Consideremos el siguiente problema para comprender los árboles de segmentos.
Tenemos una array arr[0 . . . n-1]. Deberíamos ser capaces de
1 Encontrar el producto de elementos de índice l a r donde 0 <= l <= r <= n-1 tomar su módulo por un entero m.
2 Cambiar el valor de un elemento específico de la array a un nuevo valor x. Necesitamos hacer arr[i] = x donde 0 <= i <= n-1.
Una solución simple es ejecutar un ciclo de l a r y calcular el producto de los elementos en un rango dado y modularlo por m. Para actualizar un valor, simplemente haga arr[i] = x. La primera operación toma el tiempo O(n) y la segunda operación toma el tiempo O(1).
Otra solución es crear dos arreglos y almacenar el producto módulo m desde el inicio hasta l-1 en el primer arreglo y el producto desde r+1 hasta el final del arreglo módulo m en otro arreglo. El producto de un rango dado ahora se puede calcular en tiempo O(1), pero la operación de actualización ahora toma tiempo O(n).
Digamos que el producto de todos los elementos sea P, entonces el producto P de un rango dado de l a r se puede calcular como:
P: Producto de todos los elementos de la array módulo m.
A: Producto de todos los elementos hasta l-1 módulo m.
B: Producto de todos los elementos hasta r+1 módulo m.
PDT = P*(modInverse(A))*(modInverse(B))
Esto funciona bien si la cantidad de operaciones de consulta es grande y hay muy pocas actualizaciones.
Solución de árbol de segmentos
: si el número de consultas y actualizaciones es igual, podemos realizar ambas operaciones en tiempo O (log n). Podemos usar un árbol de segmentos para hacer ambas operaciones en tiempo O (Iniciar sesión).
Representación de árboles de segmentos
1. Los Nodes hoja son los elementos del arreglo de entrada.
2. Cada Node interno representa alguna fusión de los Nodes hoja. La fusión puede ser diferente para diferentes problemas. Para este problema, la fusión es producto de las hojas debajo de un Node.
Se utiliza una representación de array de árbol para representar árboles de segmento. Para cada Node en el índice i, el hijo izquierdo está en el índice 2*i+1, el hijo derecho en 2*i+2 y el padre está en (i-1)/2.
Consulta de producto de rango dado
Una vez que se construye el árbol, cómo obtener el producto utilizando el árbol de segmento construido. El siguiente es un algoritmo para obtener el producto de los elementos.
int getPdt(node, l, r)
{
if range of node is within l and r
return value in node
else if range of node is completely outside l and r
return 1
else
return (getPdt(node's left child, l, r)%mod *
getPdt(node's right child, l, r)%mod)%mod
}
Actualizar un valor
Al igual que la construcción de árboles y las operaciones de consulta, la actualización también se puede realizar de forma recursiva. Se nos proporciona un índice que debe actualizarse. Comenzamos desde la raíz del árbol de segmentos, multiplicamos el producto del rango con el valor nuevo y dividimos el producto del rango con el valor anterior. Si un Node no tiene un índice dado en su rango, no hacemos ningún cambio en ese Node.
Implementación:
A continuación se muestra la implementación del árbol de segmentos. El programa implementa la construcción de un árbol de segmentos para cualquier array dada. También implementa operaciones de consulta y actualización.
C++
// C++ program to show segment tree operations like
// construction, query and update
#include <bits/stdc++.h>
#include <math.h>
using namespace std;
int mod = 1000000000;
// A utility function to get the middle index from
// corner indexes.
int getMid(int s, int e) { return s + (e -s)/2; }
/* A recursive function to get the Pdt of values
in given range of the array. The following are
parameters for this function.
st --> Pointer to segment tree
si --> Index of current node in the segment tree.
