Create XOR Triangle.cpp

Author: MathProgrammer

2023/Contests/Div 2/810/Programs/XOR Triangle.cpp

@@ -0,0 +1,91 @@
+#include <iostream>
+#include <vector>
+
+using namespace std;
+
+const int MOD = 998244353, MAX_N = 2e5 + 5, MAX_MASK = 7, NO_OF_TRIANGLE_SIDES = 3;
+long long no_of_triplets[MAX_N][MAX_MASK + 1][MAX_MASK + 1];
+int limit[NO_OF_TRIANGLE_SIDES], next_bit[NO_OF_TRIANGLE_SIDES], triangle_sides[NO_OF_TRIANGLE_SIDES];
+
+int is_bit_set(int n, int bit)
+{
+    return ( (n&(1 << bit)) != 0 );
+}
+
+int main()
+{
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    string S;
+    cin >> S;
+
+    no_of_triplets[0][MAX_MASK][0] = 1;
+    for(int i = 0; i < S.size(); i++)
+    {
+        int prefix = i - 1;
+        for(int prefix_match = 0; prefix_match <= MAX_MASK; prefix_match++)
+        {
+            for(int condition_met = 0; condition_met <= MAX_MASK; condition_met++)
+            {
+                for(int bit = 0; bit < NO_OF_TRIANGLE_SIDES; bit++)
+                {
+                    limit[bit] = (is_bit_set(prefix_match, bit) ? S[i] : '1') - '0';
+                }
+
+                for(next_bit[0] = 0; next_bit[0] <= limit[0]; next_bit[0]++)
+                {
+                    for(next_bit[1] = 0; next_bit[1] <= limit[1]; next_bit[1]++)
+                    {
+                        for(next_bit[2] = 0; next_bit[2] <= limit[2]; next_bit[2]++)
+                        {
+
+                            for(int bit = 0; bit < NO_OF_TRIANGLE_SIDES; bit++)
+                            {
+                                triangle_sides[bit] = next_bit[bit]^next_bit[(bit + 1)%NO_OF_TRIANGLE_SIDES];
+                            }
+
+                            int next_prefix_match = 0;
+                            for(int bit = 0; bit < NO_OF_TRIANGLE_SIDES; bit++)
+                            {
+                                if(is_bit_set(prefix_match, bit) && next_bit[bit] == S[i] - '0')
+                                {
+                                    next_prefix_match |= (1 << bit);
+                                }
+                            }
+
+                            int next_condition_met = 0;
+                            for(int bit = 0; bit < NO_OF_TRIANGLE_SIDES; bit++)
+                            {
+                                int condition_here = (triangle_sides[bit]&triangle_sides[(bit + 1)%NO_OF_TRIANGLE_SIDES] != 0);
+                                if(is_bit_set(condition_met, bit) || condition_here)
+                                {
+                                    next_condition_met |= (1 << bit);
+                                }
+                            }
+
+                            no_of_triplets[i + 1][next_prefix_match][next_condition_met] += no_of_triplets[i][prefix_match][condition_met];
+                            no_of_triplets[i + 1][next_prefix_match][next_condition_met] %= MOD;
+
+                            /*cout << "F(" << i + 1 << "," << next_prefix_match << "," << next_condition_met << ") = "
+                            << no_of_triplets[i + 1][next_prefix_match][next_condition_met] << " added "
+                            << "F(" << i << "," << prefix_match << "," << condition_met << ") = "
+                            << no_of_triplets[i][prefix_match][condition_met] << " Current "
+                            << next_bit[0] << " " << next_bit[1] << " " << next_bit[2] << "\n";*/
+                        }
+                    }
+                }
+            }
+        }
+    }
+
+    long long answer = 0;
+    for(int prefix_match = 0, all_conditions_met = MAX_MASK; prefix_match <= MAX_MASK; prefix_match++)
+    {
+        answer += no_of_triplets[S.size()][prefix_match][all_conditions_met];
+        answer %= MOD;
+    }
+
+    cout << answer << "\n";
+    return 0;
+}