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LeetCode215.数组中的第K个最大元素

August 12, 2018 • Read: 147 • LeetCode

题目链接:LeetCode215

题解

第一种做法,直接排序完了取,时间复杂度O(logn)

class Solution {
    public int findKthLargest(int[] nums, int k) {
        Arrays.sort(nums);
        return nums[nums.length - k];
    }
}

第二种做法,BFPRT算法,时间复杂度O(n)

class Solution {
    public static int getMinKthByBFPRT(int[] arr,int k) {
        int[] copyArr = new int[arr.length];
        copyArr = copyArray(arr);
        return bfprt(copyArr,0,copyArr.length - 1,k - 1);
    }
    public static int[] copyArray(int[] arr) {
        int[] tmp = new int[arr.length];    
        for(int i = 0;i != arr.length;i++) 
            tmp[i] = arr[i];
        return tmp;
    }
    public static int bfprt(int[] arr,int begin,int end,int i) {//begin到end范围内求第i小的数
        if(begin == end)
            return arr[begin];
        int pivot = medianOfMedians(arr,begin,end);//中位数作为划分值
        int[] pivotRange = partition(arr,begin,end,pivot);//进行划分,返回等于区域
        if(i >= pivotRange[0] && i <= pivotRange[1]) 
            return arr[i];
        else if(i < pivotRange[0])
            return bfprt(arr,begin,pivotRange[0] - 1,i);
        else 
            return bfprt(arr,pivotRange[1] + 1,end,i);
    }
    
    public static int medianOfMedians(int[] arr,int begin,int end) {
        int num = end - begin + 1;
        int offset = num % 5 == 0 ? 0 : 1;
        int[] mArr = new int[num / 5 + offset];
        for(int i = 0; i < mArr.length;i++) {
            int beginI = begin + i * 5;
            int endI = beginI + 4;
            mArr[i] = getMedian(arr,beginI,Math.min(end,endI));
        }
        return bfprt(mArr,0,mArr.length - 1,mArr.length / 2);
    }
    
    public static int getMedian(int[] arr,int begin,int end) {
        Arrays.sort(arr,begin,end);
        int sum = end + begin;
        int mid = (sum / 2) + (sum % 2);
        return arr[mid];
    }
    
    public static void insertSort(int[] arr,int begin,int end) {
        for(int i = begin + 1;i != end + 1;i++) {
            for(int j = i;j != begin;j--) {
                if(arr[j - 1] > arr[j]) 
                    swap(arr,j - 1,j);
                else 
                    break;
            }
        }
    }
    public static int[] partition(int[] arr,int begin,int end,int pivotValue) {
        int small = begin - 1;
        int cur = begin;
        int big = end + 1;
        while(cur != big) {
            if(arr[cur] < pivotValue)
                swap(arr,++small,cur++);
            else if(arr[cur] > pivotValue)
                swap(arr,cur,--big);
            else 
                cur++;
        }
        int[] range = new int[2];
        range[0] = small + 1;
        range[1] = big - 1;
        return range;
    }
    
    public static void swap(int[] arr,int i,int j) {
        int t = arr[i];
        arr[i] = arr[j];
        arr[j] = t;
    }
    public int findKthLargest(int[] nums, int k) {
        return getMinKthByBFPRT(nums,nums.length - k + 1);
    }
}
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