(array) prefix and prefix product and its application

What is prefix and prefix product?

The prefix and, prefix product are also called prefixes and arrays, prefixed by the plot no group.

Give an array a,

Prefix and: Create a new array B, each item in the array B[i] Save the and of [0...i] in A;

Suffix and: Create a new array B, each item in the array B[i] Save the and of [i...n-1] in A;

Prefix Product: Creates a new array B, each item in the array B[i] saves the product of a [0...i];

Suffix product: Create a new array B, each item in the array B[i] Save the product of [i...n-1] in A;

Application of prefix and prefix product (example): 1, Topic 1:

Given a floating-point group A, an array of b,b[i]=a[0]*a[1]*...*a[i-1]*a[i+1]*...*a[n-1], you cannot use division and do not allow new open arrays.

Ideas:

Ask for "suffix product" first:

for (int i=n-1;i>=0;i-) b[i]=a[i]* ((i==n-1) 1:b[i+1]);

Incidentally, "prefix product":

for (int i=0,j=1;i<n;j*=a[i++]) b[i]=j* ((i==n-1) 1:b[i+1]);

2. Topic 2:

For successive periods in an array and the absolute value of the smallest?

Ideas:

Prefix and nature of: a[i]+a[i+1]+...+a[j]=sum[j]-sum[i-1]

Prefix and sort, take minimum

3. Topic 3:

Separates an array from the middle P position so that the difference between a[0]+...+a[p-1] and a[p]+a[p+1]+...+a[n-1] is minimized?

Ideas:

• Prefix and-(sum-prefix and) =2* prefix and-sum, are the minimum of the formula;
• If all are non-negative, you can take the "two sweep" method, and the smaller one more than a number;

(array) prefix and prefix product and its application