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| 1 | +/* |
| 2 | + * Question Description: |
| 3 | + * (Question 105 in <Coding Intervies>) Given an array A[0, 1, …, n-1], please construct an array |
| 4 | + * B[0, 1, …, n-1] in which B[i]=A[0]×A[1]×… ×A[i-1]×A[i+1]×…×A[n-1]. No division should be |
| 5 | + * involved to solve this problem. |
| 6 | +*/ |
| 7 | + |
| 8 | +#include <vector> |
| 9 | +#include <stdio.h> |
| 10 | + |
| 11 | +using namespace std; |
| 12 | + |
| 13 | +void multiply(const vector<double>& array1, vector<double>& array2) |
| 14 | +{ |
| 15 | + int length1= array1.size(); |
| 16 | + int length2 = array2.size(); |
| 17 | + |
| 18 | + if(length1 == length2 && length2 > 1) |
| 19 | + { |
| 20 | + array2[0] = 1; |
| 21 | + for(int i = 1; i < length1; ++i) |
| 22 | + { |
| 23 | + array2[i] = array2[i - 1] * array1[i - 1]; |
| 24 | + } |
| 25 | + |
| 26 | + double temp = 1; |
| 27 | + for(int i = length1 - 2; i >= 0; --i) |
| 28 | + { |
| 29 | + temp *= array1[i + 1]; |
| 30 | + array2[i] *= temp; |
| 31 | + } |
| 32 | + } |
| 33 | +} |
| 34 | + |
| 35 | +//================= Test Code ================= |
| 36 | +static bool equalArrays(const vector<double>& array1, const vector<double>& array2) |
| 37 | +{ |
| 38 | + int length1= array1.size(); |
| 39 | + int length2 = array2.size(); |
| 40 | + |
| 41 | + if(length1 != length2) |
| 42 | + return false; |
| 43 | + |
| 44 | + for(int i = 0; i < length1; ++i) |
| 45 | + { |
| 46 | + if(abs(array1[i] - array2[i]) > 0.0000001) |
| 47 | + return false; |
| 48 | + } |
| 49 | + |
| 50 | + return true; |
| 51 | +} |
| 52 | + |
| 53 | +static void test(char* testName, const vector<double>& array1, vector<double>& array2, const vector<double>& expected){ |
| 54 | + printf("%s Begins: ", testName); |
| 55 | + |
| 56 | + multiply(array1, array2); |
| 57 | + if(equalArrays(array2, expected)) |
| 58 | + printf("Passed.\n"); |
| 59 | + else |
| 60 | + printf("FAILED.\n"); |
| 61 | +} |
| 62 | + |
| 63 | +static void test1() |
| 64 | +{ |
| 65 | + double array1[] = {1, 2, 3, 4, 5}; |
| 66 | + double array2[] = {0, 0, 0, 0, 0}; |
| 67 | + double expected[] = {120, 60, 40, 30, 24}; |
| 68 | + |
| 69 | + test("Test1", vector<double>(array1, array1 + sizeof(array1) / sizeof(double)), |
| 70 | + vector<double>(array2, array2 + sizeof(array2) / sizeof(double)), |
| 71 | + vector<double>(expected, expected + sizeof(expected) / sizeof(double))); |
| 72 | +} |
| 73 | + |
| 74 | +static void test2() |
| 75 | +{ |
| 76 | + double array1[] = {1, 2, 0, 4, 5}; |
| 77 | + double array2[] = {0, 0, 0, 0, 0}; |
| 78 | + double expected[] = {0, 0, 40, 0, 0}; |
| 79 | + |
| 80 | + test("Test2", vector<double>(array1, array1 + sizeof(array1) / sizeof(double)), |
| 81 | + vector<double>(array2, array2 + sizeof(array2) / sizeof(double)), |
| 82 | + vector<double>(expected, expected + sizeof(expected) / sizeof(double))); |
| 83 | +} |
| 84 | + |
| 85 | +static void test3() |
| 86 | +{ |
| 87 | + double array1[] = {1, 2, 0, 4, 0}; |
| 88 | + double array2[] = {0, 0, 0, 0, 0}; |
| 89 | + double expected[] = {0, 0, 0, 0, 0}; |
| 90 | + |
| 91 | + test("Test3", vector<double>(array1, array1 + sizeof(array1) / sizeof(double)), |
| 92 | + vector<double>(array2, array2 + sizeof(array2) / sizeof(double)), |
| 93 | + vector<double>(expected, expected + sizeof(expected) / sizeof(double))); |
| 94 | +} |
| 95 | + |
| 96 | +static void test4() |
| 97 | +{ |
| 98 | + double array1[] = {1, -2, 3, -4, 5}; |
| 99 | + double array2[] = {0, 0, 0, 0, 0}; |
| 100 | + double expected[] = {120, -60, 40, -30, 24}; |
| 101 | + |
| 102 | + test("Test4", vector<double>(array1, array1 + sizeof(array1) / sizeof(double)), |
| 103 | + vector<double>(array2, array2 + sizeof(array2) / sizeof(double)), |
| 104 | + vector<double>(expected, expected + sizeof(expected) / sizeof(double))); |
| 105 | +} |
| 106 | + |
| 107 | +static void test5() |
| 108 | +{ |
| 109 | + double array1[] = {1, -2}; |
| 110 | + double array2[] = {0, 0}; |
| 111 | + double expected[] = {-2, 1}; |
| 112 | + |
| 113 | + test("Test5", vector<double>(array1, array1 + sizeof(array1) / sizeof(double)), |
| 114 | + vector<double>(array2, array2 + sizeof(array2) / sizeof(double)), |
| 115 | + vector<double>(expected, expected + sizeof(expected) / sizeof(double))); |
| 116 | +} |
| 117 | + |
| 118 | +void main() |
| 119 | +{ |
| 120 | + test1(); |
| 121 | + test2(); |
| 122 | + test3(); |
| 123 | + test4(); |
| 124 | + test5(); |
| 125 | +} |
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