1288C Two Arrays

Meaning of the questions:

Two sequences of length M and a B, which required each number between 1 and N, while the array is not a decrement, b array is not incremented, and for all elements, a (i) <b (i), ask how many such sequences ab, the result of the modulo 1e9 + 7

answer:

B flip sequence, and with a combined sequence is a length of 2 * M is not strictly decreasing sequence, this problem and minimize the number of sequence types.

Dp opening a two-dimensional array, i represents the number of bits after the first program in the digital zoom is equal to j, and the state transition equation is derived:

dp(i)(j)=dp(i)(j+1)+dp(i-1)(j)

Time complexity is O (M * N)

#include <bits / STDC ++ H.>
 the using  namespace STD; 
typedef Long  Long LL;
 const  int MAXN = 1E3 + 100 ;
 const  int MOD = 1E9 + . 7 ; 
LL DP [MAXN << . 1 ] [MAXN];
 // DP [I] [j] denotes the i-th position may be enlarged to the number of programs is equal to j, 
int main () {
     int N, M; 
    Scanf ( " % D% D " , & N, & M);
     for ( int i = . 1 ; i < N =; I ++ ) 
        DP [ . 1 ] [I] = . 1;
    for (int i=2;i<=2*M;i++) {
        for (int j=N;j>=1;j--)
            dp[i][j]=(dp[i][j+1]+dp[i-1][j])%mod;
    } 
    ll ans=0;
    for (int i=1;i<=N;i++)
        ans+=dp[2*M][i],ans%=mod;
    printf("%lld\n",ans);
}