题解 | 蛇形矩阵

解法1：模拟，一行一行输出，先找行规律，再找列规律。

import java.util.*;
public class Main {
    public static void main(String args[]) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int sumj=1;
        int addj = 0;
        int addadd=1;
        for (int j = 0; j < n; j++) {
            int sum = sumj;
            int add = addadd;
            for (int i = 0; i < n-j; i++) {
                System.out.print(sum);
                if(i!=n-j-1){
                    System.out.print(" ");
                }
                add++;
                sum += add;
            }
            if(j!=n-1) System.out.println();
            addj++;
            sumj += addj;
            addadd++;
        }

    }
}

解法2：数字连续，矩阵下标变化规律

import java.util.*;
public class Main {
    public static void main(String args[]) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int[][] is = new int[n][n];
        for (int i = 0, add = 0; i < n; i++, add++) {
            if (i == 0) {
                is[i][0] = 1;
            } else {
                is[i][0] = is[i - 1][0] + add;
            }
            for (int j = i - 1, k = 1; j >= 0; j--,k++) {
                is[j][k] = is[j + 1][k - 1] + 1;
            }
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n - i; j++) {
                System.out.print(is[i][j] + " ");
            }
            System.out.println();
        }
    }
}

解法3：前n项和规律

import java.util.*;
public class Main {
    public static void main(String args[]) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        for (int i = 1; i <= n; i++) {
            for (int j = i; j <= n; j++) {
                System.out.print((1 + j) * j / 2-i+1);
                if (j != n) {
                    System.out.print(" ");
                }
            }
            if(i!=n){
                System.out.println();
            } 
        }
    }
}