Initially 0 is passed as root is always
at index 0
ss & se --> Starting and ending indexes of the
segment represented by current node,
i.e., st[si]
qs & qe --> Starting and ending indexes of query
range */
int getPdtUtil(int *st, int ss, int se, int qs, int qe,
int si)
{
// If segment of this node is a part of given
// range, then return the Pdt of the segment
if (qs <= ss && qe >= se)
return st[si];
// If segment of this node is outside the given range
if (se < qs || ss > qe)
return 1;
// If a part of this segment overlaps with the
// given range
int mid = getMid(ss, se);
return (getPdtUtil(st, ss, mid, qs, qe, 2*si+1)%mod *
getPdtUtil(st, mid+1, se, qs, qe, 2*si+2)%mod)%mod;
}
/* A recursive function to update the nodes which have
the given index in their range. The following are
parameters
st, si, ss and se are same as getPdtUtil()
i --> index of the element to be updated.
This index is in input array.*/
void updateValueUtil(int *st, int ss, int se, int i,
int prev_val, int new_val, int si)
{
// Base Case: If the input index lies outside
// the range of this segment
if (i < ss || i > se)
return;
// If the input index is in range of this node, then
// update the value of the node and its children
st[si] = (st[si]*new_val)/prev_val;
if (se != ss)
{
int mid = getMid(ss, se);
updateValueUtil(st, ss, mid, i, prev_val,
new_val, 2*si + 1);
updateValueUtil(st, mid+1, se, i, prev_val,
new_val, 2*si + 2);
}
}
// The function to update a value in input array
// and segment tree. It uses updateValueUtil() to
// update the value in segment tree
void updateValue(int arr[], int *st, int n, int i,
int new_val)
{
// Check for erroneous input index
if (i < 0 || i > n-1)
{
cout<<"Invalid Input";
return;
}
int temp = arr[i];
// Update the value in array
arr[i] = new_val;
// Update the values of nodes in segment tree
updateValueUtil(st, 0, n-1, i, temp, new_val, 0);
}
// Return Pdt of elements in range from index qs
// (query start)to qe (query end). It mainly
// uses getPdtUtil()
int getPdt(int *st, int n, int qs, int qe)
{
// Check for erroneous input values
if (qs < 0 || qe > n-1 || qs > qe)
{
cout<<"Invalid Input";
return -1;
}
return getPdtUtil(st, 0, n-1, qs, qe, 0);
}
// A recursive function that constructs Segment Tree
// for array[ss..se]. si is index of current node
// in segment tree st
int constructSTUtil(int arr[], int ss, int se,
int *st, int si)
{
// If there is one element in array, store it
// in current node of segment tree and return
if (ss == se)
{
st[si] = arr[ss];
return arr[ss];
}
// If there are more than one elements, then
// recur for left and right subtrees and store
// the Pdt of values in this node
int mid = getMid(ss, se);
st[si] = (constructSTUtil(arr, ss, mid, st, si*2+1)%mod *
constructSTUtil(arr, mid+1, se, st, si*2+2)%mod)%mod;
return st[si];
}
/* Function to construct segment tree from given array.
This function allocates memory for segment tree and
calls constructSTUtil() to fill the allocated memory */
int *constructST(int arr[], int n)
{
// Allocate memory for segment tree
// Height of segment tree
int x = (int)(ceil(log2(n)));
// Maximum size of segment tree
int max_size = 2*(int)pow(2, x) - 1;
// Allocate memory
int *st = new int[max_size];
// Fill the allocated memory st
constructSTUtil(arr, 0, n-1, st, 0);
// Return the constructed segment tree
return st;
}
// Driver program to test above functions
int main()
{
int arr[] = {1, 2, 3, 4, 5, 6};
int n = sizeof(arr)/sizeof(arr[0]);
// Build segment tree from given array
int *st = constructST(arr, n);
// Print Product of values in array from index 1 to 3
cout << "Product of values in given range = "
<< getPdt(st, n, 1, 3) << endl;
// Update: set arr[1] = 10 and update corresponding
// segment tree nodes
updateValue(arr, st, n, 1, 10);
// Find Product after the value is updated
cout << "Updated Product of values in given range = "
<< getPdt(st, n, 1, 3) << endl;
return 0;
}
Java
// Java program to show segment tree operations
// like construction, query and update
class GFG{
static final int mod = 1000000000;
// A utility function to get the middle
// index from corner indexes.
static int getMid(int s, int e)
{
return s + (e - s) / 2;
}
/*
* A recursive function to get the Pdt of values
* in given range of the array.
