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LeetCode "Climbing Stairs"
The best way to learn DP from DFS! Nice problem.
My intuition is that it can be solved by DFS:
class Solution {public: int climbStairs(int n) { if (n == 0) return 1; int cnt0 = climbStairs(n - 1); int cnt1 = 0; if(n >= 2) cnt1 = climbStairs(n - 2); return cnt0 + cnt1; }};
You can get correct answer by this, but it is taking too long - TLE.
Actually, the equation is quite obvious in above code: s[n] = s[n-1] + s[n-2] with s[1] = 1; s[2] = 2. Sooooo beautiful:
class Solution {public: int climbStairs(int n) { if (n == 0) return 0; if (n == 1) return 1; if (n == 2) return 2; // S[n] = S[n-1] + S[n-2]; S[1] = 1; S[2] = 2 int ret = 0; int *s = new int[n + 1]; s[1] = 1; s[2] = 2; for (int i = 3; i <= n; i++) { s[i] = s[i - 1] + s[i - 2]; } ret = s[n]; delete[] s; return ret; }};
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