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Update the solution for the paths in a grid problem.

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Hung Dang 2019-03-29 00:56:46 -04:00
parent 6a8019e2ca
commit e4506fa092
1 changed files with 12 additions and 2 deletions
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chapter07.tex
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@ -634,12 +634,22 @@ int sum[N][N];
\end{lstlisting} \end{lstlisting}
and calculate the sums as follows: and calculate the sums as follows:
\begin{lstlisting} \begin{lstlisting}
for (int y = 1; y <= n; y++) { for (int y = 1; y < N; y++) {
for (int x = 1; x <= n; x++) { for (int x = 1; x < N; x++) {
sum[y][x] = max(sum[y][x-1],sum[y-1][x])+value[y][x]; sum[y][x] = max(sum[y][x-1],sum[y-1][x])+value[y][x];
} }
} }
\end{lstlisting} \end{lstlisting}
However, below is a better solution that only uses one dimensional
array to keep track of the maximum sums
\begin{lstlisting}
for (int y = 1; y < N; ++y) {
sum[0] += value[y][0];
for (int x = 1; x < N; ++x) {
sum[x] = value[y][x] + std::max(sum[x-1], sum[x]);
}
}
\end{lstlisting}
The time complexity of the algorithm is $O(n^2)$. The time complexity of the algorithm is $O(n^2)$.
\section{Knapsack problems} \section{Knapsack problems}