Prefix and
topic
Enter a sequence of integers of length n.
Next, enter m queries, and enter a pair of l, r for each query.
For each query, output the sum from the lth number to the rth number in the original sequence.
Input format The
first line contains two integers n and m.
The second row contains n integers, representing a sequence of integers.
In the next m lines, each line contains two integers l and r, representing the range of a query.
Output format
A total of m lines, each line outputs a query result.
Data range
1≤l≤r≤n,
1≤n,m≤100000,
−1000≤The value of elements in the sequence ≤1000
Input example:
5 3
2 1 3 6 4
1 2
1 3
2 4
Output example:
3
6
10
specific methods:
First do a preprocessing, define an sum[]array, which sum[i]represents the sum aof the previous inumbers in the array .
Find the prefix and operation:
const int N=1e5+10;
int sum[N],a[N]; //sum[i]=a[1]+a[2]+a[3].....a[i];
for(int i=1;i<=n;i++)
{
sum[i]=sum[i-1]+a[i];
}
Then query operation:
scanf("%d%d",&l,&r);
printf("%d\n", sum[r]-sum[l-1]);
For each query, only need to execute sum[r]-sum[l-1], the time complexity isO(1)
principle
sum[r] =a[1]+a[2]+a[3]+a[l-1]+a[l]+a[l+1]......a[r];
sum[l-1]=a[1]+a[2]+a[3]+a[l-1];
sum[r]-sum[l-1]=a[l]+a[l+1]+......+a[r];
Illustrates
Thus, for each 只需要执行 sum[r]-sum[l-1]inquiry . lThe time complexity of outputting the sum from the number to the rth number in the original sequence becomes O(1).
We call it a one-dimensional prefix sum .
to sum up:
Summary of personal experience of prefix sum and difference
AC code
#include<iostream>
#include<cstdio>
using namespace std;
const int N=1e5+10;
int a[N],sum[N];
int main()
{
int n,m,x;
cin>>n>>m;
for(int i=1;i<=n;i++)
{
cin>>x;
sum[i]=x+sum[i-1];
}
while(m--)
{
int l,r;
cin>>l>>r;
cout<<sum[r]-sum[l-1]<<endl;
}
return 0;
}