Solution
// FindTwoMissingNumbers.cpp : Defines the entry point for the console application.
//
#include <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <iomanip>
#include <cstdlib>
using namespace std;
void InitArray(int* arr)
{
vector<int> vec;
int num1 = rand() % 100;
int num2 = num1;
while(num1 == num2){
num2 = rand() % 100 ;
}
int smallMissingNum = (num1 < num2) ? num1 : num2;
int bigMissingNum = (num1 > num2) ? num1 : num2;
cout << "The numbers to be missed are " << smallMissingNum << " and " << bigMissingNum << endl;
for(int i = 0; i < smallMissingNum; ++i){
vec.push_back(i);
}
for(int i = smallMissingNum + 1; i < bigMissingNum; ++i){
vec.push_back(i);
}
for(int i = bigMissingNum + 1; i < 100; ++i){
vec.push_back(i);
}
random_shuffle(vec.begin(), vec.end());
for(int i = 0; i < 98; ++i){
cout << setw(4) << vec.at(i);
if((i + 1) % 10 == 0){
cout << endl;
}
}
cout << endl;
for(vector<int>::iterator it = vec.begin(); it != vec.end(); ++it){
*arr ++ = *it;
}
}
void FindMissingNumbers1(int* arr, int& num1, int& num2)
{
int sum = 0;
int squareSum = 0;
for(int i = 0; i < 98; ++i){
sum += arr[i];
squareSum += arr[i] * arr[i];
}
int expectedSum = (0 + 99) * 100 / 2;
int expectedSquareSum = 99 * (99 + 1) * (2 * 99 + 1) / 6;
int aPlusB = expectedSum - sum;
int asqPlusBsq = expectedSquareSum - squareSum;
int aMulB = (aPlusB * aPlusB - asqPlusBsq) / 2;
int t = sqrt((double)aPlusB * aPlusB - 4 * aMulB);
num1 = (int)(aPlusB - t) / 2;
num2 = (int)(aPlusB + t) / 2;
}
int main(int argc, char* argv[])
{
srand(1);
for(int i = 0; i < 10; i++){
int arr[98];
InitArray(arr);
int num1, num2;
FindMissingNumbers1(arr, num1, num2);
cout << "The missing numbers are : " << endl;
cout << "Num 1 : " << num1 << endl;
cout << "Num 2 : " << num2 << endl << endl;
}
return 0;
}
Output
The numbers to be missed are 41 and 67
6 28 51 53 69 71 76 93 49 20
0 88 95 10 3 22 7 77 43 31
1 32 2 39 58 11 64 82 83 48
12 40 75 73 90 68 86 98 79 91
14 34 8 36 62 24 17 61 21 45
94 27 47 70 33 57 92 72 44 35
50 78 15 96 26 42 97 23 56 65
13 55 59 66 52 29 74 99 19 30
85 84 25 38 89 60 37 63 16 4
46 54 18 9 81 87 80 5
The missing numbers are :
Num 1 : 41
Num 2 : 67
The numbers to be missed are 15 and 33
36 71 10 60 57 2 97 84 75 47
61 24 79 32 73 62 12 50 56 5
87 98 90 6 8 16 35 40 59 49
18 9 0 43 63 31 82 20 91 29
25 95 85 17 65 54 96 88 66 27
53 55 22 83 21 3 46 42 86 34
92 4 70 58 77 52 69 26 64 19
94 7 51 80 68 41 72 99 11 39
38 1 67 30 93 44 48 89 78 28
14 37 74 81 45 23 76 13
The missing numbers are :
Num 1 : 15
Num 2 : 33
The numbers to be missed are 9 and 14
4 45 2 23 68 5 74 72 65 36
83 51 41 40 79 20 70 33 12 69
97 55 57 26 39 91 31 47 58 71
64 8 3 56 53 52 73 35 84 28
86 82 19 88 37 85 50 96 15 42
76 54 11 61 93 1 48 17 25 78
49 92 7 90 24 63 94 30 80 95
13 32 77 44 10 27 21 59 18 43
66 29 46 87 62 22 75 6 0 89
60 67 16 81 38 98 99 34
The missing numbers are :
Num 1 : 9
Num 2 : 14
