Add files via upload

Author: MathProgrammer

2022/Contests/Div 2/767/Programs/Game on Sum Hard Version.cpp

@@ -0,0 +1,100 @@
+#include <iostream>
+#include <vector>
+
+using namespace std;
+
+const int MOD = 1e9 + 7, MAX_N = 1e6 + 5;
+long long factorial[MAX_N], inverse_factorial[MAX_N];
+
+long long power_mod(long long x, long long power, long long m)
+{
+    long long result = 1;
+
+    while(power > 0)
+    {
+        if(power%2 == 1)
+            result = (result*x)%m;
+
+        x = (x*x)%m;
+        power = power >> 1;
+    }
+
+    return result;
+}
+
+long long inverse(long long x, long long m)
+{
+    return power_mod(x, m - 2, m);
+}
+
+void precompute()
+{
+    factorial[0] = 1;
+    for(int i = 1; i < MAX_N; i++)
+    {
+        factorial[i] = (i*factorial[i - 1])%MOD;
+    }
+
+    inverse_factorial[MAX_N - 1] = inverse(factorial[MAX_N - 1], MOD);
+    for(int i = MAX_N - 2; i >= 0; i--)
+    {
+        inverse_factorial[i] = ((i + 1)*inverse_factorial[i + 1])%MOD;
+    }
+}
+
+long long choose(long long n, long long r)
+{
+    long long numerator = factorial[n];
+    long long inverse_denominator = (inverse_factorial[r]*inverse_factorial[n - r])%MOD;
+
+    return (numerator*inverse_denominator)%MOD;
+}
+
+void solve()
+{
+    long long no_of_moves, add_moves, range;
+    cin >> no_of_moves >> add_moves >> range;
+
+    const int MOD = 1e9 + 7;
+    long long score = 0;
+
+    if(add_moves == no_of_moves)
+    {
+        cout << (range*add_moves)%MOD << "\n";
+        return;
+    }
+
+    for(int i = 1; i <= add_moves; i++)
+    {
+        long long base_case = (i*range)%MOD;
+
+        long long total_moves = no_of_moves - i;
+        long long total_free_moves = total_moves - 1;
+        long long total_side_moves = add_moves - i;
+
+        base_case *= choose(total_free_moves, total_side_moves);
+        base_case %= MOD;
+        long long power_2 = power_mod(2, total_moves, MOD);
+
+        //cout << "i = " << i << " Number of paths = C(" << total_free_moves <<"," << total_side_moves << ") = " << choose(total_free_moves, total_side_moves) << " 2^i = " << power_2 << "\n";
+        long long contribution = (base_case*inverse(power_2, MOD))%MOD;
+
+        score += contribution;
+        score %= MOD;
+    }
+    cout << score << "\n";
+}
+
+int main()
+{
+    precompute();
+
+    int no_of_test_cases;
+    cin >> no_of_test_cases;
+
+    while(no_of_test_cases--)
+        solve();
+
+    return 0;
+}
+