doubling

Author: potato167

ds/Doubling.hpp

@@ -0,0 +1,78 @@
+#pragma once
+#include <vector>
+#include <cassert>
+namespace po167{
+
+template<class T, T(*op)(T, T)>
+struct Doubling_op{
+    int n;
+    int depth;
+    std::vector<std::vector<int>> index;
+    std::vector<std::vector<T>> val;
+    Doubling_op(std::vector<int> p, std::vector<T> v, long long lim = (1ll << 60) - 1){
+        n = p.size();
+        for (auto x : p) assert(0 <= x && x < n);
+        assert(n == (int)v.size());
+        depth = 1;
+        while ((1ll << depth) <= lim) depth++;
+        index.resize(depth);
+        val.resize(depth);
+        index[0] = p;
+        val[0] = v;
+        for (int i = 1; i < depth; i++){
+            index[i].resize(n);
+            val[i].resize(n);
+            for (int j = 0; j < n; j++){
+                int tmp = index[i - 1][j];
+                index[i][j] = index[i - 1][tmp];
+                val[i][j] = op(val[i - 1][j], val[i - 1][tmp]);
+            }
+        }
+    }
+    std::pair<int, T> query(int start_ind, T start_val, long long times){
+        assert(0 <= start_ind && start_ind < n);
+        assert(0 <= times && times < (1ll << depth));
+        int i = 0;
+        while (times){
+            if (times & 1){
+                start_val = op(start_val, val[i][start_ind]);
+                start_ind = index[i][start_ind];
+            }
+            i++;
+            times >>= 1;
+        }
+        return std::make_pair(start_ind, start_val);
+    }
+};
+
+struct Doubling{
+    int n;
+    int depth;
+    std::vector<std::vector<int>> index;
+    Doubling(std::vector<int> p, long long lim = (1ll << 60) - 1){
+        n = p.size();
+        for (auto x : p) assert(0 <= x && x < n);
+        depth = 1;
+        while ((1ll << depth) <= lim) depth++;
+        index.resize(depth);
+        index[0] = p;
+        for (int i = 1; i < depth; i++){
+            index[i].resize(n);
+            for (int j = 0; j < n; j++){
+                index[i][j] = index[i - 1][index[i - 1][j]];
+            }
+        }
+    }
+    int query(int ind, long long times){
+        assert(0 <= ind && ind < n);
+        assert(0 <= times && times < (1ll << depth));
+        int i = 0;
+        while (times){
+            if (times & 1) ind = index[i][ind];
+            i++;
+            times >>= 1;
+        }
+        return ind;
+    }
+};
+}

test/ds/doubling_rmq.test.cpp

@@ -0,0 +1,27 @@
+#define PROBLEM "https://judge.yosupo.jp/problem/staticrmq"
+
+#include "../../ds/Doubling.hpp"
+
+int op(int a, int b){
+    return std::min(a, b);
+}
+
+#include <iostream>
+
+int main(){
+    std::ios::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+    int N, Q;
+    std::cin >> N >> Q;
+    std::vector<int> A(N), P(N);
+    for (int i = 0; i < N; i++){
+        std::cin >> A[i];
+        P[i] = std::min(i + 1, N - 1);
+    }
+    po167::Doubling_op<int, op> D(P, A, N);
+    while (Q--){
+        int l, r;
+        std::cin >> l >> r;
+        std::cout << D.query(l, 1 << 30, r - l).second << "\n";
+    }
+}