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https://leetcode.com/problems/fibonacci-number/
class Solution {
public:
    int fib(int n) {
        if (n == 0) {
            return 0;
        }
        
        long long second_last = 0;
        long long last = 1;
        for (int i = 2; i <= n; i++) {
            long long current = second_last + last;
            second_last = last;
            last = current;
        }
        return last;
    }
};

https://leetcode.com/problems/minimum-path-sum/
class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int n = grid.size();
        if (n == 0) {
            return 0;
        }
        int m = grid[0].size();
        if (m == 0) {
            return 0;
        }
        int dp[2][m];
        dp[0][0] = grid[0][0];
        for (int i = 1; i < m; i++) {
            dp[0][i] = dp[0][i - 1] + grid[0][i];
        }
        
        for (int i = 1; i < n; i++) {
            for (int j = 0; j < m; j++) {
                dp[1][j] = 1e9;
                
                dp[1][j] = min(dp[1][j], dp[0][j] + grid[i][j]);
                if (j > 0) {
                    dp[1][j] = min(dp[1][j], dp[1][j - 1] + grid[i][j]);
                }
            }
            for (int j = 0; j < m; j++) {
                dp[0][j] = dp[1][j];
            }
        }
        return dp[0][m - 1];
    }
};


https://leetcode.com/problems/longest-valid-parentheses/
class Solution {
public:
    int longestValidParentheses(string s) {
        int n = s.length();
        if (n == 0) {
            return 0;
        }
        int dp[n + 1];
        dp[0] = dp[1] = 0;
        int ans = 0;
        for (int i = 2; i <= n; i++) {
            dp[i] = 0;
            if (s[i - 2] == '(' && s[i - 1] == ')') {
                dp[i] = dp[i - 2] + 2;
            }
            if (s[i - 2] == ')' && s[i - 1] == ')' && i - dp[i - 1] - 2 >= 0 && s[i - dp[i - 1] - 2] == '(') {
                dp[i] = dp[i - 1] + dp[i - dp[i - 1] - 2] + 2;
            }
            ans = max(ans, dp[i]);
        }
        return ans;
    }
};