Our Black Box represents a primitive database. It can save an integer array and has a special i variable. At the initial moment Black Box is empty and i equals 0. This Black Box processes a sequence o
Our Black Box represents a primitive database. It can save an integer array and has a special i variable. At the initial moment Black Box is empty and i equals 0. This Black Box processes a sequence of commands (transactions). There are two types of transactions: ADD (x): put element x into Black Box; GET: increase i by 1 and give an i-minimum out of all integers containing in the Black Box. Keep in mind that i-minimum is a number located at i-th place after Black Box elements sorting by non- descending. Let us examine a possible sequence of 11 transactions: Example 1 N Transaction i Black Box contents after transaction Answer (elements are arranged by non-descending) ADD(3) 0 3 GET 1 3 3 ADD(1) 1 1, 3 GET 2 1, 3 3 ADD(-4) 2 -4, 1, 3 ADD(2) 2 -4, 1, 2, 3 ADD(8) 2 -4, 1, 2, 3, 8 ADD(-1000) 2 -1000, -4, 1, 2, 3, 8 GET 3 -1000, -4, 1, 2, 3, 8 1 GET 4 -1000, -4, 1, 2, 3, 8 2 ADD(2) 4 -1000, -4, 1, 2, 2, 3, 8 It is required to work out an efficient algorithm which treats a given sequence of transactions. The maximum number of ADD and GET transactions: 30000 of each type. Let us describe the sequence of transactions by two integer arrays: A(1), A(2), ..., A(M): a sequence of elements which are being included into Black Box. A values are integers not exceeding 2 000 000 000 by their absolute value, M <= 30000. For the Example we have A=(3, 1, -4, 2, 8, -1000, 2). u(1), u(2), ..., u(N): a sequence setting a number of elements which are being included into Black Box at the moment of first, second, ... and N-transaction GET. For the Example we have u=(1, 2, 6, 6). The Black Box algorithm supposes that natural number sequence u(1), u(2), ..., u(N) is sorted in non-descending order,N≤MN leq MN≤Mand for each p(1≤p≤N)(1 leq p leq N)(1≤p≤N)an inequality p≤u(p)≤Mp leq u(p) leq Mp≤u(p)≤M is valid. It follows from the fact that for the p-element of our u sequence we perform a GET transaction giving p-minimum number from our A(1), A(2), ..., A(u(p)) sequence.
标签： HBC51010小圆前辈的素数 筛法 数学 快速傅里叶变换（FFT）/快速数论变换（NTT）/快速沃尔什变换（FWT） 数论Black Box题解
