找到其中包含子序列的最小长度子数组

给定一个包含N 个元素的数组arr[] ，任务是找到最小子数组的长度，该子数组中包含序列{0, 1, 2, 3, 4}作为子序列。

例子：

Input: arr[] = {0, 1, 2, 3, 4, 2, 0, 3, 4} 
Output: 5 
The required Subarray is {0, 1, 2, 3, 4} with minimum length. 
The entire array also includes the sequence 
but it is not minimum in length.

Input: arr[] = {0, 1, 1, 0, 1, 2, 0, 3, 4} 
Output: 6

方法：

• 维护一个大小为5的数组pref[] (等于序列的大小)，其中pref[i]存储给定数组中i的计数直到现在。
• 只有当pref[Array[i] – 1] > 0 时，我们才可以增加任何数字的 pref 计数。这是因为，为了将完整序列作为数组的子序列，所有前面的元素序列必须发生在电流之前。此外，存储到目前为止找到的这些元素的索引。
• 每当我们看到4 时，即子序列的可能结尾和pref[3] > 0意味着我们已经在数组中找到了该序列。现在将该索引标记为结束点和起点，以及从3到0 的所有其他数字。应用二分搜索来找到最接近序列下一个元素的索引，这将为我们提供当前有效子数组的大小。
• 答案是在上一步中找到的所有有效子数组的最小大小。

下面是上述方法的实现：

C++

// C++ implementation of the approach
#include 
using namespace std;
 
#define MAX_INT 1000000
 
// Function to return the minimum length
// of a sub-array which contains
// {0, 1, 2, 3, 4} as a sub-sequence
int solve(int Array[], int N)
{
    // To store the indices where 0, 1, 2,
    // 3 and 4 are present
    vector pos[5];
 
    // To store if there exist a valid prefix
    // of sequence in array
    int pref[5] = { 0 };
 
    // Base Case
    if (Array[0] == 0) {
        pref[0] = 1;
        pos[0].push_back(0);
    }
 
    int ans = MAX_INT;
 
    for (int i = 1; i < N; i++) {
 
        // If current element is 0
        if (Array[i] == 0) {
 
            // Update the count of 0s till now
            pref[0]++;
 
            // Push the index of the new 0
            pos[0].push_back(i);
        }
        else {
 
            // To check if previous element of the
            // given sequence is found till now
            if (pref[Array[i] - 1] > 0) {
                pref[Array[i]]++;
                pos[Array[i]].push_back(i);
 
                // If it is the end of sequence
                if (Array[i] == 4) {
                    int end = i;
                    int start = i;
 
                    // Iterate for other elements of the sequence
                    for (int j = 3; j >= 0; j--) {
                        int s = 0;
                        int e = pos[j].size() - 1;
                        int temp = -1;
 
                        // Binary Search to find closest occurrence
                        // less than equal to starting point
                        while (s <= e) {
                            int m = (s + e) / 2;
                            if (pos[j][m] <= start) {
                                temp = pos[j][m];
                                s = m + 1;
                            }
                            else {
                                e = m - 1;
                            }
                        }
 
                        // Update the starting point
                        start = temp;
                    }
 
                    ans = min(ans, end - start + 1);
                }
            }
        }
    }
 
    return ans;
}
 
// Driver code
int main()
{
    int Array[] = { 0, 1, 2, 3, 4, 2, 0, 3, 4 };
    int N = sizeof(Array) / sizeof(Array[0]);
 
    cout << solve(Array, N);
 
    return 0;
}

Java

// Java implementation of the approach
class GFG
{
static int MAX_INT = 1000000;
 
// Function to return the minimum length
// of a sub-array which contains
// {0, 1, 2, 3, 4} as a sub-sequence
static int solve(int[] array, int N)
{
 
    // To store the indices where 0, 1, 2,
    // 3 and 4 are present
    int[][] pos = new int[5][10000];
 
    // To store if there exist a valid prefix
    // of sequence in array
    int[] pref = new int[5];
 
