[Noip simulation question] permutation (DP + high precision)

First, we can think like this:

Set status f [I, j] to 1 ~ Number of I sequence schemes with j '<'

So consider transfer

Because I is larger than the I-1, you can consider transferring from the I-1. First, I want to insert 1 ~ The I-1 of this sequence, so we can think about the Insertion Location:

For more information, see:

When the inserted position is '<', the answer will not change.

When the inserted position is '>', the answer will be + 1.

When the left boundary is inserted, the answer remains unchanged.

When the insert operation has a boundary, the answer is + 1.

So we know the number of '<' quantity and '>' of the previous I-1, then we can transfer it.

F [I, j] = (J + 1) * f [I-1, J] + (max {I-1-(J-1), 0} + 1) * f [I-1, j-1])

Then it is done with high precision ..

I did not speak about high-precision writing wrong places for a long time !!!!!!!!!!!!

Remember to clear the number of operations for each call !!!! That is, when assigning values, you must first clear them and then assign values !!!!!

# Include <cstdio> # include <cstring> # include <cmath> # include <string> # include <iostream> # include <algorithm> # include <queue> # include <set> # include <vector> # include <map> using namespace STD; typedef long ll; # define PII pair <int, int> # define mkpii make_pair <int, int> # define PDI pair <double, int> # define mkpdi make_pair <double, int> # define PLI pair <LL, int> # define mkpli make_pair <LL, int> # define rep (I, n) for (INT I = 0; I <(n); ++ I) # define for1 (I, A, n) for (INT I = (a); I <= (n); ++ I) # define for2 (I, A, n) for (INT I = (); I <(n); ++ I) # define for3 (I, A, n) for (INT I = (a); I> = (n); -- I) # define for4 (I, A, n) for (INT I = (a); I> (n); -- I) # define CC (I, A) memset (I, a, sizeof (I) # define read (A) A = getint () # define print (a) printf ("% d", a) # define dbg (X) cout <(# X) <"=" <(x) <Endl # define error (x )(! (X )? Puts ("error"): 0) # define printarr2 (a, B, c) for1 (_, 1, B) {for1 (__, 1, C) cout <A [_] [_]; cout <Endl ;}# define printarr1 (a, B) for1 (_, 1, B) cout <A [_] <'\ T'; cout <endlinline const int getint () {int r = 0, k = 1; char c = getchar (); for (; C <'0' | C> '9'; C = getchar () if (C = '-') k =-1; (; c> = '0' & C <= '9'; C = getchar () r = r * 10 + C-'0'; return K * r ;} inline const int max (const Int & A, const Int & B ){ Return A> B? A: B;} inline const int min (const Int & A, const Int & B) {return a <B? A: B;} const int n = 1155; int N, K; typedef int big [N]; big f [N], TP, TP2; void CLR (Big) {memset (A, 0, sizeof (INT) * (a [0] + 1); a [0] = 1;} void EQR (Big) {CLR (a); memcpy (A, TP, sizeof (INT) * (TP [0] + 1);} // clear void fix (Big A) first) {int I = A [0]; while (I> 1 &&! A [I]) -- I; A [0] = I;} void PR (Big A) {for3 (I, a [0], 1) printf ("% d", a [I]);} void MUL (Big A, int t) {CLR (TP); for1 (I, 1, a [0]) TP [I] = A [I] * t; int K = 0, I, SZ = A [0] + 32; for (I = 1; I <= SZ | K; ++ I) {TP [I] + = K; k = TP [I]/10; TP [I] % = 10 ;} TP [0] = I; fix (TP);} void PLS (Big A, Big B) {CLR (TP); int K = 0, I, SZ = max (A [0], B [0]); for (I = 1; I <= SZ | K; ++ I) {TP [I] = A [I] + B [I] + k; k = TP [I]/10; TP [I] % = 10 ;} TP [0] = I; fix (TP) ;}int main () {read (n); read (k); for1 (I, 0, K) CLR (F [I]); F [0] [1] = 1; for1 (I, 2, n) for3 (j, k, 0) {MUL (F [J], J + 1); EQR (F [J]); If (j> 0) {int T = max (0, i-1-j) + 1; mul (F [J-1], T); EQR (TP2); PLS (F [J], TP2); EQR (F [J]);} pr (F [k]); Return 0 ;}

　　

 

 

 

 

[Description]

Arrange numbers 1 to n randomly, and insert ">" and "<" between each number according to their size relationship ".

Q: In all sorts, how many are arranged exactly with K "<".

For example, arrange (3, 4, 1, 5, 2)

3 <4> 1 <5> 2

There are 2 "<"

[Input format]

N, K

[Output format]

Answer

[Example input]

52

[Sample output]

66

[Data Scope]

20%: n <= 10

50%: the answer is within 0 .. 2 ^ 63-1.

100%: k <n <= 100

[Noip simulation question] permutation (DP + high precision)