From f666edf536597a9e426a0648e76275ee4c4aaf0e Mon Sep 17 00:00:00 2001
From: subcrip <contact@subc.rip>
Date: Sun, 8 Sep 2024 14:49:18 +0800
Subject: [PATCH] Add trees/sparse_table_2d.cc

Signed-off-by: subcrip <contact@subc.rip>
---
 trees/sparse_table_2d.cc | 32 ++++++++++++++++++++++++++++++++
 1 file changed, 32 insertions(+)
 create mode 100644 trees/sparse_table_2d.cc

diff --git a/trees/sparse_table_2d.cc b/trees/sparse_table_2d.cc
new file mode 100644
index 0000000..0ee4ae6
--- /dev/null
+++ b/trees/sparse_table_2d.cc
@@ -0,0 +1,32 @@
+template<typename _Tp, typename _Op = function<_Tp(const _Tp&, const _Tp&)>> struct sparse_table_2d {
+    _Op op;
+    vector<vector<vector<vector<_Tp>>>> st;
+    sparse_table_2d(const vector<vector<_Tp>>& a, _Op&& __operation) {
+        op = __operation;
+        int n = a.size();
+        int m = int(log2(n) + 1);
+        st = vector(n, vector(n, vector(m, vector<_Tp>(m))));
+        for (int k = 0; k < m; ++k) {
+            for (int l = 0; l < m; ++l) {
+                for (int i = 0; i + (1 << k) <= n; ++i) {
+                    for (int j = 0; j + (1 << l) <= n; ++j) {
+                        if (k == 0) {
+                            if (l == 0) {
+                                st[i][j][k][l] = a[i][j];
+                            } else {
+                                st[i][j][k][l] = op(st[i][j][k][l - 1], st[i][j + (1 << l - 1)][k][l - 1]);
+                            }
+                        } else {
+                            st[i][j][k][l] = op(st[i][j][k - 1][l], st[i + (1 << k - 1)][j][k - 1][l]);
+                        }
+                    }
+                }
+            }
+        }
+    }
+    _Tp query(size_t x1, size_t y1, size_t x2, size_t y2) {
+        int s1 = lg2(x2 - x1 + 1);
+        int s2 = lg2(y2 - y1 + 1);
+        return op(st[x1][y1][s1][s2], op(st[x2 - (1 << s1) + 1][y1][s1][s2], op(st[x1][y2 - (1 << s2) + 1][s1][s2], st[x2 - (1 << s1) + 1][y2 - (1 << s2) + 1][s1][s2])));
+    }
+};