Consultas para encontrar la diferencia absoluta mínima entre elementos de array adyacentes en rangos dados

Dada una array arr[] que consta de N enteros y una array query[] que consta de consultas de la forma {L, R} , la tarea de cada consulta es encontrar el mínimo de la diferencia absoluta entre elementos adyacentes en el rango [L , R] .

Ejemplos:

Entrada: arr[] = {2, 6, 1, 8, 3, 4}, query[] = {{0, 3}, {1, 5}, {4, 5}}
Salida:
4
1
1
Explicación:
Los siguientes son los valores de las consultas realizadas:

  1. La diferencia absoluta mínima entre elementos adyacentes en el rango [0, 3] es min(|2 – 6|, |6 – 1|, |1 – 8|) = 4.
  2. La diferencia absoluta mínima entre elementos adyacentes en el rango [1, 5] es min(|6 – 1|, |1 – 8|, |8 – 3|, |3 – 4| ) = 1.
  3. La diferencia absoluta mínima entre elementos adyacentes en el rango [4, 5] es min(|3 – 4|) = 1.

Por lo tanto, imprima 4, 1, 1 como los resultados de las consultas dadas.

Entrada: arr[] = [10, 20, 1, 1, 5 ], consulta[] = [0, 1], [1, 4], [2, 3]
Salida:
10
0
0

Enfoque ingenuo: el enfoque más simple para resolver el problema dado es crear una array diff[] que almacene la diferencia absoluta entre elementos adyacentes para cada elemento de la array. Ahora, para cada consulta, recorra la array diff[] sobre el rango [L, R – 1] e imprima el valor mínimo de todos los valores en el rango [L, R – 1] .

A continuación se muestra la implementación del enfoque anterior:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Structure for query range
struct Query {
    int L, R;
};
 
int MAX = 5000;
 
// Function to find the minimum difference
// between adjacent array element over the
// given range [L, R] for Q Queries
void minDifference(int arr[], int n,
                   Query q[], int m)
{
 
    // Find the sum of all queries
    for (int i = 0; i < m; i++) {
 
        // Left and right boundaries
        // of current range
        int L = q[i].L, R = q[i].R;
 
        int ans = MAX;
        for (int i = L; i < R; i++) {
            ans = min(ans, arr[i]);
        }
 
        // Print  the sum of the
        // current query range
        cout << ans << '\n';
    }
}
 
// Function to find the minimum absolute
// difference of adjacent array elements
// for the given range
void minimumDifference(int arr[], Query q[],
                       int N, int m)
{
 
    // Stores the absolute difference of
    // adjacent elements
    int diff[N];
 
    for (int i = 0; i < N - 1; i++)
        diff[i] = abs(arr[i] - arr[i + 1]);
 
    // Find the minimum difference of
    // adjacent elements
    minDifference(diff, N - 1, q, m);
}
 
// Driver Code
int main()
{
    int arr[] = { 2, 6, 1, 8, 3, 4 };
    int N = sizeof(arr) / sizeof(arr[0]);
    Query Q[] = { { 0, 3 }, { 1, 5 }, { 4, 5 } };
    int M = sizeof(Q) / sizeof(Q[0]);
 
    minimumDifference(arr, Q, N, M);
 
    return 0;
}

Java

// Java program for the above approach
class GFG{
 
// Structure for query range
static class Query {
    int L, R;
 
    public Query(int l, int r) {
        super();
        L = l;
        R = r;
    }
     
};
 
static int MAX = 5000;
 
// Function to find the minimum difference
// between adjacent array element over the
// given range [L, R] for Q Queries
static void minDifference(int arr[], int n,
                   Query q[], int m)
{
 
    // Find the sum of all queries
    for (int i = 0; i < m; i++) {
 
        // Left and right boundaries
        // of current range
        int L = q[i].L, R = q[i].R;
 
        int ans = MAX;
        for (int j = L; j < R; j++) {
            ans = Math.min(ans, arr[j]);
        }
 
