HDU 6070 (Segment Tree) Calculate:\(\min (\frac{size(L, R)}{R – L + 1})\) where size(L, R) represents the number of different integers between index L and R (inclusive).

CODECHEF SEQUA (Exponential Reduction Formula) Calculate:\(\sum_{i=0}^{n} i\ ^{i}\ \ \%\ m\) while \(0^{0}=1, 1\leq n \leq 10^{9}, 1\leq m\leq 10^{3}\).

HDU 6053 (GCD) Give an array \(1\leq A_i\leq 10^5\) with \(n\leq 10^5\) elements, calculate the number of array \(B\) which subjects to \(1\leq B_i \leq A_i\) and \(gcd (B_1, B_2, \cdots, B_n) \geq 2\).

CODECHEF RUINEDF (Bipartite Graph) There is a floor which is divided into (n+1) * n square cells with equal size like a matrix. Some cells with character ‘*’ are dirty cells, while others with character ‘.’ are not. A robot can clean continuous n cells vertically or horizontally each time. What is the minimum time to clean this floor?