# java 2ms O(n)time, O(1)space solution without dp

• ``````// array may be consist of many separate areas of arithmetic slices
//      a1  a2  a3  a4  a5   a6  a7
// diff:  a   a   b   b    b   c   c
// an arithmetic slice cannot cross different areas
// so the question converts into find each area that has the same difference, and then do a simple math calculation for each area
public int numberOfArithmeticSlices(int[] A) {
if (A.length < 3) return 0;
int lastDiff = A[1] - A[0];
int start = 0;
int v = 0;
for (int i = 2; i < A.length; i++){
if (A[i] - A[i - 1] == lastDiff) continue;
else{
v += getNum(start, i - 1);
start = i - 1;
lastDiff = A[i] - A[i - 1];
}
}
// deal with the last area
v += getNum(start, A.length - 1);
return v;
}
private int getNum(int start, int end){
int n = end - start + 1;
//if (n < 3) return 0; not necessary in this case
//fix first 2 element, we have n - 2 choices, fix first 3 elements, we have n - 3 choices,...
//num = (n - 2) + (n - 3) + ... + 1
return (n - 1) * (n - 2) / 2;
}``````

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