        // Print  the sum of the
        // current query range
        System.out.println(ans);
    }
}
 
// Function to find the minimum absolute
// difference of adjacent array elements
// for the given range
static void minimumDifference(int arr[], Query q[],
                       int N, int m)
{
 
    // Stores the absolute difference of
    // adjacent elements
    int []diff = new int[N];
 
    for (int i = 0; i < N - 1; i++)
        diff[i] = Math.abs(arr[i] - arr[i + 1]);
 
    // Find the minimum difference of
    // adjacent elements
    minDifference(diff, N - 1, q, m);
}
 
// Driver Code
public static void main(String[] args)
{
    int arr[] = { 2, 6, 1, 8, 3, 4 };
    int N = arr.length;
    Query Q[] = {new Query( 0, 3 ),new Query( 1, 5 ),new Query( 4, 5 ) };
    int M = Q.length;
 
    minimumDifference(arr, Q, N, M);
 
}
}
 
// This code is contributed by Princi Singh

Python3

# Python3 program for the above approach
MAX = 5000;
 
# Function to find the minimum difference
# between adjacent array element over the
# given range [L, R] for Q Queries
def minDifference(arr, n, q, m) :
 
    # Find the sum of all queries
    for i in range(m) :
         
        # Left and right boundaries
        # of current range
        L = q[i][0]; R = q[i][1];
 
        ans = MAX;
        for i in range(L, R) :
            ans = min(ans, arr[i]);
 
        # Print  the sum of the
        # current query range
        print(ans);
     
 
# Function to find the minimum absolute
# difference of adjacent array elements
# for the given range
def minimumDifference(arr, q, N, m) :
 
    # Stores the absolute difference of
    # adjacent elements
    diff = [0]*N;
 
    for i in range(N - 1) :
        diff[i] = abs(arr[i] - arr[i + 1]);
 
    # Find the minimum difference of
    # adjacent elements
    minDifference(diff, N - 1, q, m);
 
# Driver Code
if __name__ == "__main__" :
 
    arr = [ 2, 6, 1, 8, 3, 4 ];
    N = len(arr);
    Q = [ [ 0, 3 ], [ 1, 5 ], [ 4, 5 ] ];
    M = len(Q);
 
    minimumDifference(arr, Q, N, M);
     
    # This code is contributed by AnkThon

C#

// C# program for the above approach
using System;
using System.Collections.Generic;
 
class GFG{
 
// Structure for query range
class Query {
    public int L, R;
 
    public Query(int l, int r) {
        this.L = l;
        this.R = r;
    }
     
};
 
static int MAX = 5000;
 
// Function to find the minimum difference
// between adjacent array element over the
// given range [L, R] for Q Queries
static void minDifference(int []arr, int n,
                   Query []q, int m)
{
 
    // Find the sum of all queries
    for (int i = 0; i < m; i++) {
 
        // Left and right boundaries
        // of current range
        int L = q[i].L, R = q[i].R;
 
        int ans = MAX;
        for (int j = L; j < R; j++) {
            ans = Math.Min(ans, arr[j]);
        }
 
        // Print  the sum of the
        // current query range
        Console.WriteLine(ans);
    }
}
 
// Function to find the minimum absolute
// difference of adjacent array elements
// for the given range
static void minimumDifference(int []arr, Query []q,
                       int N, int m)
{
 
    // Stores the absolute difference of
    // adjacent elements
    int []diff = new int[N];
 
    for (int i = 0; i < N - 1; i++)
        diff[i] = Math.Abs(arr[i] - arr[i + 1]);
 
    // Find the minimum difference of
    // adjacent elements
    minDifference(diff, N - 1, q, m);
}
 
// Driver Code
public static void Main()
{
    int []arr = { 2, 6, 1, 8, 3, 4 };
    int N = arr.Length;
    Query []Q = {new Query( 0, 3 ),new Query( 1, 5 ),new Query( 4, 5 ) };
    int M = Q.Length;
 
    minimumDifference(arr, Q, N, M);
 
}
}
 
// This code is contributed by SURENDRA_GANGWAR.

