255. 第K小数

https://www.acwing.com/problem/content/submission/code_detail/9470611/

AcWing/255/255.cpp

@@ -0,0 +1,90 @@
+#include <algorithm>
+#include <iostream>
+#include <limits>
+#include <vector>
+
+using std::cin;
+using std::cout;
+using std::endl;
+
+const int N = 100005;
+
+int n, m, l, r, k, a[N];
+std::vector<int> nums;
+
+// Helpers
+int find(int);
+
+// Segment Tree
+int cnt, root[N];
+int build(int, int);
+int insert(int, int, int, int);
+int query(int, int, int, int, int);
+
+int main() {
+    cin >> n >> m;
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i];
+        nums.push_back(a[i]);
+    }
+    std::sort(nums.begin(), nums.end());
+    nums.erase(std::unique(nums.begin(), nums.end()), nums.end());
+    root[0] = build(0, nums.size() - 1);
+    for (int i = 1; i <= n; i++) {
+        root[i] = insert(root[i - 1], 0, nums.size() - 1, find(a[i]));
+    }
+    while (m--) {
+        cin >> l >> r >> k;
+        cout << nums[query(root[r], root[l - 1], 0, nums.size() - 1, k)] << endl;
+    }
+    return 0;
+}
+
+// === Helpers ===
+
+inline int find(int x) {
+    return std::lower_bound(nums.begin(), nums.end(), x) - nums.begin();
+}
+
+// === Segment Tree ===
+
+struct node {
+    int l, r, c;
+
+    node()
+        : l(0), r(0), c(0) {}
+} tr[N << 5];
+
+int build(int l, int r) {
+    int p = ++cnt;
+    if (l == r) return p;
+    int mid = l + r >> 1;
+    tr[p].l = build(l, mid);
+    tr[p].r = build(mid + 1, r);
+    return p;
+}
+
+int insert(int p, int l, int r, int x) {
+    int q = ++cnt;
+    tr[q] = tr[p];
+    if (l == r) {
+        tr[q].c++;
+        return q;
+    }
+    int mid = l + r >> 1;
+    if (x <= mid) {
+        tr[q].l = insert(tr[p].l, l, mid, x);
+    } else {
+        tr[q].r = insert(tr[p].r, mid + 1, r, x);
+    }
+    tr[q].c = tr[tr[q].l].c + tr[tr[q].r].c;
+    return q;
+}
+
+int query(int q, int p, int l, int r, int k) {
+    if (l == r) return l;
+    int c = tr[tr[q].l].c - tr[tr[p].l].c;
+    int mid = l + r >> 1;
+    if (k <= c) return query(tr[q].l, tr[p].l, l, mid, k);
+    return query(tr[q].r, tr[p].r, mid + 1, r, k - c);
+}