题记-前缀和

7 区间和

前缀和,注意[a,b]的和为sums[b] - sums[a-1], 同时要注意a为0的情况,如果a为0,则[0,b]的区间和为sums[b]

或者统一写成 sums[b] - sums[a] +nums[a]

注意java包的导入,输出和输入,main函数的书写

题目描述
给定一个整数数组 Array，请计算该数组在每个指定区间内元素的总和。
输入描述
第一行输入为整数数组 Array 的长度 n，接下来 n 行，每行一个整数，表示数组的元素。随后的输入为需要计算总和的区间下标：a，b （b > = a），直至文件结束。
输出描述
输出每个指定区间内元素的总和。
输入示例
5
1
2
3
4
5
0 1
1 3
输出示例
3
9
    
import java.util.Scanner;
public class Main{
    
    public static void main(String[] args){
        
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] nums = new int[n];
        int[] sums = new int[n];
        int sum = 0;
        for(int i=0;i<n;i++){
            nums[i] = sc.nextInt();
            sum+=nums[i];
            sums[i] = sum;
        }
        while(sc.hasNextInt()){
            int a= sc.nextInt();
            int b=sc.nextInt();
            System.out.println(sums[b] - sums[a] +nums[a]);
        }
        sc.close();
        
    } 
}

8 开发商购买土地

因为题目横纵切割,所以横纵均为一个前缀和数组

//前缀和
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        int sum = 0;
        int[][] vec = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                vec[i][j] = scanner.nextInt();
                sum += vec[i][j];
            }
        }

        // 统计横向
        int[] horizontal = new int[n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                horizontal[i] += vec[i][j];
            }
        }

        // 统计纵向
        int[] vertical = new int[m];
        for (int j = 0; j < m; j++) {
            for (int i = 0; i < n; i++) {
                vertical[j] += vec[i][j];
            }
        }

        int result = Integer.MAX_VALUE;
        int horizontalCut = 0;
        for (int i = 0; i < n; i++) {
            horizontalCut += horizontal[i];
            result = Math.min(result, Math.abs(sum - 2 * horizontalCut));
        }

        int verticalCut = 0;
        for (int j = 0; j < m; j++) {
            verticalCut += vertical[j];
            result = Math.min(result, Math.abs(sum - 2 * verticalCut));
        }

        System.out.println(result);
        scanner.close();
    }
}

//优化版
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        int sum = 0;
        int[][] vec = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                vec[i][j] = scanner.nextInt();
                sum += vec[i][j];
            }
        }

        int result = Integer.MAX_VALUE;
        int count = 0; // 统计遍历过的行

        // 行切分
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                count += vec[i][j];
                // 遍历到行末尾时候开始统计
                if (j == m - 1) {
                    result = Math.min(result, Math.abs(sum - 2 * count));
                }
            }
        }

        count = 0;
        // 列切分
        for (int j = 0; j < m; j++) {
            for (int i = 0; i < n; i++) {
                count += vec[i][j];
                // 遍历到列末尾时候开始统计
                if (i == n - 1) {
                    result = Math.min(result, Math.abs(sum - 2 * count));
                }
            }
        }

        System.out.println(result);
        scanner.close();
    }
}