From 5e35ab77fc4b14e3d8a5284da66ff2c6240d4281 Mon Sep 17 00:00:00 2001
From: Om <78009952+OmkarAcharekar@users.noreply.github.com>
Date: Fri, 29 Oct 2021 15:50:11 +0530
Subject: [PATCH] Mo's Algorithm.cpp
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Algorithm , based on sqrt decomposition, can be used to answer range queries (Q) offline in O((N+Q)√N
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 C++ & C/Mo's Algorithm | 61 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 61 insertions(+)
 create mode 100644 C++ & C/Mo's Algorithm

diff --git a/C++ & C/Mo's Algorithm b/C++ & C/Mo's Algorithm
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+++ b/C++ & C/Mo's Algorithm	
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+// Mo's Algorithm implementation in C++
+// Author: Omkar Acharekar
+// 28 - 10 - 2021
+
+
+//The idea is to answer the queries in a special order based on the indices.
+//We will first answer all queries which have the left index in block 0, then answer all queries which have left index in block 1 and so on.
+//And also we will have to answer the queries of a block is a special order, namely sorted by the right index of the queries.
+
+
+// Implementation
+
+In Mo's algorithm we use two functions for adding an index and for removing an index from the range which we are currently maintaining.
+
+
+
+void remove(idx);  // TODO: remove value at idx from data structure
+void add(idx);     // TODO: add value at idx from data structure
+int get_answer();  // TODO: extract the current answer of the data structure
+
+int block_size;
+
+struct Query {
+    int l, r, idx;
+    bool operator<(Query other) const
+    {
+        return make_pair(l / block_size, r) <
+               make_pair(other.l / block_size, other.r);
+    }
+};
+
+vector<int> mo_s_algorithm(vector<Query> queries) {
+    vector<int> answers(queries.size());
+    sort(queries.begin(), queries.end());
+
+    // TODO: initialize data structure
+
+    int cur_l = 0;
+    int cur_r = -1;
+    // invariant: data structure will always reflect the range [cur_l, cur_r]
+    for (Query q : queries) {
+        while (cur_l > q.l) {
+            cur_l--;
+            add(cur_l);
+        }
+        while (cur_r < q.r) {
+            cur_r++;
+            add(cur_r);
+        }
+        while (cur_l < q.l) {
+            remove(cur_l);
+            cur_l++;
+        }
+        while (cur_r > q.r) {
+            remove(cur_r);
+            cur_r--;
+        }
+        answers[q.idx] = get_answer();
+    }
+    return answers;
+}