feat: add generic iterative segment tree class

iter-seg-tree/include/iter_seg_tree_lazy.hpp

@@ -0,0 +1,45 @@
+#pragma once
+#include <functional>
+#include <vector>
+
+#define LEFT(i) (i << 1)
+#define RIGHT(i) ((i << 1) | 1)
+#define IS_RIGHT_CHILD(i) ((i) & 1)
+
+// REMEMBER REMEMBER REMEMBER REMEMBER
+// Invariant: tree[p] will reflect the effect ot lazy[p]
+// the lazy is not for the node, but for the children
+
+template <typename T, typename L>
+class IterLazySegTree {
+   private:
+    int n_, h_;
+    std::vector<T> tree_;
+    std::vector<L> lazy_;
+
+    T iota_;
+    L iota_lazy_;
+
+    std::function<T(T, T)> combine_;
+    std::function<L(L, L)> combine_lazy_;
+    std::function<T(T, L, int)> apply_lazy_;
+
+    void apply(int index, L new_lazy, int len) {
+        // invariant: tree_[index] has no lazy, so just need the
+        // new val to be applied
+        tree_[index] = apply_lazy_(tree_[index], new_lazy, len);
+
+        if (index < n_) {  // not leaf
+            // combine lazy for children
+            lazy_[index] = combine_lazy_(lazy_[index], new_lazy);
+        }
+    }
+
+    void push(int index) {
+        for (int cur_h = h_; cur_h > 0; cur_h--) {
+            int par_at_level_cur_h = index >> cur_h;
+            if (lazy_[par_at_level_cur_h] != iota_lazy_) {
+            }
+        }
+    }
+};