Javascript

<script>
 
        // JavaScript program for the above approach;
        let MAX = 5000;
 
        // Function to find the minimum difference
        // between adjacent array element over the
        // given range [L, R] for Q Queries
        function minDifference(arr, n, q, m)
        {
 
            // Find the sum of all queries
            for (let i = 0; i < m; i++) {
 
                // Left and right boundaries
                // of current range
                let L = q[i][0], R = q[i][1];
 
                let ans = MAX;
                for (let i = L; i < R; i++) {
                    ans = Math.min(ans, arr[i]);
                }
 
                // Print  the sum of the
                // current query range
                document.write(ans+'<br>');
            }
        }
 
        // Function to find the minimum absolute
        // difference of adjacent array elements
        // for the given range
        function minimumDifference(arr, q, N, m) {
 
            // Stores the absolute difference of
            // adjacent elements
            let diff = new Array(N);
 
            for (let i = 0; i < N - 1; i++)
                diff[i] = Math.abs(arr[i] - arr[i + 1]);
 
            // Find the minimum difference of
            // adjacent elements
            minDifference(diff, N - 1, q, m);
        }
 
        // Driver Code
 
        let arr = [2, 6, 1, 8, 3, 4];
        let N = arr.length;
        let Q = [[0, 3], [1, 5], [4, 5]];
        let M = Q.length;
 
        minimumDifference(arr, Q, N, M);
 
//This code is contributed by Potta Lokesh
    </script>
Producción: 

4
1
1

 

Tiempo Complejidad: O(N 2 )
Espacio Auxiliar: O(N)

Enfoque eficiente: el enfoque anterior también se puede optimizar mediante el uso de la tabla dispersa que admite consultas en tiempo constante O(1) con espacio adicional O(N log N) . En lugar de pasar original arr[], pase diff[] para obtener la respuesta requerida. Siga los pasos a continuación para resolver el problema:

  1. Inicialice una búsqueda de array global [][] para la array dispersa.
  2. Defina una función preprocess(arr, N) y realice las siguientes operaciones:
    • Itere sobre el rango [0, N) usando la variable i y establezca el valor de lookup[i][0] como i .
    • Iterar sobre el rango [1, N) usando las variables j e i anidadas y si arr[buscar[i][j-1]] es menor que arr[buscar[i + (1 << (j-1))] [j-1] , luego configure lookup[i][j] como lookup[i][j-1] , de lo contrario, configure lookup[i][j] como lookup[i + (1 << (j – 1)) ][j – 1] .
  3. Defina una  consulta de función (int arr[], int L, int M) y realice las siguientes operaciones:
    • Inicialice la variable j como (int)log2(R – L + 1) .
    • Si arr[buscar[L][j]] es menor que arr[buscar[R – (1 << j) + 1][j]], entonces devuelve arr[buscar[L][j]], de lo contrario return arr[buscar[R – (1 << j) + 1][j]] .
  4. Defina una función Min_difference(arr, n, q, m) y realice las siguientes operaciones:
    • Llame a la función preprocess(arr, n) para preprocesar la array dispersa.
    • Recorra la array dada de consultas Q[] y el valor devuelto por la función query(arr, L, R – 1) da el resultado de la consulta actual.
  5. Inicialice una array diff[] de tamaño N y almacene las diferencias absolutas de arr[i]-arr[i+1] para cada valor de i .
  6. Llame a la función Min_difference(diff, N-1, q, m) para encontrar la diferencia absoluta mínima para cada consulta.