    // Base Case
    if (array[0] == 0)
    {
        pref[0] = 1;
        pos[0][pos[0].length - 1] = 0;
    }
 
    int ans = MAX_INT;
 
    for (int i = 1; i < N; i++)
    {
 
        // If current element is 0
        if (array[i] == 0)
        {
 
            // Update the count of 0s till now
            pref[0]++;
 
            // Push the index of the new 0
            pos[0][pos[0].length - 1] = i;
        }
         
        else
        {
 
            // To check if previous element of the
            // given sequence is found till now
            if (pref[array[i] - 1] > 0)
            {
                pref[array[i]]++;
                pos[array[i]][pos[array[i]].length - 1] = i;
 
                // If it is the end of sequence
                if (array[i] == 4)
                {
                    int end = i;
                    int start = i;
 
                    // Iterate for other elements of the sequence
                    for (int j = 3; j >= 0; j--)
                    {
                        int s = 0;
                        int e = pos[j].length - 1;
                        int temp = -1;
 
                        // Binary Search to find closest occurrence
                        // less than equal to starting point
                        while (s <= e)
                        {
                            int m = (s + e) / 2;
                            if (pos[j][m] <= start)
                            {
                                temp = pos[j][m];
                                s = m + 1;
                            }
                            else
                                e = m - 1;
                        }
 
                        // Update the starting point
                        start = temp;
                    }
                    ans = Math.min(ans, end - start + 1);
                }
            }
        }
    }
    return ans;
}
 
// Driver Code
public static void main(String[] args)
{
    int[] array = { 0, 1, 2, 3, 4, 2, 0, 3, 4 };
    int N = array.length;
 
    System.out.println(solve(array, N));
}
}
 
// This code is contributed by
// sanjeev2552

Python3

# Python3 implementation of the approach
 
MAX_INT=1000000
 
# Function to return the minimum length
# of a sub-array which contains
# 0, 1, 2, 3, 4 as a sub-sequence
def solve(Array, N):
 
    # To store the indices where 0, 1, 2,
    # 3 and 4 are present
    pos=[[] for i in range(5)]
 
    # To store if there exist a valid prefix
    # of sequence in array
    pref=[0 for i in range(5)]
 
    # Base Case
    if (Array[0] == 0):
        pref[0] = 1
        pos[0].append(0)
     
 
    ans = MAX_INT
 
    for i in range(N):
 
        # If current element is 0
        if (Array[i] == 0):
 
            # Update the count of 0s till now
            pref[0]+=1
 
            # Push the index of the new 0
            pos[0].append(i)
         
        else :
 
            # To check if previous element of the
            # given sequence is found till now
            if (pref[Array[i] - 1] > 0):
                pref[Array[i]]+=1
                pos[Array[i]].append(i)
 
                # If it is the end of sequence
                if (Array[i] == 4) :
                    end = i
                    start = i
 
                    # Iterate for other elements of the sequence
                    for j in range(3,-1,-1):
                        s = 0
                        e = len(pos[j]) - 1
                        temp = -1
 
                        # Binary Search to find closest occurrence
                        # less than equal to starting point
                        while (s <= e):
                            m = (s + e) // 2
                            if (pos[j][m] <= start) :
                                temp = pos[j][m]
                                s = m + 1
                             
                            else :
                                e = m - 1
                             
                         
 
                        # Update the starting point
                        start = temp
                     
 
                    ans = min(ans, end - start + 1)
                 
             
         
     
 
    return ans
 
# Driver code
 
Array = [ 0, 1, 2, 3, 4, 2, 0, 3, 4]
N = len(Array)
 
print(solve(Array, N))
 
# This code is contributed by mohit kumar 29

C#

// C# implementation of the approach
using System;
 
class GFG
{
static int MAX_INT = 1000000;
  
// Function to return the minimum length
// of a sub-array which contains
// {0, 1, 2, 3, 4} as a sub-sequence
static int solve(int[] array, int N)
{
  
    // To store the indices where 0, 1, 2,
    // 3 and 4 are present
    int[,] pos = new int[5,10000];
  
    // To store if there exist a valid prefix
    // of sequence in array
    int[] pref = new int[5];
  