The numbers to be missed are 21 and 89
29 65 71 23 41 81 36 19 80 82
4 34 69 50 12 9 31 62 73 96
94 28 49 13 75 97 95 22 83 42
1 10 66 70 0 6 35 98 76 99
57 7 55 26 91 47 11 32 54 60
2 44 39 90 86 52 79 8 87 33
40 43 46 18 53 20 84 59 51 56
27 92 72 37 77 63 25 88 93 48
5 85 78 24 74 58 3 45 14 68
67 38 16 61 17 15 64 30
The missing numbers are :
Num 1 : 21
Num 2 : 89
The numbers to be missed are 18 and 97
47 15 14 19 92 42 8 35 36 6
40 55 64 22 67 7 17 43 66 54
44 74 56 76 29 82 98 70 77 57
41 73 68 71 93 79 81 63 94 0
69 78 88 65 89 16 24 86 31 25
21 50 39 1 72 48 33 37 11 4
49 59 95 34 51 27 3 90 2 13
85 28 30 46 20 9 58 45 91 10
83 62 96 26 87 32 75 61 52 23
53 38 84 80 5 12 99 60
The missing numbers are :
Num 1 : 18
Num 2 : 97
The numbers to be missed are 37 and 61
19 66 17 11 41 3 60 71 74 1
31 50 23 96 15 68 8 43 45 42
34 46 82 49 62 65 53 77 78 59
72 14 63 40 4 55 21 91 39 10
32 85 51 67 69 73 36 97 2 79
70 16 9 13 89 0 56 54 87 22
58 25 90 35 64 52 28 88 38 95
47 99 18 20 83 7 44 6 26 81
94 75 92 76 93 84 5 33 80 29
12 24 98 57 48 86 30 27
The missing numbers are :
Num 1 : 37
Num 2 : 61
The numbers to be missed are 48 and 75
70 47 68 8 22 77 94 56 78 30
53 18 92 79 23 61 16 76 29 12
2 91 50 45 37 32 83 74 60 97
63 66 42 85 95 89 44 39 52 98
24 28 82 73 15 6 21 27 14 4
25 58 93 11 43 65 62 67 87 99
35 41 10 80 55 5 38 57 3 81
88 0 36 19 51 9 84 20 46 13
49 96 1 7 59 26 17 33 54 69
31 34 40 71 72 64 86 90
The missing numbers are :
Num 1 : 48
Num 2 : 75
The numbers to be missed are 13 and 92
27 64 97 84 29 46 20 36 31 82
70 21 66 83 71 87 12 67 42 77
68 73 37 58 63 60 5 7 80 14
47 17 23 98 99 79 26 38 9 15
69 57 18 10 45 35 62 49 96 86
22 53 30 89 25 24 93 85 91 33
32 50 19 52 40 51 43 74 94 61
59 95 72 2 34 65 11 48 81 4
8 56 41 28 44 6 55 1 78 3
90 54 0 16 76 75 88 39
The missing numbers are :
Num 1 : 13
Num 2 : 92
The numbers to be missed are 49 and 90
69 5 84 4 47 27 19 7 40 43
77 31 32 3 55 30 93 76 75 67
52 66 11 71 95 79 74 10 16 42
65 24 41 0 21 89 88 2 96 81
58 73 82 64 15 9 8 99 57 20
39 48 1 62 23 53 70 46 97 51
44 87 80 50 38 35 86 12 6 13
18 22 59 91 33 25 36 63 34 37
68 28 92 56 14 72 45 78 83 17
54 98 29 26 85 60 94 61
The missing numbers are :
Num 1 : 49
Num 2 : 90
The numbers to be missed are 61 and 64
48 83 20 47 5 59 37 58 97 30
87 51 77 67 91 63 90 93 36 17
11 95 10 70 86 28 26 69 85 19
71 60 84 73 18 32 46 24 4 39
2 3 68 35 16 96 31 56 50 14
8 22 44 52 80 89 62 76 74 34
65 81 40 33 13 21 88 98 1 27
92 43 99 7 25 45 82 41 72 79
66 75 94 55 53 57 12 42 38 54
0 49 6 9 78 29 23 15
The missing numbers are :
Num 1 : 61
Num 2 : 64
Press any key to continue . . .
Problem
Two numbers are missing from the first hundred numbers. They are NOT sorted. How to find them?
You can't sort.. and can't iterate one by one.. has to be less than O(N)? Can't use stack , set or any collection interface or in fact any other data structure or array!