A non-empty array A consisting of N integers is given. Array A represents numbers on a tape.
Any integer P, such that 0 < P < N, splits this tape into two non-empty parts: A[0], A[1], ..., A[P − 1] and A[P], A[P + 1], ..., A[N − 1].
The difference between the two parts is the value of: |(A[0] + A[1] + ... + A[P − 1]) − (A[P] + A[P + 1] + ... + A[N − 1])|
In other words, it is the absolute difference between the sum of the first part and the sum of the second part.
For example, consider array A such that:
A[0] = 3 A[1] = 1 A[2] = 2 A[3] = 4 A[4] = 3We can split this tape in four places:
- P = 1, difference = |3 − 10| = 7
- P = 2, difference = |4 − 9| = 5
- P = 3, difference = |6 − 7| = 1
- P = 4, difference = |10 − 3| = 7
Write a function:
int solution(int A[], int N);
that, given a non-empty array A of N integers, returns the minimal difference that can be achieved.
For example, given:
A[0] = 3 A[1] = 1 A[2] = 2 A[3] = 4 A[4] = 3the function should return 1, as explained above.
Write an efficient algorithm for the following assumptions:
- N is an integer within the range [2..100,000];
- each element of array A is an integer within the range [−1,000..1,000].
// you can write to stdout for debugging purposes, e.g.
// printf("this is a debug message\n");
int solution(int A[], int N) {
// write your code in C99
uint8_t current_index;
uint16_t solution = 65535;
uint16_t tmp_solution = 0;
uint16_t right_hand_side_sum = 0;
uint16_t left_hand_side_sum = 0;
if(N == 1)
{
return A[0];
}
else if(N == 2)
{
return abs(A[0] - A[1]);
}
/* Calculating sum of left hand side elements start with index 1*/
for(current_index = 0U; current_index < N; current_index++)
{
left_hand_side_sum += A[current_index];
}
/* Find the minimum difference value */
for(current_index = 0U; current_index < N - 1; current_index++)
{
right_hand_side_sum += A[current_index];
left_hand_side_sum -= A[current_index];
tmp_solution = (uint16_t)(abs(left_hand_side_sum - right_hand_side_sum));
if((tmp_solution < solution))
{
solution = tmp_solution;
}
else
{
/* MISRA standard */
}
if(solution == 0)
{
return 0;
}
else
{
/* MISRA standard */
}
}
return solution;
}
func.c: In function 'solution': func.c:6:5: error: unknown type name 'uint8_t' uint8_t current_index; ^ func.c:7:5: error: unknown type name 'uint16_t' uint16_t solution = 65535; ^ func.c:8:5: error: unknown type name 'uint16_t' uint16_t tmp_solution = 0; ^ func.c:9:5: error: unknown type name 'uint16_t' uint16_t right_hand_side_sum = 0; ^ func.c:10:5: error: unknown type name 'uint16_t' uint16_t left_hand_side_sum = 0; ^ func.c:34:25: error: 'uint16_t' undeclared (first use in this function) tmp_solution = (uint16_t)(abs(left_hand_side_sum - right_hand_side_sum)); ^ func.c:34:25: note: each undeclared identifier is reported only once for each function it appears in
// you can write to stdout for debugging purposes, e.g.
// printf("this is a debug message\n");
int solution(int A[], int N) {
// write your code in C99
char current_index;
int solution = 65535;
int tmp_solution = 0;
int right_hand_side_sum = 0;
int left_hand_side_sum = 0;
if(N == 1)
{
return A[0];
}
else if(N == 2)
{
return abs(A[0] - A[1]);
}
/* Calculating sum of left hand side elements start with index 1*/
for(current_index = 0U; current_index < N; current_index++)
{
left_hand_side_sum += A[current_index];
}
/* Find the minimum difference value */
for(current_index = 0U; current_index < N - 1; current_index++)
{
right_hand_side_sum += A[current_index];
left_hand_side_sum -= A[current_index];
tmp_solution = (uint16_t)(abs(left_hand_side_sum - right_hand_side_sum));
if((tmp_solution < solution))
{
solution = tmp_solution;
}
else
{
/* MISRA standard */
}
if(solution == 0)
{
return 0;
}
else
{
/* MISRA standard */
}
}
return solution;
}
func.c: In function 'solution': func.c:25:9: warning: array subscript has type 'char' [-Wchar-subscripts] left_hand_side_sum += A[current_index]; ^ func.c:31:10: warning: array subscript has type 'char' [-Wchar-subscripts] right_hand_side_sum += A[current_index]; ^ func.c:32:10: warning: array subscript has type 'char' [-Wchar-subscripts] left_hand_side_sum -= A[current_index]; ^ func.c:34:25: error: 'uint16_t' undeclared (first use in this function) tmp_solution = (uint16_t)(abs(left_hand_side_sum - right_hand_side_sum)); ^ func.c:34:25: note: each undeclared identifier is reported only once for each function it appears in
// you can write to stdout for debugging purposes, e.g.
