前缀和模板(java实现)

一.一维前缀和

import java.util.Scanner;

// 注意类名必须为 Main, 不要有任何 package xxx 信息
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt(); // 长度为n
        int q = sc.nextInt(); // 查询q次
        int[] arr = new int[n + 1];
        long[] dp = new long[n + 1]; // 防止溢出
        for (int i = 1; i <= n; i++) {
            arr[i] = sc.nextInt();
        }
        for (int i = 1; i <= n; i++) {
            dp[i] = dp[i - 1] + arr[i];
        }
        while (q > 0) { //为0时查询结束
            int l = sc.nextInt();
            int r = sc.nextInt();
            System.out.println(dp[r] - dp[l - 1]);
            q--; 
        }
    }
}

二.二维前缀和

import java.util.Scanner;

// 注意类名必须为 Main, 不要有任何 package xxx 信息
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt(); // n行
        int m = sc.nextInt(); // m列
        int q = sc.nextInt(); // 查询q次
        int[][] array = new int[n + 1][m + 1];
        long[][] dp = new long[n + 1][m + 1]; // 防止溢出

        // 读入数据
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                array[i][j] = sc.nextInt();
            }
        }

        // 处理前缀和矩阵
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1] - dp[i - 1][j - 1] + array[i][j];
            }
        }

        // 使用前缀矩阵
        while (q > 0) {
            int x1 = sc.nextInt(), y1 = sc.nextInt();
            int x2 = sc.nextInt(), y2 = sc.nextInt();
            long ret = dp[x2][y2] - dp[x1 - 1][y2] - dp[x2][y1 - 1] + dp[x1 - 1][y1 - 1];
            System.out.println(ret);
            q--;
        }
    }
}