A continuación se muestra la implementación del enfoque anterior:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
#define MAX 500
 
// Stores the index for the minimum
// value in the subarray arr[i, j]
int lookup[MAX][MAX];
 
// Structure for query range
struct Query {
    int L, R;
};
 
// Function to fill the lookup array
// lookup[][] in the bottom up manner
void preprocess(int arr[], int n)
{
    // Initialize M for the intervals
    // with length 1
    for (int i = 0; i < n; i++)
        lookup[i][0] = i;
 
    // Find the values from smaller
    // to bigger intervals
    for (int j = 1; (1 << j) <= n; j++) {
 
        // Compute minimum value for
        // all intervals with size 2^j
        for (int i = 0; (i + (1 << j) - 1) < n; i++) {
 
            // For arr[2][10], compare
            // arr[lookup[0][3]] and
            // arr[lookup[3][3]]
            if (arr[lookup[i][j - 1]]
                < arr[lookup[i + (1 << (j - 1))][j - 1]])
                lookup[i][j] = lookup[i][j - 1];
 
            // Otherwise
            else
                lookup[i][j]
                    = lookup[i + (1 << (j - 1))][j - 1];
        }
    }
}
 
// Function find minimum of absolute
// difference of all adjacent element
// in subarray arr[L..R]
int query(int arr[], int L, int R)
{
    // For [2, 10], j = 3
    int j = (int)log2(R - L + 1);
 
    // For [2, 10], compare arr[lookup[0][3]]
    // and arr[lookup[3][3]],
    if (arr[lookup[L][j]]
        <= arr[lookup[R - (1 << j) + 1][j]])
        return arr[lookup[L][j]];
 
    else
        return arr[lookup[R - (1 << j) + 1][j]];
}
 
// Function to find the minimum of the
// ranges for M queries
void Min_difference(int arr[], int n,
                    Query q[], int m)
{
    // Fills table lookup[n][Log n]
    preprocess(arr, n);
 
    // Compute sum of all queries
    for (int i = 0; i < m; i++) {
 
        // Left and right boundaries
        // of current range
        int L = q[i].L, R = q[i].R;
 
        // Print sum of current query range
        cout << query(arr, L, R - 1) << '\n';
    }
}
 
// Function to find the minimum absolute
// difference in a range
void minimumDifference(int arr[], Query q[],
                       int N, int m)
{
 
    // diff[] is to stores the absolute
    // difference of adjacent elements
    int diff[N];
    for (int i = 0; i < N - 1; i++)
        diff[i] = abs(arr[i] - arr[i + 1]);
 
    // Call Min_difference to get minimum
    // difference of adjacent elements
    Min_difference(diff, N - 1, q, m);
}
 
// Driver Code
int main()
{
    int arr[] = { 2, 6, 1, 8, 3, 4 };
    int N = sizeof(arr) / sizeof(arr[0]);
    Query Q[] = { { 0, 3 }, { 1, 5 }, { 4, 5 } };
    int M = sizeof(Q) / sizeof(Q[0]);
 
    minimumDifference(arr, Q, N, M);
 
    return 0;
}

Java

// Java program for the above approach
import java.util.*;
import javax.management.Query;
 
class GFG{
static final int MAX = 500;
 
// Stores the index for the minimum
// value in the subarray arr[i, j]
static int [][]lookup = new int[MAX][MAX];
 
// Structure for query range
static class Query {
    int L, R;
 
    public Query(int l, int r) {
        super();
        L = l;
        R = r;
    }
};
 
// Function to fill the lookup array
// lookup[][] in the bottom up manner
static void preprocess(int arr[], int n)
{
    // Initialize M for the intervals
    // with length 1
    for (int i = 0; i < n; i++)
        lookup[i][0] = i;
 
    // Find the values from smaller
    // to bigger intervals
    for (int j = 1; (1 << j) <= n; j++) {
 
        // Compute minimum value for
        // all intervals with size 2^j
        for (int i = 0; (i + (1 << j) - 1) < n; i++) {
 
            // For arr[2][10], compare
            // arr[lookup[0][3]] and
            // arr[lookup[3][3]]
            if (arr[lookup[i][j - 1]]
                < arr[lookup[i + (1 << (j - 1))][j - 1]])
                lookup[i][j] = lookup[i][j - 1];
 
