第28474题 单选题
以下C++递推实现爬楼梯问题的代码中,正确的是?

爬楼梯问题描述:楼梯共有n级台阶,每次可以选择爬1级或2级台阶,求爬到第n级台阶的总共有多少种不同的爬法。已知该问题的边界条件为:当n=1时只有1种爬法,n=2时有2种爬法;递推关系式为:当n≥3时,f(n) = f(n-1) + f(n-2)。以下四个C++代码片段均实现了该问题的递推求解,其中正确的是?

A
int climbStairs(int n) {
    if(n <= 0) return 0;
    if(n == 1) return 1;
    if(n == 2) return 2;
    int prev1 = 2, prev2 = 1, curr;
    for(int i = 3; i <= n; ++i) {
        curr = prev1 + prev2;
        prev2 = prev1;
        prev1 = curr;
    }
    return curr;
}
B
int climbStairs(int n) {
    if(n <= 0) return 0;
    if(n == 1) return 2;
    if(n == 2) return 1;
    int prev1 = 1, prev2 = 2, curr;
    for(int i = 3; i <= n; ++i) {
        curr = prev1 + prev2;
        prev2 = prev1;
        prev1 = curr;
    }
    return curr;
}
C
int climbStairs(int n) {
    if(n <= 0) return 0;
    if(n == 1) return 1;
    if(n == 2) return 2;
    int prev1 = 2, prev2 = 1, curr;
    for(int i = 3; i <= n; ++i) {
        curr = prev1 + 1;
        prev2 = prev1;
        prev1 = curr;
    }
    return curr;
}
D
int climbStairs(int n) {
    if(n <= 0) return 0;
    if(n == 1) return 1;
    if(n == 2) return 2;
    int prev1 = 2, prev2 = 1, curr;
    for(int i = 3; i <= n; ++i) {
        curr = prev1 + prev2;
        prev1 = prev2;
        prev2 = curr;
    }
    return curr;
}
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