The biggest reason for learning is to get rid of mediocrity. One day earlier, there will be more splendor in life; one day later, one day more mediocrity.
study diary
1. What is a prefix and
The prefix sum is the sum of all array elements before (including) an item subscript of an array .
Let b[] be the prefix sum array, and a[] be the original array. According to this sentence, the definition and recursion formula of the prefix sum can be obtained:
Definition Recursive One-dimensional prefix sum two-dimensional prefix and
Two, one-dimensional prefix and
According to the above definition, we can easily get sum[i] = sum[i-1] + a[i]
In this way, the sum of the first i numbers can be obtained. According to the above expression, we can find the interval sum of the interval [i, j] with O(1)
It is generally used to find the sum of elements in the interval [L, R]:
ans[1]=ans[0]+q[1]
ans[2]=ans[1]+q[2]
……… ………
ans[i]=ans[i-1]+q[i]
The sum of elements between [L,R] tmp=ans[R]-ans[L-1]
3. Two-dimensional prefixes and exercises
Original array q[ ][ ]
0
1
2
3
4
5
6
7
8
9
1
1
2
1
0
-1
0
2
0
0
2
1
0
0
1
2
1
1
0
0
3
2
1
1
3
1
-1
0
0
0
4
1
1
-1
0
-1
1
1
0
0
5
1
1
2
1
3
1
4
0
0
6
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
prefix and array ans[ ][ ]
0
1
2
3
4
5
6
7
8
1
1
3
4
4
3
2
2
4
5
6
7
3
4
7
9
13
15
4
5
(i-1,j)
5
6
(i,j-1)
(i , j)
6
7
求ans[ ][ ] ans[I,j]=ans[i-1,j]+ans[I,j-1]-ans[i-1][j-1]+q[i][j]:
0
1
2
3
4
5
6
7
8
1
2
(x1-1,y1-1)
(x1-1,y2)
3
(x1,y1)
4
5
(x2,y1-1)
(x2,y2)
6
7
Find the sum of the elements in the specified rectangle:
Upper left (x1,y1) Lower right (x2,y2)
tmp=years[x2][y2]-years[x2][y1-1]-years[x1-1][y2]+years[x1-1][y1-1]