* The following are parameters for this function.
*
* st --> Pointer to segment tree
* si --> Index of current node in the segment tree.
* Initially 0 is passed as root is always
* at index 0
* ss & se --> Starting and ending indexes of the
* segment represented by current node,
* i.e., st[si]
* qs & qe --> Starting and ending indexes of query range
*/
static int getPdtUtil(int[] st, int ss, int se,
int qs, int qe, int si)
{
// If segment of this node is a part of given
// range, then return the Pdt of the segment
if (qs <= ss && qe >= se)
return st[si];
// If segment of this node is outside
// the given range
if (se < qs || ss > qe)
return 1;
// If a part of this segment overlaps
// with the given range
int mid = getMid(ss, se);
return (getPdtUtil(st, ss, mid, qs,
qe, 2 * si + 1) % mod *
getPdtUtil(st, mid + 1, se, qs,
qe, 2 * si + 2) % mod) % mod;
}
/*
* A recursive function to update the nodes which have
* the given index in their range. The following are
* parameters
* st, si, ss and se are same as getPdtUtil()
* i --> index of the element to be updated.
* This index is in input array.
*/
static void updateValueUtil(int[] st, int ss, int se,
int i, int prev_val,
int new_val, int si)
{
// Base Case: If the input index lies outside
// the range of this segment
if (i < ss || i > se)
return;
// If the input index is in range of this node, then
// update the value of the node and its children
st[si] = (st[si] * new_val) / prev_val;
if (se != ss)
{
int mid = getMid(ss, se);
updateValueUtil(st, ss, mid, i, prev_val,
new_val, 2 * si + 1);
updateValueUtil(st, mid + 1, se, i, prev_val,
new_val, 2 * si + 2);
}
}
// The function to update a value in input array
// and segment tree. It uses updateValueUtil() to
// update the value in segment tree
static void updateValue(int arr[], int[] st, int n,
int i, int new_val)
{
// Check for erroneous input index
if (i < 0 || i > n - 1)
{
System.out.println("Invalid Input");
return;
}
int temp = arr[i];
// Update the value in array
arr[i] = new_val;
// Update the values of nodes in segment tree
updateValueUtil(st, 0, n - 1, i,
temp, new_val, 0);
}
// Return Pdt of elements in range from index qs
// (query start)to qe (query end). It mainly
// uses getPdtUtil()
static int getPdt(int[] st, int n, int qs, int qe)
{
// Check for erroneous input values
if (qs < 0 || qe > n - 1 || qs > qe)
{
System.out.println("Invalid Input");
return -1;
}
return getPdtUtil(st, 0, n - 1, qs, qe, 0);
}
// A recursive function that constructs Segment Tree
// for array[ss..se]. si is index of current node
// in segment tree st
static int constructSTUtil(int arr[], int ss, int se,
int[] st, int si)
{
// If there is one element in array, store it
// in current node of segment tree and return
if (ss == se)
{
st[si] = arr[ss];
return arr[ss];
}
// If there are more than one elements, then
// recur for left and right subtrees and store
// the Pdt of values in this node
int mid = getMid(ss, se);
st[si] = (constructSTUtil(arr, ss, mid, st,
si * 2 + 1) % mod *
constructSTUtil(arr, mid + 1, se, st,
si * 2 + 2) % mod) % mod;
return st[si];
}
/*
* Function to construct segment tree from
* given array. This function allocates memory
* for segment tree and calls constructSTUtil()
* to fill the allocated memory
*/
static int[] constructST(int arr[], int n)
{
// Allocate memory for segment tree
// Height of segment tree
int x = (int)(Math.ceil(Math.log(n) /
Math.log(2)));
// Maximum size of segment tree
int max_size = 2 * (int)Math.pow(2, x) - 1;
// Allocate memory
int[] st = new int[max_size];
// Fill the allocated memory st
constructSTUtil(arr, 0, n - 1, st, 0);
// Return the constructed segment tree
return st;
}
// Driver code
