algorithm - An unparenthesized arithmetic expression -


an arithmetic expression can have many possible values

can me?

there dynamic programming solution.

for expression, can define "outmost split point" first operator not within parentheses. after split, if on +, need maximize left sub expression , right sub expression; if -, maximize left side , minimize right side.

you can use either dynamic programming or memoization implement algorithm. memoization straightforward: search each split point, , save answer in data structure (two 2d matrices, m[x][y] string max/min value of expression beginning @ x , ending @ y); when data in matrices, use instead of recompute.

use dynamic programming bit trickier, can think of way:

  1. first, loop through expression, finding max/min each consecutive 2 values operator between them (well, fancy way of saying compute it);
  2. loop through expression, finding max/min each consecutive 3 values operator between them (for a ? b ? c, computed assuming split point between a , b, , assuming split point on b , c, , store max/min values of these two);
  3. once know max/min k-length sequences, compute k + 1-length ones using same method in step 2, until k length of array, , return max value length k.

this same matrix chain multiplication algorithm, has o(n^3) complexity. complexity can proved crudely reasoning: need loop n - 1 times, each time @ n - 1 subsequences, , need try @ n - 1 split points. so, n ^ 3 time complexity.


Comments

Post a Comment

Popular posts from this blog

jquery - How can I dynamically add a browser tab? -

since using iframes house external pages are, accounts "not preferred method" , disallowed sites (flickr, one), want dynamically generate browser tabs. e.g., when user submits form, want dynamically generate tab on browser in response submitted. e.g., might want add new tab url like: http://www.bigsurgarrapata.com/contact how in jquery? you want form target attribute action attribute. http://www.w3schools.com/tags/att_form_target.asp browsers have ultimate control on result of target attribute open new tab value of _blank. <form action="contact_submit.php" target="_blank" method="post">
Read more

node.js - Getting the socket id,user id pair of a logged in user(s) -

i have web application done using node js , in it,i have authentication system requires users log in before can access pages. have 2 pages,the homepage , updates page. from read docs,a new socket id issued when user opens tab in browser. me being admin,i know socket id of logged in user , more so,the socket id,logged in user id pair logged in users. what method can use socket id,logged in user id pair make sure broadcast realtime info users online?.
Read more

keyboard - C++ GetAsyncKeyState alternative -

i using windows.h library's getasynckeystate function define key pushed on keyboard . here program returns int value of pushed key example. #include <iostream> #include <windows.h> using namespace std; int main (){ char i; for(i=8;i<190;i++){ if(getasynckeystate(i)== -32767){ cout<<int (i)<<endl; } } return 0; } but trying make opengl simple game , function appeared slow . there function not need cycle 180 times , if statement . thanks you're trying make opengl game, you're going use glfw. if that's case can away using glfwgetkey() such: if (glfwgetkey(glfw_key_up) == glfw_press) {...} if (glfwgetkey(glfw_key_down) == glfw_press) {...} that method nicely explained in tutorial 6 opengl-tutorial.org . should start first tutorial of beginners tutorials , later intermediate tutorials . if you're going make win32 window can listen wm_keydown or wm_keyup messages , virtua
Read more