【题解】【数组】【Prefix Sums】【Codility】Passing Cars

A non-empty zero-indexed array A consisting of N integers is given. The consecutive elements of array A represent consecutive cars on a road.

Array A contains only 0s and/or 1s:

  • 0 represents a car traveling east,
  • 1 represents a car traveling west.

The goal is to count passing cars. We say that a pair of cars (P, Q), where 0 ≤ P < Q < N, is passing when P is traveling to the east and Q is traveling to the west.

For example, consider array A such that:

 A[0] = 0 A[1] = 1 A[2] = 0 A[3] = 1 A[4] = 1

We have five pairs of passing cars: (0, 1), (0, 3), (0, 4), (2, 3), (2, 4).

Write a function:

int solution(vector<int> &A);

that, given a non-empty zero-indexed array A of N integers, returns the number of passing cars.

The function should return −1 if the number of passing cars exceeds 1,000,000,000.

For example, given:

 A[0] = 0 A[1] = 1 A[2] = 0 A[3] = 1 A[4] = 1

the function should return 5, as explained above.

Assume that:

  • N is an integer within the range [1..100,000];
  • each element of array A is an integer within the range [0..1].

Complexity:

  • expected worst-case time complexity is O(N);
  • expected worst-case space complexity is O(1), beyond input storage (not counting the storage required for input arguments).

Elements of input arrays can be modified.

思路:

这题用Prefix Sums做非常简单,不过题目要求“return −1 if the number of passing cars exceeds 1,000,000,000.”这点我忘了处理,所以大数据没过得了66分,各位看官自行脑补一下。

代码:

 int solution(vector<int> &A) {
int res = ;
int n = A.size();
int last = ;
for(int i = n-; i >= ; i--){
if(A[i] == ) continue;
A[i] += last;
last = A[i];
}
last = ;
for(int i = n-; i >= ; i--){
if(A[i] == )
res += last;
if(A[i] != )
last = A[i];
}
return res;
}
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