public static void main(String[] args)
{
int arr[] = { 1, 2, 3, 4, 5, 6 };
int n = arr.length;
// Build segment tree from given array
int[] st = constructST(arr, n);
// Print Product of values in array from
// index 1 to 3
System.out.printf("Product of values in " +
"given range = %d\n",
getPdt(st, n, 1, 3));
// Update: set arr[1] = 10 and update
// corresponding segment tree nodes
updateValue(arr, st, n, 1, 10);
// Find Product after the value is updated
System.out.printf("Updated Product of values " +
"in given range = %d\n",
getPdt(st, n, 1, 3));
}
}
// This code is contributed by sanjeev2552
Python3
# Python3 program to show segment tree operations like
# construction, query and update
from math import ceil,log
mod = 1000000000
# A utility function to get the middle index from
# corner indexes.
def getMid(s, e):
return s + (e -s)//2
"""A recursive function to get the Pdt of values
in given range of the array. The following are
parameters for this function.
st --> Pointer to segment tree
si --> Index of current node in the segment tree.
Initially 0 is passed as root is always
at index 0
ss & se --> Starting and ending indexes of the
segment represented by current node,
i.e., st[si]
qs & qe --> Starting and ending indexes of query
range"""
def getPdtUtil(st, ss, se, qs, qe,si):
# If segment of this node is a part of given
# range, then return the Pdt of the segment
if (qs <= ss and qe >= se):
return st[si]
# If segment of this node is outside the given range
if (se < qs or ss > qe):
return 1
# If a part of this segment overlaps with the
# given range
mid = getMid(ss, se)
return (getPdtUtil(st, ss, mid, qs, qe, 2*si+1)%mod*
getPdtUtil(st, mid+1, se, qs, qe, 2*si+2)%mod)%mod
"""A recursive function to update the nodes which have
the given index in their range. The following are
parameters
st, si, ss and se are same as getPdtUtil()
i --> index of the element to be updated.
This index is in input array."""
def updateValueUtil(st, ss, se, i, prev_val, new_val, si):
# Base Case: If the input index lies outside
# the range of this segment
if (i < ss or i > se):
return
# If the input index is in range of this node, then
# update the value of the node and its children
st[si] = (st[si]*new_val)//prev_val
if (se != ss):
mid = getMid(ss, se)
updateValueUtil(st, ss, mid, i, prev_val,
new_val, 2*si + 1)
updateValueUtil(st, mid+1, se, i, prev_val,
new_val, 2*si + 2)
# The function to update a value in input array
# and segment tree. It uses updateValueUtil() to
# update the value in segment tree
def updateValue(arr, st, n, i, new_val):
# Check for erroneous input index
if (i < 0 or i > n-1):
cout<<"Invalid Input"
return
temp = arr[i]
# Update the value in array
arr[i] = new_val
# Update the values of nodes in segment tree
updateValueUtil(st, 0, n-1, i, temp, new_val, 0)
# Return Pdt of elements in range from index qs
# (query start)to qe (query end). It mainly
# uses getPdtUtil()
def getPdt(st, n, qs, qe):
# Check for erroneous input values
if (qs < 0 or qe > n-1 or qs > qe):
print("Invalid Input")
return -1
return getPdtUtil(st, 0, n-1, qs, qe, 0)
# A recursive function that constructs Segment Tree
# for array[ss..se]. si is index of current node
# in segment tree st
def constructSTUtil(arr, ss, se,st, si):
# If there is one element in array, store it
# in current node of segment tree and return
if (ss == se):
st[si] = arr[ss]
return arr[ss]
# If there are more than one elements, then
# recur for left and right subtrees and store
# the Pdt of values in this node
mid = getMid(ss, se)
st[si] = (constructSTUtil(arr, ss, mid, st, si*2+1)%mod*
constructSTUtil(arr, mid+1, se, st, si*2+2)%mod)%mod
return st[si]
""" Function to construct segment tree from given array.
