From 10e84ee5db81ed36144413f3d48a0a3ad9e68ba5 Mon Sep 17 00:00:00 2001
From: Tarun Singh <tarunsinghofficial236@gmail.com>
Date: Thu, 27 Oct 2022 13:53:08 +0530
Subject: [PATCH] Add a program to check whether a substring is a palindrome or
 not in logn time complexity

---
 ...heck_Substring_Palindrome_in_logn_time.cpp | 120 ++++++++++++++++++
 1 file changed, 120 insertions(+)
 create mode 100644 C++/Check_Substring_Palindrome_in_logn_time.cpp

diff --git a/C++/Check_Substring_Palindrome_in_logn_time.cpp b/C++/Check_Substring_Palindrome_in_logn_time.cpp
new file mode 100644
index 0000000..7e69817
--- /dev/null
+++ b/C++/Check_Substring_Palindrome_in_logn_time.cpp
@@ -0,0 +1,120 @@
+#include <bits/stdc++.h>
+typedef long long int ll;
+#define M 1000000007
+using namespace std;
+
+ll prefix_hash[200005];
+ll prefix_hashr[200005];
+
+ll power(ll base, ll n, ll m)
+{
+    ll ans = 1;
+    while (n != 0)
+    {
+        if (n % 2 == 1)
+        {
+            n = n - 1;
+            ans = (ans * base) % m;
+        }
+        else
+        {
+            n = n / 2;
+            base = (base * base) % m;
+        }
+    }
+    return ans;
+}
+
+ll compute_substring_hash(ll l, ll r)
+{
+    ll hash = prefix_hash[r];
+
+    if (l > 0)
+    {
+        hash = (hash - prefix_hash[l - 1] + M) % M;
+    }
+
+    // divide
+
+    hash = (hash * power(power(31, l, M), M - 2, M)) % M;
+
+    return hash;
+}
+
+ll compute_substring_hash1(ll l, ll r)
+{
+    ll hash = prefix_hashr[r];
+
+    if (l > 0)
+    {
+        hash = (hash - prefix_hashr[l - 1] + M) % M;
+    }
+
+    // divide
+
+    hash = (hash * power(power(31, l, M), M - 2, M)) % M;
+
+    return hash;
+}
+
+void compute(string &s)
+{
+    ll pr = 1;
+    ll hash = 0;
+    for (ll i = 0; i < s.size(); i++)
+    {
+        hash = (hash + ((s[i] - 'a' + 1) * pr) % M) % M;
+        prefix_hash[i] = hash;
+        pr = (pr * 31) % M;
+    }
+}
+
+void computeR(string &s)
+{
+    string temp = s;
+    reverse(temp.begin(), temp.end());
+    ll pr = 1;
+    ll hash = 0;
+    for (ll i = 0; i < temp.size(); i++)
+    {
+        hash = (hash + ((temp[i] - 'a' + 1) * pr) % M) % M;
+        prefix_hashr[i] = hash;
+        pr = (pr * 31) % M;
+    }
+}
+
+bool checkPalindrome(ll l, ll r, ll n)
+{
+    ll a = compute_substring_hash(l, r);
+    ll b = compute_substring_hash1(n - 1 - r, n - 1 - l);
+    return (a == b);
+}
+
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+
+    string s;
+    cin >> s;
+    compute(s);
+    computeR(s);
+    ll q;
+    cin >> q;
+    ll n = s.size();
+    // Each query can be answered in logn time complexity
+    while (q--)
+    {
+        ll l, r;
+        cin >> l >> r;
+        if (checkPalindrome(l, r, n))
+        {
+            cout << "YES" << endl;
+        }
+        else
+        {
+            cout << "NO" << endl;
+        }
+    }
+    return 0;
+}
\ No newline at end of file