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?
分析:
解题思路:归纳法(列举出n=1,2,3,4,5 总结规律)
得到:
f(1)=1
f(2)=2
f(3)=3
f(4)=5
f(5)=8
即:n>2时,f(n)=f(n-1) + f(n-2)
代码1:使用递归
public class Solution {
public int RectCover(int target) {
if(target == 1){
return 1;
}else if(target == 2){
return 2;
}else{
return RectCover(target - 1) + RectCover(target - 2);
}
}
public static void main(String[] args) {
Solution s = new Solution();
System.out.println(s.RectCover(5));
}
}
代码2
public class Solution1 {
public int RectCover(int target) {
int one = 1;
int two = 2;
if(target == 1){
return 1;
}
if(target == 2){
return 2;
}
int result = 0;
for(int i = 3;i <= target;i++){
result = one + two;
one = two;
two = result;
}
return result;
}
public static void main(String[] args) {
Solution1 s = new Solution1();
System.out.println(s.RectCover(5));
}
}