This function allocates memory for segment tree and
calls constructSTUtil() to fill the allocated memory
"""
def constructST(arr, n):
# Allocate memory for segment tree
# Height of segment tree
x = (ceil(log(n,2)))
# Maximum size of segment tree
max_size = 2*pow(2, x) - 1
# Allocate memory
st = [0]*max_size
# Fill the allocated memory st
constructSTUtil(arr, 0, n-1, st, 0)
# Return the constructed segment tree
return st
# Driver program to test above functions
if __name__ == '__main__':
arr=[1, 2, 3, 4, 5, 6]
n = len(arr)
# Build segment tree from given array
st = constructST(arr, n)
# Print Product of values in array from index 1 to 3
print("Product of values in given range = ",getPdt(st, n, 1, 3))
# Update: set arr[1] = 10 and update corresponding
# segment tree nodes
updateValue(arr, st, n, 1, 10)
# Find Product after the value is updated
print("Updated Product of values in given range = ",getPdt(st, n, 1, 3))
# This code is contributed by mohit kumar 29
C#
// C# program to show segment tree operations
// like construction, query and update
using System;
class GFG
{
static int mod = 1000000000;
// A utility function to get the middle
// index from corner indexes.
public static int getMid(int s, int e)
{
return s + (e - s) / 2;
}
/*
* A recursive function to get the Pdt of values
* in given range of the array.
* The following are parameters for this function.
*
* st --> Pointer to segment tree
* si --> Index of current node in the segment tree.
* Initially 0 is passed as root is always
* at index 0
* ss & se --> Starting and ending indexes of the
* segment represented by current node,
* i.e., st[si]
* qs & qe --> Starting and ending indexes of query range
*/
public static int getPdtUtil(int[] st, int ss,
int se,int qs,
int qe, int si)
{
// If segment of this node is a part of given
// range, then return the Pdt of the segment
if(qs <= ss && qe >= se)
{
return st[si];
}
// If segment of this node is outside
// the given range
if(se < qs || ss > qe)
{
return 1;
}
// If a part of this segment overlaps
// with the given range
int mid=getMid(ss, se);
return (getPdtUtil(st, ss, mid, qs,qe, 2 * si + 1) % mod *
getPdtUtil(st, mid + 1, se, qs,qe, 2 * si + 2) % mod) % mod;
}
/*
* A recursive function to update the nodes which have
* the given index in their range. The following are
* parameters
* st, si, ss and se are same as getPdtUtil()
* i --> index of the element to be updated.
* This index is in input array.