    // Base Case
    if (array[0] == 0)
    {
        pref[0] = 1;
        pos[0,pos.GetLength(0)- 1] = 0;
    }
  
    int ans = MAX_INT;
  
    for (int i = 1; i < N; i++)
    {
  
        // If current element is 0
        if (array[i] == 0)
        {
  
            // Update the count of 0s till now
            pref[0]++;
  
            // Push the index of the new 0
            pos[0,pos.GetLength(0) - 1] = i;
        }
          
        else
        {
  
            // To check if previous element of the
            // given sequence is found till now
            if (pref[array[i] - 1] > 0)
            {
                pref[array[i]]++;
                pos[array[i],pos.GetLength(1) - 1] = i;
  
                // If it is the end of sequence
                if (array[i] == 4)
                {
                    int end = i;
                    int start = i;
  
                    // Iterate for other elements of the sequence
                    for (int j = 3; j >= 0; j--)
                    {
                        int s = 0;
                        int e = pos.GetLength(1) - 1;
                        int temp = -1;
  
                        // Binary Search to find closest occurrence
                        // less than equal to starting point
                        while (s <= e)
                        {
                            int m = (s + e) / 2;
                            if (pos[j,m] <= start)
                            {
                                temp = pos[j,m];
                                s = m + 1;
                            }
                            else
                                e = m - 1;
                        }
  
                        // Update the starting point
                        start = temp;
                    }
                    ans = Math.Min(ans, end - start + 1);
                }
            }
        }
    }
    return ans;
}
  
// Driver Code
public static void Main(String[] args)
{
    int[] array = { 0, 1, 2, 3, 4, 2, 0, 3, 4 };
    int N = array.Length;
  
    Console.WriteLine(solve(array, N));
}
}
 
// This code is contributed by PrinciRaj1992

Javascript

// Javascript implementation of the approach
 
let MAX_INT = 1000000;
 
// Function to return the minimum length
// of a sub-array which contains
// {0, 1, 2, 3, 4} as a sub-sequence
function solve(array,N)
{
    // To store the indices where 0, 1, 2,
    // 3 and 4 are present
    let pos = new Array(5);
    for(let i=0;i<5;i++)
    {
        pos[i]=new Array(10000);
        for(let j=0;j<10000;j++)
        {
            pos[i][j]=0;
        }
    }
   
    // To store if there exist a valid prefix
    // of sequence in array
    let pref = new Array(5);
      for(let i=0;i<5;i++)
    {
        pref[i]=0;
    }
     
    // Base Case
    if (array[0] == 0)
    {
        pref[0] = 1;
        pos[0][pos[0].length - 1] = 0;
    }
   
    let ans = MAX_INT;
   
    for (let i = 1; i < N; i++)
    {
   
        // If current element is 0
        if (array[i] == 0)
        {
   
            // Update the count of 0s till now
            pref[0]++;
   
            // Push the index of the new 0
            pos[0][pos[0].length - 1] = i;
        }
           
        else
        {
   
            // To check if previous element of the
            // given sequence is found till now
            if (pref[array[i] - 1] > 0)
            {
                pref[array[i]]++;
                pos[array[i]][pos[array[i]].length - 1] = i;
   
                // If it is the end of sequence
                if (array[i] == 4)
                {
                    let end = i;
                    let start = i;
   
                    // Iterate for other elements of the sequence
                    for (let j = 3; j >= 0; j--)
                    {
                        let s = 0;
                        let e = pos[j].length - 1;
                        let temp = -1;
   
                        // Binary Search to find closest occurrence
                        // less than equal to starting point
                        while (s <= e)
                        {
                            let m = Math.floor((s + e) / 2);
                            if (pos[j][m] <= start)
                            {
                                temp = pos[j][m];
                                s = m + 1;
                            }
                            else
                                e = m - 1;
                        }
   
                        // Update the starting point
                        start = temp;
                    }
                    ans = Math.min(ans, end - start + 1);
                }
            }
        }
    }
    return ans;
}
 
// Driver Code
let array=[0, 1, 2, 3, 4, 2, 0, 3, 4];
let N = array.length;
document.write(solve(array, N));
 
 
// This code is contributed by patel2127

输出：

5

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