!isEqual(arr1, arr2)) {
                succeed = false;
                printArray(arr1);
                printArray(arr2);
                break;
            }
        }
        System.out.println(succeed ? "Nice!" : "Oops!");
    }

}

Code02_SmallSum

package class03;

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
    // merge
    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 = 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 test
    public 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 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;
        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!");
    }

}

Code03_PartitionAndQuickSort

package class03;

public class Code03_PartitionAndQuickSort {

    public static void swap(int[] arr, int i, int j) {
        int tmp = arr[i];
        arr[i] = arr[j];
        arr[j] = tmp;
    }

    public static int partition(int[] arr, int L, int R) {
        if (L > R) {
            return -1;
        }
        if (L == R) {
            return L;
        }
        int lessEqual = L - 1;
        int index = L;
        while (index < R) {
            if (arr[index] <= arr[R]) {
                swap(arr, index, ++lessEqual);
            }
            index++;
        }
        swap(arr, ++lessEqual, R);
        return lessEqual;
    }

    // arr[L...R] 玩荷兰国旗问题的划分，以arr[R]做划分值
    //  <arr[R]  ==arr[R]  > arr[R]
    public static int[] netherlandsFlag(int[] arr, int L, int R) {
        if (L > R) {
            return new int[] { -1, -1 };
        }
        if (L == R) {
            return new int[] { L, R };
        }
        int less = L - 1; // < 区 右边界
        int more = R;     // > 区 左边界
        int index = L;
        while (index < more) {
            if (arr[index] == arr[R]) {
                index++;
            } else if (arr[index] < arr[R]) {
                swap(arr, index++, ++less);
            } else { // >
                swap(arr, index, --more);
            }
        }
        swap(arr, more, R);
        return new int[] { less + 1, more };
    }

    public static void quickSort1(int[] arr) {
        if (arr == null || arr.length < 2) {
            return;
        }
        process1(arr, 0, arr.length - 1);
    }

    public static void process1(int[] arr, int L, int R) {
        if (L >= R) {
            return;
        }
        // L..R partition arr[R]  [   <=arr[R]   arr[R]    >arr[R]  ]
        int M = partition(arr, L, R);
        process1(arr, L, M - 1);
        process1(arr, M + 1, R);
    }

    public static void quickSort2(int[] arr) {
        if (arr == null || arr.length < 2) {
            return;
        }
        process2(arr, 0, arr.length - 1);
    }

    public static void process2(int[] arr, int L, int R) {
        if (L >= R) {
            return;
        }
        int[] equalArea = netherlandsFlag(arr, L, R);
        process2(arr, L, equalArea[0] - 1);
        process2(arr, equalArea[1] + 1, R);
    }

    public static void quickSort3(int[] arr) {
        if (arr == null || arr.length < 2) {
            return;
        }
        process3(arr, 0, arr.length - 1);
    }

    public static void process3(int[] arr, int L, int R) {
        if (L >= R) {
            return;
        }
        swap(arr, L + (int) (Math.random() * (R - L + 1)), R);
        int[] equalArea = netherlandsFlag(arr, L, R);
        process3(arr, L, equalArea[0] - 1);
        process3(arr, equalArea[1] + 1, R);
    }

    // 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;
        boolean succeed = true;
        for (int i = 0; i < testTime; i++) {
            int[] arr1 = generateRandomArray(maxSize, maxValue);
            int[] arr2 = copyArray(arr1);
            int[] arr3 = copyArray(arr1);
            quickSort1(arr1);
            quickSort2(arr2);
            quickSort3(arr3);
            if (!isEqual(arr1, arr2) || !isEqual(arr2, arr3)) {
                succeed = false;
                break;
            }
        }
        System.out.println(succeed ? "Nice!" : "Oops!");

    }

}