*/
public static void updateValueUtil(int[] st, int ss,
int se, int i,
int prev_val,
int new_val, int si)
{
// Base Case: If the input index lies outside
// the range of this segment
if(i < ss || i > se)
{
return;
}
// If the input index is in range of this node, then
// update the value of the node and its children
st[si] = (st[si] * new_val) / prev_val;
if (se != ss)
{
int mid = getMid(ss, se);
updateValueUtil(st, ss, mid, i, prev_val,new_val, 2 * si + 1);
updateValueUtil(st, mid + 1, se, i, prev_val,new_val, 2 * si + 2);
}
}
// The function to update a value in input array
// and segment tree. It uses updateValueUtil() to
// update the value in segment tree
public static void updateValue(int[] arr, int[] st,
int n,int i, int new_val)
{
// Check for erroneous input index
if(i < 0 || i > n - 1)
{
Console.WriteLine("Invalid Input");
return;
}
int temp = arr[i];
// Update the value in array
arr[i] = new_val;
// Update the values of nodes in segment tree
updateValueUtil(st, 0, n - 1, i, temp, new_val, 0);
}
// Return Pdt of elements in range from index qs
// (query start)to qe (query end). It mainly
// uses getPdtUtil()
public static int getPdt(int[] st, int n, int qs, int qe)
{
// Check for erroneous input values
if(qs < 0 || qe > n - 1 || qs > qe)
{
Console.WriteLine("Invalid Input");
return -1;
}
return getPdtUtil(st, 0, n - 1, qs, qe, 0);
}
// A recursive function that constructs Segment Tree
// for array[ss..se]. si is index of current node
// in segment tree st
public static int constructSTUtil(int[] arr, int ss,
int se,int[] st, int si)
{
// If there is one element in array, store it
// in current node of segment tree and return
if (ss == se)
{
st[si] = arr[ss];
return arr[ss];
}
// If there are more than one elements, then
// recur for left and right subtrees and store
// the Pdt of values in this node
int mid = getMid(ss, se);
st[si] = (constructSTUtil(arr, ss, mid, st, si * 2 + 1) % mod *
constructSTUtil(arr, mid + 1, se, st,si * 2 + 2) % mod) % mod;
return st[si];
}
/*
* Function to construct segment tree from
* given array. This function allocates memory
* for segment tree and calls constructSTUtil()
* to fill the allocated memory
*/
public static int[] constructST(int[] arr, int n)
{
// Allocate memory for segment tree
// Height of segment tree
int x = (int)(Math.Ceiling(Math.Log(n) /Math.Log(2)));
// Maximum size of segment tree
int max_size = 2 * (int)Math.Pow(2, x) - 1;
// Allocate memory
int[] st = new int[max_size];
// Fill the allocated memory st
constructSTUtil(arr, 0, n - 1, st, 0);
// Return the constructed segment tree
return st;
}
// Driver code
static public void Main ()
{
int[] arr = { 1, 2, 3, 4, 5, 6 };
int n = arr.Length;
// Build segment tree from given array
int[] st = constructST(arr, n);
// Print Product of values in array from
// index 1 to 3
Console.WriteLine("Product of values in " +
"given range = " + getPdt(st, n, 1, 3));
// Update: set arr[1] = 10 and update
// corresponding segment tree nodes
updateValue(arr, st, n, 1, 10);
// Find Product after the value is updated
Console.WriteLine("Updated Product of values " +
"in given range = " + getPdt(st, n, 1, 3));
}
}
// This code is contributed by avanitrachhadiya2155
Javascript
<script>
// JavaScript program to
// show segment tree operations
// like construction, query and update
let mod = 1000000000;
// A utility function to get the middle
// index from corner indexes.
function getMid(s,e)
{
return s + Math.floor((e - s) / 2);
}
/*
* A recursive function to get the Pdt of values
* in given range of the array.
* The following are parameters for this function.
*
* st --> Pointer to segment tree
* si --> Index of current node in the segment tree.
* Initially 0 is passed as root is always
* at index 0
* ss & se --> Starting and ending indexes of the
* segment represented by current node,
* i.e., st[si]
* qs & qe --> Starting and ending indexes of query range
*/
function getPdtUtil(st,ss,se,qs,qe,si)
{
// If segment of this node is a part of given
// range, then return the Pdt of the segment
if (qs <= ss && qe >= se)
return st[si];
// If segment of this node is outside
// the given range
if (se < qs || ss > qe)
return 1;
// If a part of this segment overlaps
// with the given range
let mid = getMid(ss, se);
return (getPdtUtil(st, ss, mid, qs,
qe, 2 * si + 1) % mod *
getPdtUtil(st, mid + 1, se, qs,
qe, 2 * si + 2) % mod) % mod;
}
/*
* A recursive function to update the nodes which have
* the given index in their range. The following are
* parameters
* st, si, ss and se are same as getPdtUtil()
* i --> index of the element to be updated.