            // Otherwise
            else
                lookup[i][j]
                    = lookup[i + (1 << (j - 1))][j - 1];
        }
    }
}
 
// Function find minimum of absolute
// difference of all adjacent element
// in subarray arr[L..R]
static int query(int arr[], int L, int R)
{
    // For [2, 10], j = 3
    int j = (int)Math.log(R - L + 1);
 
    // For [2, 10], compare arr[lookup[0][3]]
    // and arr[lookup[3][3]],
    if (arr[lookup[L][j]]
        <= arr[lookup[R - (1 << j) + 1][j]])
        return arr[lookup[L][j]];
 
    else
        return arr[lookup[R - (1 << j) + 1][j]];
}
 
// Function to find the minimum of the
// ranges for M queries
static void Min_difference(int arr[], int n,
                    Query q[], int m)
{
    // Fills table lookup[n][Log n]
    preprocess(arr, n);
 
    // Compute sum of all queries
    for (int i = 0; i < m; i++) {
 
        // Left and right boundaries
        // of current range
        int L = q[i].L, R = q[i].R;
 
        // Print sum of current query range
        System.out.println(query(arr, L, R - 1));
    }
}
 
// Function to find the minimum absolute
// difference in a range
static void minimumDifference(int arr[], Query q[],
                       int N, int m)
{
 
    // diff[] is to stores the absolute
    // difference of adjacent elements
    int []diff = new int[N];
    for (int i = 0; i < N - 1; i++)
        diff[i] = Math.abs(arr[i] - arr[i + 1]);
 
    // Call Min_difference to get minimum
    // difference of adjacent elements
    Min_difference(diff, N - 1, q, m);
}
 
// Driver Code
public static void main(String[] args)
{
    int arr[] = { 2, 6, 1, 8, 3, 4 };
    int N = arr.length;
    Query Q[] = { new Query( 0, 3 ), new Query( 1, 5 ), new Query( 4, 5 ) };
    int M = Q.length;
 
    minimumDifference(arr, Q, N, M);
 
}
}
 
// This code is contributed by 29AjayKumar

Python3

# Python program for the above approach:
import math
 
MAX = 500
 
## Structure for query range
class Query:
    def __init__(self, l, r):
        self.L = l
        self.R = r
 
## Function to fill the lookup array
## lookup[][] in the bottom up manner
def preprocess(arr, n):
    ## Initialize M for the intervals
    ## with length 1
    for i in range(n):
        lookup[i][0] = i;
 
    ## Find the values from smaller
    ## to bigger intervals
    j = 1
    while True:
        if (1 << j) > n:
            break
 
        ## Compute minimum value for
        ## all intervals with size 2^j
        for i in range(n + 1 - (1 << j)):
 
            ## For arr[2][10], compare
            ## arr[lookup[0][3]] and
            ## arr[lookup[3][3]]
            if (arr[lookup[i][j - 1]] < arr[lookup[i + (1 << (j - 1))][j - 1]]):
                lookup[i][j] = lookup[i][j - 1];
 
            ## Otherwise
            else:
                lookup[i][j] = lookup[i + (1 << (j - 1))][j - 1]
 
        j+=1
 
## Function find minimum of absolute
## difference of all adjacent element
## in subarray arr[L..R]
def query(arr, L, R):
    ## For [2, 10], j = 3
    j = int(math.log2(R - L + 1))
 
    ## For [2, 10], compare arr[lookup[0][3]]
    ## and arr[lookup[3][3]],
    if (arr[lookup[L][j]] <= arr[lookup[R - (1 << j) + 1][j]]):
        return arr[lookup[L][j]]
 
    else:
        return arr[lookup[R - (1 << j) + 1][j]]
 
## Function to find the minimum of the
## ranges for M queries
def Min_difference(arr, n, q, m):
    ## Fills table lookup[n][Log n]
    preprocess(arr, n)
 
