Data Structure topic of the data structure of the ultraviolet A 442-matrix chain Multiplication

442-Matrix Chain Multiplication

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Question Link: Http://uva.onlinejudge.org/index.php? Option = com_onlinejudge & Itemid = 8 & category = 103 & page = show_problem & problem = 383

Question type: data structure, linked list

Sample input:

9A 50 10B 10 20C 20 5D 30 35E 35 15F 15 5G 5 10H 10 20I 20 25ABC(AA)(AB)(AC)(A(BC))((AB)C)(((((DE)F)G)H)I)(D(E(F(G(HI)))))((D(EF))((GH)I))

Sample output:

000error10000error350015000405004750015125

Question:

Give them a series of matrices named a, B ...... And their number of rows and columns. After the expression is given, a series of expressions are required to find the number of multiplication steps for calculation based on these expressions.

Disintegration ideas:

This question matches the question with the brackets. The key step is to calculate the number of matrix multiplications.

# Include <cstdio> # include <cctype> # include <cstring> # include <cstdlib> # include <stack> using namespace STD; int sum, N; int mat [30] [2]; int arr [30], Prev [30], next [30]; char STR [1000]; void solve () {// if there is only one matrix, the result 0 if (strlen (STR) = 1 & isupper (STR [0]) is directly output. {printf ("0 \ n") ;}else {char copymat [30] [2]; int I, j; // copy an array for operation. Because the subsequent operations need to modify these matrices for (I = 0; I <n; ++ I) {copymat [I] [0] = mat [I] [0]; copymat [I] [1] = mat [I] [1];} sum = 0; stack <char> st; for (I = 0; I <strlen (STR); ++ I) {If (STR [I] = '(' | isupper (STR [I]) ST. push (STR [I]); else if (STR [I] = ') {stack <char> temp; // when') 'is encountered, calculate all the matrices in the stack while (isupper (St. top () {temp. push (St. top (); ST. pop ();} // put '(' Also pops up St. pop (); char ex; // retrieve the first Matrix (the leftmost one in the original expression) if (! Temp. Empty () {EX = temp. Top (); temp. Pop ();} while (! Temp. empty () {char multi = temp. top (); temp. pop (); // if the number of columns in the left matrix is different from the function in the right matrix, the error if (copymat [ex-'a'] [1] is directly output. = Copymat [multi-'a'] [0]) {printf ("error \ n"); return;} // calculates the number of times of multiplication, add sum + = copymat [ex-'a'] [0] * copymat [multi-'a'] [0] * copymat [multi-'a'] [1]; // obtain a new matrix after multiplication, and update the size of copymat [ex-'a'] [1] = copymat [multi-'a'] [1];} St. push (Ex) ;}} printf ("% d \ n", sum) ;}} int main () {freopen ("input.txt", "r", stdin ); char ch; int I, j; scanf ("% d % * C", & N); for (I = 0; I <n; ++ I) {scanf ("% C % d % * C", & Ch, & mat [I] [0], & mat [I] [1]);} while (gets (STR) {solve ();} return 0 ;}

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