http://poj.org/problem?id=1348
Computing
| Time Limit: 1000MS | Memory Limit: 10000K | |
| Total Submissions: 1681 | Accepted: 248 |
Description
Input any five positive integral numbers n1, n2, n3, n4, n5, such that 0<=ni<=100, 1<=i<=5. To the first four positive integral numbers (n1, n2, n3, n4) the arithmetic operation, such as addition (+), subtraction (-), multiplication (*), or division (/) and brackets ('(',')') may be freely applied, but in the arithmetic expression formed with these numbers and operations, every one of the four integral numbers should be used once and only once. Write a program for finding an arithmetic expression that satisfies the above requirement and equals n5.
Input
The input file consists of a number of data sets.Each data set is a line of 5 numbers separated by blank.A line of a single -1 represents the end of input.
Output
For each data set output the original data set first.If the program finds out the expression for these four arbitrary input numbers, then it gives out the output "OK!"；On the contrary, if the program could not get the result of n5 by any arithmetic operations to the four input numbers, it gives output "NO!".
Sample Input
1 2 3 4 50 2 3 10 1 61 -1
Sample Output
1 2 3 4 50 NO! 2 3 10 1 61 OK!
Source
思路：
采用 分子分母 表示一个整数，进行四则运算；
利用STL中algorithm中的next_permutation(a,a+n)获取下一个字典序
代码：
1 #include<iostream> 2 #include<stdio.h> 3 #include<string.h> 4 #include<algorithm> 5 6 using namespace std; 7 8 struct Nod 9 { 10 int son; //分子 11 int mon; //分母 12 }num[5]; //以 分子/分母 形式保存一个数 13 14 15 void getNum(int *a) //将a数组转换成 分子/分母 形式 16 { 17 int i; 18 for(i=0;i<4;i++) 19 { 20 num[i].son = a[i]; 21 num[i].mon = 1; 22 } 23 } 24 25 Nod operate(Nod a,Nod b,int ch) //进行四则运算 26 { 27 Nod temp; 28 if(ch==0) // '+' 29 { 30 temp.mon = a.mon * b.mon; 31 temp.son = a.son * b.mon + b.son * a.mon; 32 } 33 else if(ch==1) // '-' 34 { 35 temp.mon = a.mon * b.mon; 36 temp.son = a.son * b.mon - b.son * a.mon; 37 } 38 else if(ch==2) // '*' 39 { 40 temp.mon = a.mon * b.mon; 41 temp.son = a.son * b.son; 42 } 43 else if(ch==3) // '/' 44 { 45 temp.mon = a.mon * b.son; 46 temp.son = b.mon * a.son; 47 } 48 return temp; 49 } 50 51 int computing(int *a,int e) 52 { 53 getNum(a); //获得 分子/分母 的表示方式 54 Nod temp1,temp2,temp3; 55 int i,j,k; 56 57 // ((a#b)#c)#d '#'号代表运算符号 58 for(i=0;i<4;i++) 59 { 60 temp1 = operate(num[0],num[1],i); 61 if(temp1.mon == 0) continue; //分母为0情况 62 for(j=0;j<4;j++) 63 { 64 temp2 = operate(temp1,num[2],j); 65 if(temp2.mon == 0) continue; 66 for(k=0;k<4;k++) 67 { 68 temp3 = operate(temp2,num[3],k); 69 if(temp3.mon == 0) continue; 70 if(temp3.son%temp3.mon==0&&temp3.son/temp3.mon==e) return 1; 71 } 72 } 73 } 74 75 //(a#(b#(c#d))) 76 for(i=0;i<4;i++) 77 { 78 temp1 = operate(num[2],num[3],i); 79 if(temp1.mon == 0) continue; 80 for(j=0;j<4;j++) 81 { 82 temp2 = operate(num[1],temp1,j); 83 if(temp2.mon == 0) continue; 84 for(k=0;k<4;k++) 85 { 86 temp3 = operate(num[0],temp2,k); 87 if(temp3.mon == 0) continue; 88 if(temp3.son%temp3.mon==0&&temp3.son/temp3.mon==e) return 1; 89 } 90 } 91 } 92 //(a#b)#(c#d) 93 for(i=0;i<4;i++) 94 { 95 temp1 = operate(num[0],num[1],i); 96 if(temp1.mon == 0) continue; 97 for(j=0;j<4;j++) 98 { 99 temp2 = operate(num[2],num[3],j); 100 if(temp2.mon == 0) continue; 101 for(k=0;k<4;k++) 102 { 103 temp3 = operate(temp1,temp2,k); 104 if(temp3.mon == 0) continue; 105 if(temp3.son%temp3.mon==0&&temp3.son/temp3.mon==e) return 1; 106 } 107 } 108 } 109 return 0; 110 } 111 112 int main() 113 { 114 int a[5],e; 115 while(~scanf("%d",&a[0])&&a[0]!=-1) 116 { 117 scanf("%d%d%d%d",&a[1],&a[2],&a[3],&e); 118 int i,j; 119 for(j=0;j<4;j++) printf("%d ",a[j]); 120 for(i=0;i<24;i++) 121 { 122 if(computing(a,e) == 1) break; 123 next_permutation(a,a+4); //获取下一个字典序 124 } 125 printf("%d ",e); 126 if(i<24) puts("OK!"); 127 else puts("NO!"); 128 } 129 return 0; 130 }