    ## Compute sum of all queries
    for i in range(0, m):
 
        ## Left and right boundaries
        ## of current range
        L = q[i].L
        R = q[i].R;
 
        ## Print sum of current query range
        print(query(arr, L, R - 1))
 
## Function to find the minimum absolute
## difference in a range
def minimumDifference(arr, q, N, m):
 
    ## diff[] is to stores the absolute
    ## difference of adjacent elements
    diff = [];
    for i in range(N):
        diff.append(0)
     
    for i in range(0, N-1):
        diff[i] = abs(arr[i] - arr[i + 1]);
 
    ## Call Min_difference to get minimum
    ## difference of adjacent elements
    Min_difference(diff, N - 1, q, m)
 
 
## Driver code
if __name__=='__main__':
 
    arr = [ 2, 6, 1, 8, 3, 4 ]
    N = len(arr)
    Q = [ Query(0, 3), Query(1, 5), Query(4, 5) ]
    M = len(Q)
 
    ## Stores the index for the minimum
    ## value in the subarray arr[i, j]
    global lookup
    lookup = []
    for i in range(0, MAX):
        lookup.append([])
        for j in range(0, MAX):
            lookup[i].append(0)
 
    minimumDifference(arr, Q, N, M)
     
    # This code is contributed by subhamgoyal2014.

C#

// C# program for the above approach
using System;
 
public class GFG{
static readonly int MAX = 500;
 
// Stores the index for the minimum
// value in the subarray arr[i, j]
static int [,]lookup = new int[MAX, MAX];
 
// Structure for query range
class Query {
    public int L, R;
 
    public Query(int l, int r) {
        
        L = l;
        R = r;
    }
};
 
// Function to fill the lookup array
// lookup[,] in the bottom up manner
static void preprocess(int []arr, int n)
{
   
    // Initialize M for the intervals
    // with length 1
    for (int i = 0; i < n; i++)
        lookup[i,0] = i;
 
    // Find the values from smaller
    // to bigger intervals
    for (int j = 1; (1 << j) <= n; j++) {
 
        // Compute minimum value for
        // all intervals with size 2^j
        for (int i = 0; (i + (1 << j) - 1) < n; i++) {
 
            // For arr[2,10], compare
            // arr[lookup[0,3]] and
            // arr[lookup[3,3]]
            if (arr[lookup[i,j - 1]]
                < arr[lookup[i + (1 << (j - 1)),j - 1]])
                lookup[i,j] = lookup[i,j - 1];
 
            // Otherwise
            else
                lookup[i,j]
                    = lookup[i + (1 << (j - 1)),j - 1];
        }
    }
}
 
// Function find minimum of absolute
// difference of all adjacent element
// in subarray arr[L..R]
static int query(int []arr, int L, int R)
{
   
    // For [2, 10], j = 3
    int j = (int)Math.Log(R - L + 1);
 
    // For [2, 10], compare arr[lookup[0,3]]
    // and arr[lookup[3,3]],
    if (arr[lookup[L,j]]
        <= arr[lookup[R - (1 << j) + 1,j]])
        return arr[lookup[L,j]];
 
    else
        return arr[lookup[R - (1 << j) + 1,j]];
}
 
// Function to find the minimum of the
// ranges for M queries
static void Min_difference(int []arr, int n,
                    Query []q, int m)
{
   
    // Fills table lookup[n,Log n]
    preprocess(arr, n);
 
    // Compute sum of all queries
    for (int i = 0; i < m; i++) {
 
        // Left and right boundaries
        // of current range
        int L = q[i].L, R = q[i].R;
 
        // Print sum of current query range
        Console.WriteLine(query(arr, L, R - 1));
    }
}
 
// Function to find the minimum absolute
// difference in a range
static void minimumDifference(int []arr, Query []q,
                       int N, int m)
{
 
    // diff[] is to stores the absolute
    // difference of adjacent elements
    int []diff = new int[N];
    for (int i = 0; i < N - 1; i++)
        diff[i] = Math.Abs(arr[i] - arr[i + 1]);
 
