# 算法-差异数组：O(1)时间范围更新查询

## 本文概述

1. update(l, r, x)：将x添加到从A[l]到A[r]的所有值(包括两者)。
2. printArray()：打印当前修改后的数组。

``````Input : A[] { 10, 5, 20, 40 }
update(0, 1, 10)
printArray()
update(1, 3, 20)
update(2, 2, 30)
printArray()
Output : 20 15 20 40
20 35 70 60
Explanation : The query update(0, 1, 10)
adds 10 to A[0] and A[1]. After update, A[] becomes {20, 15, 20, 40}
Query update(1, 3, 20) adds 20 to A[1], A[2] and A[3]. After update, A[] becomes
{20, 35, 40, 60}.
Query update(2, 2, 30) adds 30 to A[2].
After update, A[] becomes {20, 35, 70, 60}.``````

1. update(l, r, x)：从l到r运行循环, 并将x添加到从A[l]到A[r]的所有元素中
2. printArray()：仅打印A[]。

1. update(l, r, x)：将x添加到D [l]并将其从D [r + 1]中减去, 即, 我们做D [l] + = x, D [r + 1]-= x
2. printArray()：执行A[0] = D [0]并打印。对于其余元素, 执行A[i] = A[i-1] + D [i]并打印它们。

## C ++

``````//C++ code to demonstrate Difference Array
#include <bits/stdc++.h>
using namespace std;

//Creates a diff array D[] for A[] and returns
//it after filling initial values.
vector<int> initializeDiffArray(vector<int>& A)
{
int n = A.size();

//We use one extra space because
vector<int> D(n + 1);

D[0] = A[0], D[n] = 0;
for ( int i = 1; i <n; i++)
D[i] = A[i] - A[i - 1];
return D;
}

//Does range update
void update(vector<int>& D, int l, int r, int x)
{
D[l] += x;
D[r + 1] -= x;
}

//Prints updated Array
int printArray(vector<int>& A, vector<int>& D)
{
for ( int i = 0; i <A.size(); i++) {
if (i == 0)
A[i] = D[i];

//Note that A[0] or D[0] decides
//values of rest of the elements.
else
A[i] = D[i] + A[i - 1];

cout <<A[i] <<" " ;
}
cout <<endl;
}

//Driver Code
int main()
{
//Array to be updated
vector<int> A{ 10, 5, 20, 40 };

//Create and fill difference Array
vector<int> D = initializeDiffArray(A);

//After below update(l, r, x), the
//elements should become 20, 15, 20, 40
update(D, 0, 1, 10);
printArray(A, D);

//array should become 30, 35, 70, 60
update(D, 1, 3, 20);
update(D, 2, 2, 30);
printArray(A, D);

return 0;
}``````

## Java

``````//Java code to demonstrate Difference Array
class GFG {

//Creates a diff array D[] for A[] and returns
//it after filling initial values.
static void initializeDiffArray( int A[], int D[])
{

int n = A.length;

D[ 0 ] = A[ 0 ];
D[n] = 0 ;
for ( int i = 1 ; i <n; i++)
D[i] = A[i] - A[i - 1 ];
}

//Does range update
static void update( int D[], int l, int r, int x)
{
D[l] += x;
D[r + 1 ] -= x;
}

//Prints updated Array
static int printArray( int A[], int D[])
{
for ( int i = 0 ; i <A.length; i++) {

if (i == 0 )
A[i] = D[i];

//Note that A[0] or D[0] decides
//values of rest of the elements.
else
A[i] = D[i] + A[i - 1 ];

System.out.print(A[i] + " " );
}

System.out.println();

return 0 ;
}

//Driver Code
public static void main(String[] args)
{
//Array to be updated
int A[] = { 10 , 5 , 20 , 40 };
int n = A.length;
//Create and fill difference Array
//We use one extra space because
int D[] = new int [n + 1 ];
initializeDiffArray(A, D);

//After below update(l, r, x), the
//elements should become 20, 15, 20, 40
update(D, 0 , 1 , 10 );
printArray(A, D);

//array should become 30, 35, 70, 60
update(D, 1 , 3 , 20 );
update(D, 2 , 2 , 30 );

printArray(A, D);
}
}

//This code is contributed by Anant Agarwal.``````

## Python3

``````# Python3 code to demonstrate Difference Array

# Creates a diff array D[] for A[] and returns
# it after filling initial values.
def initializeDiffArray( A):
n = len (A)

# We use one extra space because
# update(l, r, x) updates D[r+1]
D = [ 0 for i in range ( 0 , n + 1 )]

D[ 0 ] = A[ 0 ]; D[n] = 0

for i in range ( 1 , n ):
D[i] = A[i] - A[i - 1 ]
return D

# Does range update
def update(D, l, r, x):

D[l] + = x
D[r + 1 ] - = x

# Prints updated Array
def printArray(A, D):

for i in range ( 0 , len (A)):
if (i = = 0 ):
A[i] = D[i]

# Note that A[0] or D[0] decides
# values of rest of the elements.
else :
A[i] = D[i] + A[i - 1 ]

print (A[i], end = " " )

print ("")

# Driver Code
A = [ 10 , 5 , 20 , 40 ]

# Create and fill difference Array
D = initializeDiffArray(A)

# After below update(l, r, x), the
# elements should become 20, 15, 20, 40
update(D, 0 , 1 , 10 )
printArray(A, D)

# array should become 30, 35, 70, 60
update(D, 1 , 3 , 20 )
update(D, 2 , 2 , 30 )
printArray(A, D)

# This code is contributed by Gitanjali.``````

## C#

``````//C# code to demonstrate Difference Array
using System;

class GFG {

//Creates a diff array D[] for A[] and returns
//it after filling initial values.
static void initializeDiffArray( int []A, int []D)
{

int n = A.Length;

D[0] = A[0];
D[n] = 0;
for ( int i = 1; i <n; i++)
D[i] = A[i] - A[i - 1];
}

//Does range update
static void update( int []D, int l, int r, int x)
{
D[l] += x;
D[r + 1] -= x;
}

//Prints updated Array
static int printArray( int []A, int []D)
{
for ( int i = 0; i <A.Length; i++) {

if (i == 0)
A[i] = D[i];

//Note that A[0] or D[0] decides
//values of rest of the elements.
else
A[i] = D[i] + A[i - 1];

Console.Write(A[i] + " " );
}

Console.WriteLine();

return 0;
}

//Driver Code
public static void Main()
{
//Array to be updated
int []A = { 10, 5, 20, 40 };
int n = A.Length;
//Create and fill difference Array
//We use one extra space because
int []D = new int [n + 1];
initializeDiffArray(A, D);

//After below update(l, r, x), the
//elements should become 20, 15, 20, 40
update(D, 0, 1, 10);
printArray(A, D);

//array should become 30, 35, 70, 60
update(D, 1, 3, 20);
update(D, 2, 2, 30);

printArray(A, D);
}
}

//This code is contributed by vt_m.``````

``````20 15 20 40
20 35 70 60``````

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