Codeforces Round #274 (Div. 2) E. Riding in a Lift(DP)
2016-03-10 12:05
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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 number b 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).
Input
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).
Output
Print a single integer — the remainder after dividing the sought number of sequences by 1000000007 (109 + 7).
Sample test(s)
input
output
input
output
input
output
题意:做电梯。刚開始的时候你在a层,不能到b层,每次你到新的地方的y,必须满足|x-y|<|x-b|,求坐k次有多少种可能
思路:比較easy想到的是dp[i][j]表示第i次到了j层的可能。分情况讨论。比如:当a<b的时候。下一次的层数i是不能超过j+(b-j-1)/2的,然后每次预先处理出前j层的可能。
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 number b 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).
Input
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).
Output
Print a single integer — the remainder after dividing the sought number of sequences by 1000000007 (109 + 7).
Sample test(s)
input
5 2 4 1
output
2
input
5 2 4 2
output
2
input
5 3 4 1
output
0
题意:做电梯。刚開始的时候你在a层,不能到b层,每次你到新的地方的y,必须满足|x-y|<|x-b|,求坐k次有多少种可能
思路:比較easy想到的是dp[i][j]表示第i次到了j层的可能。分情况讨论。比如:当a<b的时候。下一次的层数i是不能超过j+(b-j-1)/2的,然后每次预先处理出前j层的可能。
#include <iostream> #include <cstdio> #include <cstring> #include <algorithm> #include <cmath> using namespace std; const int mod = 1000000007; const int maxn = 5005; int n, a, b, k, dp[maxn][maxn]; int sum[maxn]; int main() { scanf("%d%d%d%d", &n, &a, &b, &k); memset(dp, 0, sizeof(dp)); if (a < b) { dp[0][a] = 1; for (int j = 1; j < b; j++) sum[j] = sum[j-1] + dp[0][j]; for (int i = 1; i <= k; i++) { for (int j = 1; j < b; j++) dp[i][j] = (sum[(b-j-1)/2+j] - dp[i-1][j] + mod) % mod; sum[0] = 0; for (int j = 1; j < b; j++) sum[j] = (sum[j-1] + dp[i][j]) % mod; } printf("%d\n", sum[b-1]); } else { dp[0][a] = 1; for (int j = n; j >= b+1; j--) sum[j] = sum[j+1] + dp[0][j]; for (int i = 1; i <= k; i++) { for (int j = b+1; j <= n; j++) dp[i][j] = (sum[j-(j-b-1)/2] - dp[i-1][j] + mod) % mod; sum[0] = 0; for (int j = n; j >= b+1; j--) sum[j] = (sum[j+1] + dp[i][j]) % mod; } printf("%d\n", sum[b+1]); } return 0; }
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