    // Call Min_difference to get minimum
    // difference of adjacent elements
    Min_difference(diff, N - 1, q, m);
} 
 
// Driver Code
public static void Main(String[] args)
{
    int []arr = { 2, 6, 1, 8, 3, 4 };
    int N = arr.Length;
    Query []Q = { new Query( 0, 3 ), new Query( 1, 5 ), new Query( 4, 5 ) };
    int M = Q.Length;
 
    minimumDifference(arr, Q, N, M);
 
}
}
 
// This code is contributed by shikhasingrajput

Javascript

<script>
// Javascript program for the above approach
let MAX = 500;
 
// Stores the index for the minimum
// value in the subarray arr[i, j]
let lookup = new Array(MAX).fill(0).map(() => new Array(MAX).fill(0));
 
// Structure for query range
class Query {
  constructor(l, r) {
    this.L = l;
    this.R = r;
  }
}
 
// Function to fill the lookup array
// lookup[][] in the bottom up manner
function preprocess(arr, n)
{
 
  // Initialize M for the intervals
  // with length 1
  for (let i = 0; i < n; i++) lookup[i][0] = i;
 
  // Find the values from smaller
  // to bigger intervals
  for (let j = 1; 1 << j <= n; j++)
  {
   
    // Compute minimum value for
    // all intervals with size 2^j
    for (let i = 0; i + (1 << j) - 1 < n; i++)
    {
     
      // For arr[2][10], compare
      // arr[lookup[0][3]] and
      // arr[lookup[3][3]]
      if (arr[lookup[i][j - 1]] < arr[lookup[i + (1 << (j - 1))][j - 1]])
        lookup[i][j] = lookup[i][j - 1];
         
      // Otherwise
      else lookup[i][j] = lookup[i + (1 << (j - 1))][j - 1];
    }
  }
}
 
// Function find minimum of absolute
// difference of all adjacent element
// in subarray arr[L..R]
function query(arr, L, R)
{
 
  // For [2, 10], j = 3
  let j = Math.floor(Math.log(R - L + 1));
 
  // For [2, 10], compare arr[lookup[0][3]]
  // and arr[lookup[3][3]],
  if (arr[lookup[L][j]] <= arr[lookup[R - (1 << j) + 1][j]])
    return arr[lookup[L][j]];
  else return arr[lookup[R - (1 << j) + 1][j]];
}
 
// Function to find the minimum of the
// ranges for M queries
function Min_difference(arr, n, q, m)
{
 
  // Fills table lookup[n][Log n]
  preprocess(arr, n);
 
  // Compute sum of all queries
  for (let i = 0; i < m; i++)
  {
   
    // Left and right boundaries
    // of current range
    let L = q[i].L,
      R = q[i].R;
 
    // let sum of current query range
    document.write(query(arr, L, R - 1) + "<br>");
  }
}
 
// Function to find the minimum absolute
// difference in a range
function minimumDifference(arr, q, N, m)
{
 
  // diff[] is to stores the absolute
  // difference of adjacent elements
  let diff = new Array(N);
  for (let i = 0; i < N - 1; i++) diff[i] = Math.abs(arr[i] - arr[i + 1]);
 
  // Call Min_difference to get minimum
  // difference of adjacent elements
  Min_difference(diff, N - 1, q, m);
}
 
// Driver Code
 
let arr = [2, 6, 1, 8, 3, 4];
let N = arr.length;
let Q = [new Query(0, 3), new Query(1, 5), new Query(4, 5)];
let M = Q.length;
 
minimumDifference(arr, Q, N, M);
 
// This code is contributed by _saurabh_jaiswal.
 
</script>
Producción: 

4
1
1

 

Complejidad de tiempo: O(N*log(N))
Espacio auxiliar: O(N*N)

Publicación traducida automáticamente

Artículo escrito por ashutoshtiwari22111998 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA

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