分治算法求序列中第K小数

题目

P1138 第 k 小整数

算法标签: 分治, 快速选择算法, $Partition$算法

思路

每次选择一个基准元素, 进行考虑

$Hoare$划分方法

#include <iostream>
#include <algorithm>
#include <cstring>using namespace std;const int N = 10010, M = 30010;int n, k, w[N];
int cnt;
bool vis[M];int find(int l, int r) {if (l == r) return w[l];int mid = w[l + r >> 1];int i = l - 1, j = r + 1;while (i < j) {while (w[++i] < mid);while (w[--j] > mid);if (i < j) swap(w[i], w[j]);}if (k <= j) return find(l, j);return find(j + 1, r);
}int main() {ios::sync_with_stdio(false);cin.tie(0), cout.tie(0);cin >> n >> k;for (int i = 1; i <= n; ++i) {int val;cin >> val;if (!vis[val]) {w[++cnt] = val;vis[val] = true;}}if (cnt < k) {cout << "NO RESULT" << "\n";return 0;}int ans = find(1, cnt);cout << ans << "\n";return 0;
}

*$Lomuto$划分方法

这个逻辑的边界问题处理非常麻烦

#include <iostream>
#include <algorithm>
#include <cstring>using namespace std;const int N = 10010, M = 30010;int n, k, cnt;
int w[N];
bool vis[M];int find(int l, int r) {if (l == r && l == k) return w[l];if (l < k) {int val = w[l];int i = l, j = r;while (i < j) {while (i < j && w[j] > val) j--;if (i < j) swap(w[i], w[j]);while (i < j && w[i] <= val) i++;if (i < j) swap(w[i], w[j]);}w[i] = val;if (i == k) return w[k];else if (k < i) return find(l, i - 1);return find(i + 1, r);}
}int main() {ios::sync_with_stdio(false);cin.tie(0), cout.tie(0);cin >> n >> k;for (int i = 0; i < n; ++i) {int val;cin >> val;if (!vis[val]) {w[++cnt] = val;vis[val] = true;}}if (cnt < k) {cout << "NO RESULT" << "\n";return 0;}int ans = find(1, cnt);cout << ans << "\n";return 0;
}