JZ-010-Rectangular Cover

Rectangular coverage

Title description

We can use 1 to cover a larger rectangle horizontally or vertically. How many ways are there to cover a large 2*n rectangle with n 2

title link : rectangle cover

Code

/**
 * 标题：矩形覆盖
 * 题目描述
 * 我们可以用2*1的小矩形横着或者竖着去覆盖更大的矩形。请问用n个2*1的小矩形无重叠地覆盖一个2*n的大矩形，总共有多少种方法？
 * <p>
 * 比如n=3时，2*3的矩形块有3种覆盖方法：
 * 题目链接
 * https://www.nowcoder.com/practice/72a5a919508a4251859fb2cfb987a0e6?tpId=13&&tqId=11163&rp=1&ru=/ta/coding-interviews&qru=/ta/coding-interviews/question-ranking
 */
public class Jz10 {

    /**
     * 迭代法
     * 方法：要覆盖 2*n 的大矩形，可以先覆盖 2*1 的矩形，再覆盖 2*(n-1) 的矩形；
     * 或者先覆盖 2*2 的矩形，再覆盖 2*(n-2) 的矩形。而覆盖 2*(n-1) 和 2*(n-2) 的矩形可以看成子问题。
     *
     * @param target
     * @return
     */
    public static int rectCover(int target) {
        if (target <= 2) {
            return target;
        }
        int first = 1, second = 2;
        for (int i = 3; i <= target; i++) {
            second = second + first;
            first = second - first;
        }
        return second;
    }

    public static void main(String[] args) {
        for (int i = 1; i < 10; i++) {
            System.out.println(rectCover(i));
        }
    }
}

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