215 Kth Largest Element in an Array

Author: int32bit

README.md

@@ -121,6 +121,7 @@
 + [210 Course Schedule II(拓扑排序)](algorithms/CourseScheduleII)
 + [211 Add and Search Word - Data structure design(Trie树)](algorithms/AddandSearchWord)
 + [213 House Robber II(DP)](algorithms/HouseRobberII)
++ [215 Kth Largest Element in an Array(快排partition函数)](algorithms/KthLargestElementinanArray)
 
 ## Database
 

algorithms/KthLargestElementinanArray/README.md

@@ -0,0 +1,59 @@
+## Kth Largest Element in an Array
+
+Find the kth largest element in an unsorted array. Note that it is the kth largest element in the sorted order, not the kth distinct element.
+
+For example,
+Given `[3,2,1,5,6,4]` and k = 2, return 5.
+
+Note: 
+You may assume k is always valid, 1 ≤ k ≤ array's length.
+
+Credits:
+Special thanks to @mithmatt for adding this problem and creating all test cases.
+
+## Solution
+
+利用快排法的partition函数:
+
+```cpp
+int partition(vector<int> &nums, int s, int t)
+{
+	int i = s, j = t;
+	int k = nums[s];
+	while (i < j) {
+		while (nums[j] <= k && i < j) --j;
+		if (i < j) {
+			nums[i] = nums[j];
+		}
+		while (nums[i] >= k && i < j) ++i;
+		if (i < j) {
+			nums[j] = nums[i];
+		}
+	}
+	nums[i] = k;
+	return i;
+}
+```
+
+设返回的位置为pos，这个pos的值一定是排序后的正确顺序，因此若:
+
+* pos == k - 1, 则直接返回pos位置的值即可
+* 若pos < k - 1, 则在左边查找
+* 否则在右边查找.
+
+```cpp
+int findKthLargest(vector<int> &nums, int k) {
+	int s = 0, t = nums.size() - 1;
+	while (true) {
+		int pos = partition(nums, s, t);
+		if (pos == k - 1)
+			return nums[pos];
+		if (pos > k - 1) {
+			t = pos - 1;
+		} else {
+			s = pos + 1;
+		}
+	}
+	return -1;
+}
+```

algorithms/KthLargestElementinanArray/solve.cpp

@@ -0,0 +1,57 @@
+#include <cstdio>
+#include <cstdlib>
+#include <iostream>
+#include <vector>
+#include <algorithm>
+using namespace std;
+
+void print(const vector<int> &nums)
+{
+	for (auto i : nums)
+		cout << i << " ";
+	cout << endl;
+}
+class Solution {
+	public:
+		int findKthLargest(vector<int> &nums, int k) {
+			int s = 0, t = nums.size() - 1;
+			while (true) {
+				int pos = partition(nums, s, t);
+				if (pos == k - 1)
+					return nums[pos];
+				if (pos > k - 1) {
+					t = pos - 1;
+				} else {
+					s = pos + 1;
+				}
+			}
+			return -1;
+		}
+	private:
+		int partition(vector<int> &nums, int s, int t)
+		{
+			int i = s, j = t;
+			int k = nums[s];
+			while (i < j) {
+				while (nums[j] <= k && i < j) --j;
+				if (i < j) {
+					nums[i] = nums[j];
+				}
+				while (nums[i] >= k && i < j) ++i;
+				if (i < j) {
+					nums[j] = nums[i];
+				}
+			}
+			nums[i] = k;
+			return i;
+		}
+};
+int main(int argc, char **argv)
+{
+	Solution solution;
+	vector<int> nums = {1,1,1,1};
+	print(nums);
+	int result = solution.findKthLargest(nums, 3);
+	printf("result = %d\n", result);
+	return 0;
+}