【CODEFORCES】 C. Riding in a Lift
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Imagine that you are in a building that has exactly n floors. You can move between the floors in a lift. Let's number the floors from bottom to top with integers from 1 to n. Now you're on the floor number a. You are very bored, so you want to take the lift. Floor numberb has a secret lab, the entry is forbidden. However, you already are in the mood and decide to make k consecutive trips in the lift.
Let us suppose that at the moment you are on the floor number x (initially, you were on floor a). For another trip between floors you choose some floor with number y (y ≠ x) and the lift travels to this floor. As you cannot visit floor b with the secret lab, you decided that the distance from the current floor x to the chosen y must be strictly less than the distance from the current floor x to floor b with the secret lab. Formally, it means that the following inequation must fulfill: |x - y| < |x - b|. After the lift successfully transports you to floor y, you write down number y in your notepad.
Your task is to find the number of distinct number sequences that you could have written in the notebook as the result of k trips in the lift. As the sought number of trips can be rather large, find the remainder after dividing the number by 1000000007 (109 + 7).
The first line of the input contains four space-separated integers n, a, b, k (2 ≤ n ≤ 5000, 1 ≤ k ≤ 5000, 1 ≤ a, b ≤ n, a ≠ b).
Print a single integer — the remainder after dividing the sought number of sequences by 1000000007 (109 + 7).
5 2 4 1
2
5 2 4 2
2
5 3 4 1
0
Two sequences p1, p2, ..., pk and q1, q2, ..., qk are distinct, if there is such integer j (1 ≤ j ≤ k), that pj ≠ qj.
Notes to the samples:
- In the first sample after the first trip you are either on floor 1, or on floor 3, because |1 - 2| < |2 - 4| and |3 - 2| < |2 - 4|.
- In the second sample there are two possible sequences: (1, 2); (1, 3). You cannot choose floor 3 for the first trip because in this case no floor can be the floor for the second trip.
- In the third sample there are no sought sequences, because you cannot choose the floor for the first trip.
#include <iostream>#include <cstdio>#include <cstring>#include <cstdlib>const long long mod=1000000007;using namespace std;long long n,a,b,k,d[5005][5005],ans,sum[5005];void solve(int p){ if (a<b) for (int i=1;i<=b;i++) sum[i]=(sum[i-1]+d[p][i])%mod; else for (int i=n;i>=b;i--) sum[i]=(sum[i+1]+d[p][i])%mod;}int main(){ scanf("%I64d%I64d%I64d%I64d",&n,&a,&b,&k); memset(d,0,sizeof(d)); d[0][a]=1; for (int i=1;i<=k;i++) { solve(i-1); for (int j=1;j<=n;j++) if ((b-a)*(b-j)>0 && a<b) d[i][j]=(sum[(j+b-1)/2]%mod-d[i-1][j]%mod+mod)%mod; else if ((b-a)*(b-j)>0 && a>b) d[i][j]=(sum[(j+b)/2+1]%mod-d[i-1][j]%mod+mod)%mod; } for (int j=1;j<=n;j++) ans=(ans+d[k][j])%mod; printf("%I64d",ans); return 0;}
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