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Last Updated: April 18, 2019
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407
· jg2019

# Two Missing Numbers question....

###### code

Question
Given an array containing all the numbers from 1 to n except two, find the two missing numbers.

eg.
missing([4, 2, 3]) = 1, 5

Answer

// Determine the single number that is missing.
// XOR the actual array and the expected array from 1 to N together. All
// the repeated numbers cancel out, leaving us with the desired result.
// (1 ^ 2 ^ ... ^ N-1 ^ N) ^ (1 ^ 2 ^ ... ^ N-1) = N
public static int oneMissing(int[] arr) {
int totalXor = 0;
int arrXor = 0;

``````// XOR the numbers from 1 to N, ie. the input if no numbers were missing
for (int i = 1; i <= arr.length + 1; i++) totalXor ^= i;

// XOR the input array
for (int i : arr) arrXor ^= i;

// XOR the two values together. x^x = 0 and x^0 = x. That means that any
// repeated number cancels out, so we are left with the single
// non-repeated number.
// eg. (1 ^ 2 ^ ... ^ N-1 ^ N) ^ (1 ^ 2 ^ ... ^ N-1) = N
return totalXor ^ arrXor;``````

}

// Determine the two numbers missing from an array. Returns an array of
// length 2
public static int[] twoMissing(int[] arr) {
int size = arr.length + 2;

``````// 1 + 2 + ... + N-1 + N = N * (N + 1) / 2
long totalSum = size * (size + 1) / 2;

// Sum up the input array
long arrSum = 0;
for (int i : arr) arrSum += i;

// totalSum - arrSum = the sum of the two results. Therefore we know
// that since our two results are not equal, one result is
// > (sum of two results) / 2 and the other is
// < (sum of two results) / 2
int pivot = (int) ((totalSum - arrSum) / 2);

// Use the same technique as oneMissing() on each half of the array.
int totalLeftXor = 0;
int arrLeftXor = 0;
int totalRightXor = 0;
int arrRightXor = 0;

for (int i = 1; i <= pivot; i++) totalLeftXor ^= i;
for (int i = pivot + 1; i <= size; i++) totalRightXor ^= i;
for (int i : arr) {
if (i <= pivot) arrLeftXor ^= i;
else arrRightXor ^= i;
}

return new int[]{totalLeftXor ^ arrLeftXor, totalRightXor ^ arrRightXor};``````

}
// Determine the single number that is missing.
// XOR the actual array and the expected array from 1 to N together. All
// the repeated numbers cancel out, leaving us with the desired result.
// (1 ^ 2 ^ ... ^ N-1 ^ N) ^ (1 ^ 2 ^ ... ^ N-1) = N
public static int oneMissing(int[] arr) {
int totalXor = 0;
int arrXor = 0;

``````// XOR the numbers from 1 to N, ie. the input if no numbers were missing
for (int i = 1; i <= arr.length + 1; i++) totalXor ^= i;

// XOR the input array
for (int i : arr) arrXor ^= i;

// XOR the two values together. x^x = 0 and x^0 = x. That means that any
// repeated number cancels out, so we are left with the single
// non-repeated number.
// eg. (1 ^ 2 ^ ... ^ N-1 ^ N) ^ (1 ^ 2 ^ ... ^ N-1) = N
return totalXor ^ arrXor;``````

}

// Determine the two numbers missing from an array. Returns an array of
// length 2
public static int[] twoMissing(int[] arr) {
int size = arr.length + 2;

``````// 1 + 2 + ... + N-1 + N = N * (N + 1) / 2
long totalSum = size * (size + 1) / 2;

// Sum up the input array
long arrSum = 0;
for (int i : arr) arrSum += i;

// totalSum - arrSum = the sum of the two results. Therefore we know
// that since our two results are not equal, one result is
// > (sum of two results) / 2 and the other is
// < (sum of two results) / 2
int pivot = (int) ((totalSum - arrSum) / 2);

// Use the same technique as oneMissing() on each half of the array.
int totalLeftXor = 0;
int arrLeftXor = 0;
int totalRightXor = 0;
int arrRightXor = 0;

for (int i = 1; i <= pivot; i++) totalLeftXor ^= i;
for (int i = pivot + 1; i <= size; i++) totalRightXor ^= i;
for (int i : arr) {
if (i <= pivot) arrLeftXor ^= i;
else arrRightXor ^= i;
}

return new int[]{totalLeftXor ^ arrLeftXor, totalRightXor ^ arrRightXor};``````