// printf("this is a debug message\n");
int solution(int A[], int N) {
// write your code in C99
char current_index;
int solution = 65535;
int tmp_solution = 0;
int right_hand_side_sum = 0;
int left_hand_side_sum = 0;
if(N == 1)
{
return A[0];
}
else if(N == 2)
{
return abs(A[0] - A[1]);
}
/* Calculating sum of left hand side elements start with index 1*/
for(current_index = 0U; current_index < N; current_index++)
{
left_hand_side_sum += A[current_index];
}
/* Find the minimum difference value */
for(current_index = 0U; current_index < N - 1; current_index++)
{
right_hand_side_sum += A[current_index];
left_hand_side_sum -= A[current_index];
tmp_solution = (int)(abs(left_hand_side_sum - right_hand_side_sum));
if((tmp_solution < solution))
{
solution = tmp_solution;
}
else
{
/* MISRA standard */
}
if(solution == 0)
{
return 0;
}
else
{
/* MISRA standard */
}
}
return solution;
}
// you can write to stdout for debugging purposes, e.g.
// printf("this is a debug message\n");
int solution(int A[], int N) {
// write your code in C99
unsigned char current_index;
unsigned int solution = 65535;
unsigned int tmp_solution = 0;
unsigned int right_hand_side_sum = 0;
unsigned int left_hand_side_sum = 0;
if(N == 1)
{
return A[0];
}
else if(N == 2)
{
return abs(A[0] - A[1]);
}
/* Calculating sum of left hand side elements start with index 1*/
for(current_index = 0U; current_index < N; current_index++)
{
left_hand_side_sum += A[current_index];
}
/* Find the minimum difference value */
for(current_index = 0U; current_index < N - 1; current_index++)
{
right_hand_side_sum += A[current_index];
left_hand_side_sum -= A[current_index];
tmp_solution = (unsigned int)(abs(left_hand_side_sum - right_hand_side_sum));
if((tmp_solution < solution))
{
solution = tmp_solution;
}
else
{
/* MISRA standard */
}
if(solution == 0)
{
return 0;
}
else
{
/* MISRA standard */
}
}
return solution;
}
// you can write to stdout for debugging purposes, e.g.
// printf("this is a debug message\n");
int solution(int A[], int N) {
// write your code in C99
unsigned char current_index;
unsigned int solution = 65535;
unsigned int tmp_solution = 0;
unsigned int right_hand_side_sum = 0;
unsigned int left_hand_side_sum = 0;
if(N == 1)
{
return A[0];
}
else if(N == 2)
{
return abs(A[0] - A[1]);
}
/* Calculating sum of left hand side elements start with index 1*/
for(current_index = 0U; current_index < N; current_index++)
{
left_hand_side_sum += A[current_index];
}
/* Find the minimum difference value */
for(current_index = 0U; current_index < N - 1; current_index++)
{
right_hand_side_sum += A[current_index];
left_hand_side_sum -= A[current_index];
tmp_solution = (unsigned int)(abs(left_hand_side_sum - right_hand_side_sum));
if((tmp_solution < solution))
{
solution = tmp_solution;
}
else
{
/* MISRA standard */
}
if(solution == 0)
{
return 0;
}
else
{
/* MISRA standard */
}
}
return solution;
}
// you can write to stdout for debugging purposes, e.g.
// printf("this is a debug message\n");
int solution(int A[], int N) {
// write your code in C99
unsigned char current_index;
unsigned int solution = 65535;
unsigned int tmp_solution = 0;
unsigned int right_hand_side_sum = 0;
unsigned int left_hand_side_sum = 0;
if(N == 1)
{
return A[0];
}
else if(N == 2)
{
return abs(A[0] - A[1]);
}
/* Calculating sum of left hand side elements start with index 1*/
for(current_index = 0U; current_index < N; current_index++)
{
left_hand_side_sum += A[current_index];
}
/* Find the minimum difference value */
for(current_index = 0U; current_index < N - 1; current_index++)
{
right_hand_side_sum += A[current_index];
left_hand_side_sum -= A[current_index];
tmp_solution = (unsigned int)(abs(left_hand_side_sum - right_hand_side_sum));
if((tmp_solution < solution))
{
solution = tmp_solution;
}
else
{
/* MISRA standard */
}
if(solution == 0)
{
return 0;
}
else
{
/* MISRA standard */
}
}
return solution;
}
The following issues have been detected: timeout errors.
range sequence, length = ~1,000
running time: >11.00 sec., time limit: 8.00 sec.
random medium, numbers from 0 to 100, length = ~10,000
running time: >6.00 sec., time limit: 0.10 sec.
random medium, numbers from -1,000 to 50, length = ~10,000
running time: >6.00 sec., time limit: 0.10 sec.
large sequence, numbers from -1 to 1, length = ~100,000
running time: >6.00 sec., time limit: 0.10 sec.
random large, length = ~100,000
running time: >6.00 sec., time limit: 0.10 sec.
large sequence, length = ~100,000
running time: >6.00 sec., time limit: 0.10 sec.
large test with maximal and minimal values, length = ~100,000
running time: >6.00 sec., time limit: 0.10 sec.