剑指 Offer 40. 最小的k个数

, ,

Priority Queue

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
class Solution {
    public int[] getLeastNumbers(int[] arr, int k) {
        if (k == 0) {
            return new int[0];
        }
        
        PriorityQueue<Integer> maxHeap = new PriorityQueue<>((o1, o2) -> o2 - o1);

        for (int i = 0; i < k; i++) {
            maxHeap.offer(arr[i]);
        }

        for (int i = k; i < arr.length; i++) {
            if (arr[i] < maxHeap.peek()) {
                maxHeap.offer(arr[i]);
                maxHeap.poll();
            }
        }

        int[] res = new int[k];
        for (int i = 0; i < res.length; i++) {
            res[i] = maxHeap.poll();
        }
        return res;
    }
}

QuickSort

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
class Solution {
    public int[] getLeastNumbers(int[] arr, int k) {
        if (k == 0) {
            return new int[0];
        }

        int targetIndex = k - 1;
        quickSort(arr, 0, arr.length - 1, targetIndex);
        return Arrays.copyOf(arr, k);
    }

    private void quickSort(int[] arr, int i, int j, int targetIndex) {
        if (i >= j) {
            return;
        }

        int pivotIndex = partition(arr, i, j);
        if (pivotIndex == targetIndex) {
            return;
        }
        quickSort(arr, i, pivotIndex - 1, targetIndex);
        quickSort(arr, pivotIndex + 1, j, targetIndex);
    }

    private int partition(int[] arr, int i, int j) {
        int pivotIndex = i + ThreadLocalRandom.current().nextInt(j - i + 1); // i + [0, j - i] -> [i, j]
        int pivotValue = arr[pivotIndex];
        swap(arr, pivotIndex, i);

        int index = i;
        for (int k = i + 1; k <= j; k++) {
            if (arr[k] <= pivotValue) {
                swap(arr, k, ++index);
            }
        }

        swap(arr, i, index);
        return index;
    }

    private void swap(int[] nums, int i, int j) {
        int tmp = nums[i];
        nums[i] = nums[j];
        nums[j] = tmp;
    }
}

该解法效率不高的原因为为 pivotIndex 左右侧的数组都进行了排序，可以优化为仅对 targetIndex 一侧的数组进行排序。

QuickSort

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
class Solution {
    public int[] getLeastNumbers(int[] arr, int k) {
        if (k == 0) {
            return new int[0];
        }

        int targetIndex = k - 1;
        quickSort(arr, 0, arr.length - 1, targetIndex);
        return Arrays.copyOf(arr, k);
    }

    private void quickSort(int[] arr, int i, int j, int targetIndex) {
        if (i >= j) {
            return;
        }

        int pivotIndex = partition(arr, i, j);
        if (pivotIndex < targetIndex) {
            quickSort(arr, pivotIndex + 1, j, targetIndex);
        } else if (pivotIndex > targetIndex) {
            quickSort(arr, i, pivotIndex - 1, targetIndex);
        }
    }

    private int partition(int[] arr, int i, int j) {
        int pivotIndex = i + ThreadLocalRandom.current().nextInt(j - i + 1); // i + [0, j - i] -> [i, j]
        int pivotValue = arr[pivotIndex];
        swap(arr, pivotIndex, i);

        int index = i;
        for (int k = i + 1; k <= j; k++) {
            if (arr[k] <= pivotValue) {
                swap(arr, k, ++index);
            }
        }

        swap(arr, i, index);
        return index;
    }

    private void swap(int[] nums, int i, int j) {
        int tmp = nums[i];
        nums[i] = nums[j];
        nums[j] = tmp;
    }
}

QuickSort

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
class Solution {
    public int[] getLeastNumbers(int[] arr, int k) {
        if (k == 0) {
            return new int[0];
        }

        int targetIndex = k - 1;
        return quickSort(arr, 0, arr.length - 1, targetIndex);
    }

    private int[] quickSort(int[] arr, int i, int j, int targetIndex) {
        int pivotIndex = partition(arr, i, j);
        if (pivotIndex < targetIndex) {
            return quickSort(arr, pivotIndex + 1, j, targetIndex);
        } else if (pivotIndex > targetIndex) {
            return quickSort(arr, i, pivotIndex - 1, targetIndex);
        } else {
            return Arrays.copyOf(arr, targetIndex + 1);
        }
    }

    private int partition(int[] arr, int i, int j) {
        int pivotIndex = i + ThreadLocalRandom.current().nextInt(j - i + 1); // i + [0, j - i] -> [i, j]
        int pivotValue = arr[pivotIndex];
        swap(arr, pivotIndex, i);

        int index = i;
        for (int k = i + 1; k <= j; k++) {
            if (arr[k] <= pivotValue) {
                swap(arr, k, ++index);
            }
        }

        swap(arr, i, index);
        return index;
    }

    private void swap(int[] nums, int i, int j) {
        int tmp = nums[i];
        nums[i] = nums[j];
        nums[j] = tmp;
    }
}

QuickSort + Two Pointers

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
class Solution {
    public int[] getLeastNumbers(int[] arr, int k) {
        if (k == 0) {
            return new int[0];
        }

        int targetIndex = k - 1;
        return quickSort(arr, 0, arr.length - 1, targetIndex);
    }

    private int[] quickSort(int[] arr, int i, int j, int targetIndex) {
        int pivotIndex = partition(arr, i, j);
        if (pivotIndex < targetIndex) {
            return quickSort(arr, pivotIndex + 1, j, targetIndex);
        } else if (pivotIndex > targetIndex) {
            return quickSort(arr, i, pivotIndex - 1, targetIndex);
        } else {
            return Arrays.copyOf(arr, targetIndex + 1);
        }
    }

    private int partition(int[] arr, int l, int r) {
        int i = l, j = r;
        while (i < j) {
            while (i < j && arr[j] >= arr[l]) {
                j--;
            }
            while (i < j && arr[i] <= arr[l]) {
                i++;
            }
            swap(arr, i, j);
        }

        swap(arr, i, l);
        return i;
    }

    private void swap(int[] nums, int i, int j) {
        int tmp = nums[i];
        nums[i] = nums[j];
        nums[j] = tmp;
    }
}

References

剑指 Offer 40. 最小的k个数