动态规划经典算法状态转移方程总结

最大连续子序列和

dp[i] = max(dp[i - 1] + nums[i], nums[i])

最长上升子序列

dp[i] = max(1, dp[j] + 1) (j = 0...i - 1 && nums[j] < nums[i])

最长公共子序列

if (A[i] == B[j])
    dp[i][j] = dp[i - 1][j - 1] + 1;
else
    dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);

最长回文子串

if (S[i] == S[j])
    dp[i][j] = dp[i + 1][j - 1]
else
    dp[i][j] = 0;

最长回文子序列

if (S[i] == S[j])
    dp[i][j] = dp[i + 1][j - 1] + 2;
else 
    dp[i][j] = max(dp[i + 1][j], dp[i][j - 1]);