Sword refers to offer-supplement 3. Rectangular coverage-analysis and code (Java)

1. Title

We can use 2 * 1 small rectangles horizontally or vertically to cover larger rectangles. How many ways are there to cover a large 2 * n rectangle with n small 2 * 1 rectangles without overlap?

Two, analysis and code

1. Dynamic programming

(1) Thinking

When n> 2, its covering method can be regarded as the covering method of the large rectangle of n-1 plus 1 small vertical rectangle or the covering method of the large rectangle of n-2 plus 2 small horizontal rectangles , That is, F(n) = F(n-1) + F(n-2). According to this characteristic, it can be solved by combining with dynamic programming method.

(2) Code

public class Solution {
    
    
    public int RectCover(int target) {
    
    
        if (target < 3)
            return target;
        int [] ans = new int[target + 1];
        ans[1] = 1;
        ans[2] = 2;
        for (int i = 3; i <= target; i++)
            ans[i] = ans[i - 1] + ans[i - 2];
        return ans[target];
    }
}

(3) Results

Running time: 13 ms, occupying 9292 k of memory.

Three, other

Nothing.