2D 数组核心算法详解 (AP CSA 范围)
Setup: 基础 2D 数组准备
public class TwoDArrayAlgorithms {
public static void main(String[] args) {
// 初始化一个 3行 4列 的二维数组
int[][] grid = {
{3, 5, 1, 7},
{9, 2, 6, 4},
{8, 10, 12, 11}
};
// AP CSA 标准打印方法：嵌套 for 循环
for (int r = 0; r < grid.length; r++) { // 遍历每一行
for (int c = 0; c < grid[r].length; c++) { // 遍历当前行的每一列
System.out.print(grid[r][c] + " ");
}
System.out.println(); // 换行
}
}
}
1. 确定最大值或最小值 (Min/Max)
查找整个 2D 数组的最大值
public class MaxIn2D {
public static void main(String[] args) {
int[][] grid = {
{3, 5, 1},
{9, 2, 6},
{8, 10, 12}
};
int max = grid[0][0]; // 初始化最大值为第一个元素
// 方法 A: 使用索引嵌套循环
for (int r = 0; r < grid.length; r++) {
for (int c = 0; c < grid[r].length; c++) {
if (grid[r][c] > max) {
max = grid[r][c];
}
}
}
// 方法 B: 使用增强型 for 循环 (更简洁)
max = grid[0][0];
for (int[] row : grid) { // 每一行是一个 int[]
for (int val : row) { // 遍历行中的每个元素
if (val > max) {
max = val;
}
}
}
System.out.println("最大值: " + max);
}
}
查找指定列 (Column) 的最大值
public class MaxInColumn {
public static void main(String[] args) {
int[][] grid = {
{3, 5, 1},
{9, 2, 6},
{8, 10, 12}
};
int targetCol = 1; // 目标列索引
// 查找某一列时，列索引固定，行索引变化
int max = grid[0][targetCol];
for (int r = 1; r < grid.length; r++) {
if (grid[r][targetCol] > max) {
max = grid[r][targetCol];
}
}
System.out.println("第 " + targetCol + " 列的最大值: " + max);
}
}
2. 计算总和与平均数 (Sum/Average)
计算子区域 (Subsection) 的平均数
public class AverageSubsection {
public static void main(String[] args) {
int[][] grid = {
{3, 5, 1, 7},
{9, 2, 6, 4},
{8, 10, 12, 11}
};
int r0 = 0, r1 = 1; // 行范围 [0, 1]
int c0 = 1, c1 = 3; // 列范围 [1, 3]
int sum = 0;
int count = 0;
for (int r = r0; r <= r1; r++) {
for (int c = c0; c <= c1; c++) {
sum += grid[r][c];
count++;
}
}
// 强转 double 确保计算精度
double avg = (double) sum / count;
System.out.println("子区域平均值: " + avg);
}
}
3. 判断是否至少有一个元素符合条件 (At Least One)
检查是否存在偶数
public class AnyEven2D {
public static void main(String[] args) {
int[][] grid = {
{3, 5, 1},
{9, 2, 6}
};
boolean found = false;
// 使用 !found 标志位控制循环，避免使用 break
for (int r = 0; r < grid.length && !found; r++) {
for (int c = 0; c < grid[r].length && !found; c++) {
if (grid[r][c] % 2 == 0) {
found = true;
}
}
}
System.out.println("是否存在偶数: " + found);
}
}
4. 统计符合条件的元素数量 (Count)
统计某一列中偶数的个数
public class CountEvenCol {
public static void main(String[] args) {
int[][] grid = {
{2, 5},
{4, 2},
{7, 10}
};
int targetCol = 0;
int count = 0;
for (int r = 0; r < grid.length; r++) {
if (grid[r][targetCol] % 2 == 0) {
count++;
}
}
System.out.println("该列偶数数量: " + count);
}
}
5. 访问所有相邻元素对 (Pairs)
垂直邻居 (同一列，相邻行)
public class ConsecutiveVertical {
public static void main(String[] args) {
int[][] grid = {
{3, 5},
{9, 2},
{8, 10}
};
int cols = grid[0].length;
for (int c = 0; c < cols; c++) {
// 注意：r 只能到 length - 1，防止 r + 1 越界
for (int r = 0; r < grid.length - 1; r++) {
System.out.println("垂直相邻对: " + grid[r][c] + " 和 " + grid[r + 1][c]);
}
}
}
}
6. 检查是否存在重复元素 (Duplicates)
检查整个 2D 数组是否有重复值
public class DuplicateCheck2D {
public static void main(String[] args) {
int[][] grid = {
{1, 2},
{3, 1}
};
boolean hasDup = false;
// 将每个位置 (r1, c1) 与其他所有位置 (r2, c2) 进行比较
for (int r1 = 0; r1 < grid.length && !hasDup; r1++) {
for (int c1 = 0; c1 < grid[r1].length && !hasDup; c1++) {
for (int r2 = 0; r2 < grid.length && !hasDup; r2++) {
for (int c2 = 0; c2 < grid[r2].length && !hasDup; c2++) {
// 排除自己跟自己比较的情况
if (r1 != r2 || c1 != c2) {
if (grid[r1][c1] == grid[r2][c2]) {
hasDup = true;
}
}
}
}
}
}
System.out.println("是否存在重复: " + hasDup);
}
}
7. 移动或旋转元素 (Shift/Rotate)
将某一列向下移动一位 (首尾衔接)
public class ShiftColumnDown {
public static void main(String[] args) {
int[][] grid = {
{1, 2},
{3, 4},
{5, 6}
};
int col = 0;
// 1. 暂存最底部的元素
int temp = grid[grid.length - 1][col];
// 2. 从下往上覆盖，确保数据不会被提前覆盖
for (int r = grid.length - 1; r > 0; r--) {
grid[r][col] = grid[r - 1][col];
}
// 3. 将暂存的元素放到最顶部
grid[0][col] = temp;
}
}
8. 反转元素 (Reverse)
原地反转某一列
public class ReverseColumn {
public static void main(String[] args) {
int[][] grid = {
{1, 0},
{2, 0},
{3, 0},
{4, 0}
};
int col = 0;
// 交换该列的上半部分和下半部分
for (int r = 0; r < grid.length / 2; r++) {
int temp = grid[r][col];
int oppositeRow = grid.length - 1 - r;
grid[r][col] = grid[oppositeRow][col];
grid[oppositeRow][col] = temp;
}
}
}