给定一个整数N ，代表楼梯的数量，值从1到N ，以及一个起始位置S ，任务是计算可以通过准确地向前或向后移动A或B楼梯步骤到达的唯一楼梯的最大数量任何位置，任何次数。
例子：
Input: N = 10, S = 2, A = 5, B = 7
Output: 4
Explanation:
Starting Position S: Stair 2
From Stair 2, it is possible to reach the stairs 7, i.e. ( S + A ), and 9, i.e. (S + B).
From Stair 9, it is possible to reach stair 4, i.e. ( S – A ).
Therefore, the unique number of stairs that can be reached is 4 {2, 4, 7, 9}.
Input: N = 10, S = 2, A = 3, B = 4
Output: 10
方法：给定的问题可以使用 BFS 遍历技术解决。请按照以下步骤解决问题：
- 初始化一个队列和一个大小为(N + 1)的数组vis[]并将其初始化为false 。
- 将起始节点S标记为已访问，即vis[S]为1 。将S推入队列Q 。
- 现在迭代直到Q不为空并执行以下步骤：
- 弹出队列的前端元素并将其存储在一个变量中，比如currStair 。
- 考虑来自currStair 的所有 4 种可能的移动类型，即{+A, -A, +B, -B} 。
- 对于每一个新楼梯，检查它是否是一个有效且未被访问过的楼梯。如果发现为真，则将其推入Q 。将楼梯标记为已访问。否则，继续。
- 最后，使用数组vis[]计算已访问楼梯的数量。
- 完成上述步骤后，打印访问楼梯的数量作为结果。
下面是上述方法的实现：
C++
// C++ program for the above approach
#include
using namespace std;
// Function to count the number
// of unique stairs visited
void countStairs(int n, int x, int a, int b)
{
// Checks whether the current
// stair is visited or not
int vis[n + 1] = { 0 };
// Store the possible moves
// from the current position
int moves[] = { +a, -a, +b, -b };
// Initialize a queue
queue q;
/// Push the starting position
q.push(x);
// Mark the starting
// position S as visited
vis[x] = 1;
// Interate until queue is not empty
while (!q.empty()) {
// Store the current stair number
int currentStair = q.front();
// Pop it from the queue
q.pop();
// Check for all possible moves
// from the current stair
for (int j = 0; j < 4; j++) {
// Store the new stair number
int newStair = currentStair + moves[j];
// If it is valid and unvisited
if (newStair > 0 && newStair <= n
&& !vis[newStair]) {
// Push it into queue
q.push(newStair);
// Mark the stair as visited
vis[newStair] = 1;
}
}
}
// Store the result
int cnt = 0;
// Count the all visited stairs
for (int i = 1; i <= n; i++)
if (vis[i] == 1)
cnt++;
// Print the result
cout << cnt;
}
// Driver Code
int main()
{
int N = 10, S = 2, A = 5, B = 7;
countStairs(N, S, A, B);
return 0;
} Java
// Java program for the above approach
import java.util.LinkedList;
import java.util.Queue;
class GFG{
// Function to count the number
// of unique stairs visited
static void countStairs(int n, int x, int a, int b)
{
// Checks whether the current
// stair is visited or not
int[] vis = new int[n + 1];
// Store the possible moves
// from the current position
int[] moves = { +a, -a, +b, -b };
// Initialize a queue
Queue q = new LinkedList();
/// Push the starting position
q.add(x);
// Mark the starting
// position S as visited
vis[x] = 1;
// Interate until queue is not empty
while (!q.isEmpty())
{
// Store the current stair number
int currentStair = q.peek();
// Pop it from the queue
q.remove();
// Check for all possible moves
// from the current stair
for(int j = 0; j < 4; j++)
{
// Store the new stair number
int newStair = currentStair + moves[j];
// If it is valid and unvisited
if (newStair > 0 && newStair <= n &&
vis[newStair] == 0)
{
// Push it into queue
q.add(newStair);
// Mark the stair as visited
vis[newStair] = 1;
}
}
}
// Store the result
int cnt = 0;
// Count the all visited stairs
for(int i = 1; i <= n; i++)
if (vis[i] == 1)
cnt++;
// Print the result
System.out.print(cnt);
}
// Driver Code
public static void main(String args[])
{
int N = 10, S = 2, A = 5, B = 7;
countStairs(N, S, A, B);
}
}
// This code is contributed by abhinavjain194 Python3
# Python3 program for the above approach
from collections import deque
# Function to count the number
# of unique stairs visited
def countStairs(n, x, a, b):
# Checks whether the current
# stair is visited or not
vis = [0] * (n + 1)
# Store the possible moves
# from the current position
moves = [+a, -a, +b, -b]
# Initialize a queue
q = deque()
# Push the starting position
q.append(x)
# Mark the starting
# position S as visited
vis[x] = 1
# Interate until queue is not empty
while (len(q) > 0):
# Store the current stair number
currentStair = q.popleft()
# Pop it from the queue
# q.pop()
# Check for all possible moves
# from the current stair
for j in range(4):
# Store the new stair number
newStair = currentStair + moves[j]
# If it is valid and unvisited
if (newStair > 0 and newStair <= n and
(not vis[newStair])):
# Push it into queue
q.append(newStair)
# Mark the stair as visited
vis[newStair] = 1
# Store the result
cnt = 0
# Count the all visited stairs
for i in range(1, n + 1):
if (vis[i] == 1):
cnt += 1
# Print the result
print (cnt)
# Driver Code
if __name__ == '__main__':
N, S, A, B = 10, 2, 5, 7
countStairs(N, S, A, B)
# This code is contributed by mohit kumar 29C#
// C# program for the above approach
using System;
using System.Collections.Generic;
class GFG{
// Function to count the number
// of unique stairs visited
static void countStairs(int n, int x,
int a, int b)
{
// Checks whether the current
// stair is visited or not
int []vis = new int[n + 1];
Array.Clear(vis, 0, vis.Length);
// Store the possible moves
// from the current position
int []moves = { +a, -a, +b, -b };
// Initialize a queue
Queue q = new Queue();
/// Push the starting position
q.Enqueue(x);
// Mark the starting
// position S as visited
vis[x] = 1;
// Interate until queue is not empty
while (q.Count > 0)
{
// Store the current stair number
int currentStair = q.Peek();
// Pop it from the queue
q.Dequeue();
// Check for all possible moves
// from the current stair
for(int j = 0; j < 4; j++)
{
// Store the new stair number
int newStair = currentStair + moves[j];
// If it is valid and unvisited
if (newStair > 0 && newStair <= n &&
vis[newStair] == 0)
{
// Push it into queue
q.Enqueue(newStair);
// Mark the stair as visited
vis[newStair] = 1;
}
}
}
// Store the result
int cnt = 0;
// Count the all visited stairs
for(int i = 1; i <= n; i++)
if (vis[i] == 1)
cnt++;
// Print the result
Console.WriteLine(cnt);
}
// Driver Code
public static void Main()
{
int N = 10, S = 2, A = 5, B = 7;
countStairs(N, S, A, B);
}
}
// This code is contributed by ipg2016107 Javascript
输出：
4时间复杂度： O(N)
辅助空间： O(N)