Codeforces round #274 div.1 C riding in a lift -- DP

Given n floors, the first floor is in a. The second floor cannot be stayed. Select a floor X at a time. When | X-now | <| X-B | and X! = Now (now indicates the current position), records X to the sequence, takes K steps, and finally asks how many possible numbers there are.

Solution:

Definition: DP [I] [J] indicates the number of different sequences in step I on Building J.

Transfer equation: When j <B, then DP [I] [J] + = DP [I-1] [0 ~ (The midpoint of J and B (below)]

When J> B, then DP [I] [J] + = DP [I-1] [(the midpoint of J and B (below ))~ N]

Since the value of DP [I] [J] is only related to some values of DP [I-1] [], scrolling array greatly reduces memory.

Use a sum [I] [J] to maintain the prefix and.

Code:

#include <iostream>#include <cstdio>#include <cstring>#include <cstdlib>#include <cmath>#include <algorithm>#define Mod 1000000007#define lll __int64using namespace std;#define N 100007lll dp[2][5002],sum[2][5002];int n;int main(){    int a,b,k,i,j;    while(cin>>n>>a>>b>>k)    {        memset(dp,0,sizeof(dp));        memset(sum,0,sizeof(sum));        dp[0][a] = 1LL;        for(i=a;i<=n;i++)            sum[0][i] = 1LL;        int now = 0;        for(i=1;i<=k;i++)        {            now ^= 1;            memset(dp[now],0,sizeof(dp[now]));            memset(sum[now],0,sizeof(sum[now]));            for(j=1;j<=n;j++)            {                if(j < b)                {                    int k = (j+b-1)/2;                    dp[now][j] = (dp[now][j]+sum[now^1][k]-dp[now^1][j])%Mod;                }                else if(j > b)                {                    int k = (j+b+2)/2;                    dp[now][j] = (dp[now][j]+sum[now^1][n]-sum[now^1][k-1]-dp[now^1][j])%Mod;                }                sum[now][j] = (sum[now][j-1]+dp[now][j])%Mod;            }        }        lll sum = 0;        for(i=1;i<=n;i++)            sum = (sum+dp[now][i])%Mod;        cout<<(sum+Mod)%Mod<<endl;    }    return 0;}

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Codeforces round #274 div.1 C riding in a lift -- DP