* This index is in input array.
*/
function updateValueUtil(st,ss,se,i,prev_val,new_val,si)
{
// Base Case: If the input index lies outside
// the range of this segment
if (i < ss || i > se)
return;
// If the input index is in range of this node, then
// update the value of the node and its children
st[si] = Math.floor((st[si] * new_val) / prev_val);
if (se != ss)
{
let mid = getMid(ss, se);
updateValueUtil(st, ss, mid, i, prev_val,
new_val, 2 * si + 1);
updateValueUtil(st, mid + 1, se, i, prev_val,
new_val, 2 * si + 2);
}
}
// The function to update a value in input array
// and segment tree. It uses updateValueUtil() to
// update the value in segment tree
function updateValue(arr,st,n,i,new_val)
{
// Check for erroneous input index
if (i < 0 || i > n - 1)
{
document.write("Invalid Input<br>");
return;
}
let temp = arr[i];
// Update the value in array
arr[i] = new_val;
// Update the values of nodes in segment tree
updateValueUtil(st, 0, n - 1, i,
temp, new_val, 0);
}
// Return Pdt of elements in range from index qs
// (query start)to qe (query end). It mainly
// uses getPdtUtil()
function getPdt(st,n,qs,qe)
{
// Check for erroneous input values
if (qs < 0 || qe > n - 1 || qs > qe)
{
document.write("Invalid Input<br>");
return -1;
}
return getPdtUtil(st, 0, n - 1, qs, qe, 0);
}
// A recursive function that constructs Segment Tree
// for array[ss..se]. si is index of current node
// in segment tree st
function constructSTUtil(arr,ss,se,st,si)
{
// If there is one element in array, store it
// in current node of segment tree and return
if (ss == se)
{
st[si] = arr[ss];
return arr[ss];
}
// If there are more than one elements, then
// recur for left and right subtrees and store
// the Pdt of values in this node
let mid = getMid(ss, se);
st[si] = (constructSTUtil(arr, ss, mid, st,
si * 2 + 1) % mod *
constructSTUtil(arr, mid + 1, se, st,
si * 2 + 2) % mod) % mod;
return st[si];
}
/*
* Function to construct segment tree from
* given array. This function allocates memory
* for segment tree and calls constructSTUtil()
* to fill the allocated memory
*/
function constructST(arr,n)
{
// Allocate memory for segment tree
// Height of segment tree
let x = (Math.ceil(Math.log(n) /
Math.log(2)));
// Maximum size of segment tree
let max_size = 2 * Math.pow(2, x) - 1;
// Allocate memory
let st = new Array(max_size);
// Fill the allocated memory st
constructSTUtil(arr, 0, n - 1, st, 0);
// Return the constructed segment tree
return st;
}
// Driver code
let arr=[1, 2, 3, 4, 5, 6 ];
let n = arr.length;
// Build segment tree from given array
let st = constructST(arr, n);
// Print Product of values in array from
// index 1 to 3
document.write("Product of values in " +
"given range = ",
getPdt(st, n, 1, 3)+"<br>");
// Update: set arr[1] = 10 and update
// corresponding segment tree nodes
updateValue(arr, st, n, 1, 10);
// Find Product after the value is updated
document.write("Updated Product of values " +
"in given range = ",
getPdt(st, n, 1, 3)+"<br>");
// This code is contributed by patel2127
</script>
Producción:
Product of values in given range = 24 Updated Product of values in given range = 120
Publicación traducida automáticamente
Artículo escrito por sahilkhoslaa y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA