UVa 727 - Equation

题目：求表达式的后缀式。

分析：递归、栈。利用递归或栈求解即可。本人采用递归求解，每次找到运算优先级最低的点，然后递归两端即可。寻找优先级最低的点利用线段树优化。

注意：数据读入出错会RE；如果数据过大递归会暴栈。

#include <iostream>#include <stdio.h>#include <stdlib.h>#include <cstring>#include <stack> using namespace std;char str[ 51 ];int  mat[ 51 ];//segment_tree__begintypedef struct tnode{tnode* Lchild;tnode* Rchild;int   Lvalue;int    Rvalue;int    Min;int   Spa;}tnode;tnode Node[ 105 ];tnode* Root;int    Count;tnode* madetree( int a, int b ) {tnode* np  = &Node[ Count ++ ];np->Lvalue = a;np->Rvalue = b;np->Min = 100000;if ( a < b ) {np->Lchild = madetree( a, (a+b)/2 );np->Rchild = madetree( (a+b)/2+1, b );}else {np->Lchild = NULL;np->Rchild = NULL;}return np;}void segment_tree( int a, int b ) {Count = 0;Root = madetree( a, b );}void Insert( tnode* r, int p, int v ) {if ( r->Lvalue == p && r->Rvalue == p ) {r->Min = v;r->Spa = p;return;}int mid = (r->Lvalue+r->Rvalue)/2;if ( p <= mid ) {Insert( r->Lchild, p, v );if ( r->Min == r->Lchild->Min && r->Spa < r->Lchild->Spa )r->Spa = r->Lchild->Spa;else if ( r->Min > r->Lchild->Min ) {r->Min = r->Lchild->Min;r->Spa = r->Lchild->Spa;}}else {Insert( r->Rchild, p, v );if ( r->Min == r->Rchild->Min && r->Spa < r->Rchild->Spa )r->Spa = r->Rchild->Spa;else if ( r->Min > r->Rchild->Min ) {r->Min = r->Rchild->Min;r->Spa = r->Rchild->Spa;}}}tnode Query( tnode* r, int a, int b ) {if ( r->Lvalue == a && r->Rvalue == b )return *r;int mid = (r->Lvalue+r->Rvalue)/2;if ( b <= mid ) return Query( r->Lchild, a, b );else if ( a > mid )return Query( r->Rchild, a, b );else {tnode A = Query( r->Lchild, a, mid );tnode B = Query( r->Rchild, mid+1, b );if ( A.Min >= B.Min )return B;else return A;}}void Insert( int p, int v ) {Insert( Root, p, v );}tnode Query( int a, int b ) {return Query( Root, a, b );}//segment_tree__endint level( char c ){switch( c ) {case '(': case ')': return 10000;case '+':case '-': return 1;case '*':case '/': return 5;}return 10000;}void f( char* s, int l, int r ){if ( l == r ) {printf("%c",s[l]);return;}//去括号if ( str[l] == '(' && mat[l] == r ) {f( s, l+1, r-1 );return;}//寻找最低优先级int spa = Query( l, r ).Spa;f( s, l ,spa-1 );f( s, spa+1, r );printf("%c",s[spa]);}int main(){int n;while ( cin >> n ) {getchar();getchar();while ( n -- ) {int count = 0;while ( gets(&str[count]) ) {if( !str[count] )break;++ count;}str[count] = 0;stack<int>S;for ( int i = 0 ; i < count ; ++ i ) {if ( str[i] == '(' )S.push(i);if ( str[i] == ')' ) {mat[S.top()] = i;S.pop();}}segment_tree( 0, count-1 );int add = 0;for ( int i = 0 ; i < count ; ++ i ) {if ( str[i] == '(' ) add += 100;if ( str[i] == ')' ) add -= 100;Insert( i, add+level(str[i]) );}f( str, 0, count-1 );printf("\n");if ( n ) printf("\n");}}return 0;}