一维前缀和、二维前缀和、一维差分、二维差分

一、一维前缀和

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		int n=in.nextInt();
		int m=in.nextInt();
		int[] prefix=new int[n+1];
		int[] arr=new int[n+1];
		for (int i = 1; i < arr.length; i++) {
			arr[i]=in.nextInt();
			prefix[i]=prefix[i-1]+arr[i];
		}
		int l=0;
		int r=0;
		for (int i = 0; i < m; i++) {
			l=in.nextInt();
			r=in.nextInt();
			System.out.println(prefix[r]-prefix[l-1]);
		}
	}
}

二、二维前缀和

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		int n=in.nextInt();
		int m=in.nextInt();
		int q=in.nextInt();
		long[][] dp=new long[n+1][m+1];
		int[][] arr=new int[n+1][m+1];
		for (int i = 1; i < arr.length; i++) {
			for (int j = 1; j < arr[0].length; j++) {
				arr[i][j]=in.nextInt();
				dp[i][j]=dp[i-1][j]+dp[i][j-1]-dp[i-1][j-1]+arr[i][j];
			}
		}
		int x1=0;
		int y1=0;
		int x2=0;
		int y2=0;
		for (int i = 0; i < q; i++) {
			x1=in.nextInt();
			y1=in.nextInt();
			x2=in.nextInt();
			y2=in.nextInt();
			System.out.println(dp[x2][y2]-dp[x2][y1-1]-dp[x1-1][y2]+dp[x1-1][y1-1]);
		}
	}
}

三、一维差分

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		int n=in.nextInt();
		int q=in.nextInt();
		int[] diff=new int[n+2];
		int[] arr=new int[n+1];
		int[] res=new int[n+1];
		for (int i = 1; i < arr.length; i++) {
			arr[i]=in.nextInt();
			diff[i]=arr[i]-arr[i-1];
		}
		int l=0;
		int r=0;
		int x=0;
		for (int i = 0; i < q; i++) {
			l=in.nextInt();
			r=in.nextInt();
			x=in.nextInt();
			diff[l]+=x;
			diff[r+1]-=x;
		}
		for (int i = 1; i < res.length; i++) {
			res[i]=res[i-1]+diff[i];
		}
		for (int i = 1; i < res.length; i++) {
			System.out.print(res[i]+" ");
		}
	}
}

四、二维差分

待更。。