<>4.18 Personal summary of Lanqiao provincial competition
<> Completion
<>A. space
Xiaolan is ready to use 256MB Open an array in the memory space of , Every element of the array is 32 Bit binary integer , If the space occupied by the program and the auxiliary space required to maintain memory are not considered , Excuse me? 256MB
How many can you store in your space 32 Bit binary integer ?
Memory computing , I'm sorry for the wrong calculation, the teacher of computer composition principle .
Direct written calculation ：256MB = 28MB = 28 * 220 *8 position = 228 * 8 position
32 position = 4 * 8 position = 22 * 8 position
ans=（228 * 8 position ）/ （22 * 8 position ）=226 = 67108864
<>B card
Xiaolan has many digital cards , There are numbers on every card 0 reach 9.
Xiao Lan is going to spell some numbers with these cards , He wants to start from 1 Start spelling positive integers , Each spell one , Just keep it , Cards can't be used to spell other numbers .
Xiaolan wants to know what she can do from 1 How much do you spell .
for example , When Xiaolan has 30 Card , among 0 reach 9 various 3 Zhang , Then little blue can spell 1 reach 10, But spell 11 Time card 1 There's only one , Not enough spelling 11.
Now Xiaolan has it in her hand 0 reach 9 Each card 2021 Zhang , common 20210 Zhang , Can Xiaolan go from 1 How much do you spell ?
Tips ： It is recommended to use computer programming to solve the problem .
Excel The search mechanism and replacement mechanism are different ...
Find is the number of cells , Replacement is the number of actual contents
I believe in myself too much Excel You can't be wrong , In fact, it should be programmed directly . such as ： I have to 4640, Found 2021 individual 1,2021 individual 2,2021 individual 3, Less than 2021 Other numbers , But actually 100 There are in this cell 2 individual 0, But there is only one cell , therefore Excel The correct usage is direct substitution , take 1 replace with ! The result is 2434 Replaced at , So the answer is wrong , The correct result is 3181.
<>C. straight line
In plane rectangular coordinate system , Two points can determine a straight line . If there are many points in a straight line , Then the straight line determined by any two of these points is the same .
On a given plane 2 × 3 A whole point {(x, y)|0 ≤ x < 2, 0 ≤ y < 3, x ∈ Z, y ∈ Z}, Abscissa yes 0 reach 1 ( contain 0
and 1) Integer between , The ordinate is 0 reach 2 ( contain 0 and 2) Integer between Point of . These points have been determined 11 Different lines .
On a given plane 20 × 21 A whole point {(x, y)|0 ≤ x < 20, 0 ≤ y < 21, x ∈ Z, y ∈ Z}, Namely horizontal The coordinates are 0 reach 19
( contain 0 and 19) Integer between , The ordinate is 0 reach 20 ( contain 0 and 20) of Point of integer between . How many different straight lines are determined by these points .
<>D. Cargo placement
Xiaolan has a huge warehouse , Can put a lot of goods .
Now? , Xiao Lanyou n Boxes of goods shall be placed in the warehouse , Each box of goods is a regular cube . Blue The length is specified , wide , Three directions perpendicular to each other , The sides of each case must be strictly parallel to the length , wide , high .
Xiaolan hopes that all the goods will eventually be placed into a big cube . That is, in the long , wide , High direction Separate heap L,W,H Goods , satisfy n = L × W × H.
given n, How many schemes for stacking goods meet the requirements . for example , When n = 4 Time , Have the following 6 Kinds of schemes ：1×1×4,1×2×2,1×4×1,2×1×2, 2 × 2
× 1,4 × 1 × 1.
Excuse me? , When n = 2021041820210418 （ Attention there 16 Digit number ） Time , How many options are there altogether ?
The idea of the examination room is to decompose the quality factor ,O(N3) Violence must not come to an end .
<>E. route
Xiaolan is very happy after learning the shortest path , He defined a special graph , Hope to find the map Shortest path in .
Little blue's picture is by 2021 Composed of nodes , Serial number 1 to 2021.
For two different nodes a, b, If a and b The absolute value of the difference is greater than 21, Then there are two nodes There is no edge connection between them ; If a and b The absolute value of the difference is less than or equal to
21, Then there is a line between the two points Count Reg a and b The undirected edge of the least common multiple of .
for example ： node 1 And node 23 There is no edge connection between them ; node 3 And node 24 There is a none between To the side , Count Reg 24; node 15 And node 25 There is an undirected edge between , Count Reg
75.
Please calculate , node 1 And node 2021 What is the shortest path length between .
<> Programming problem
1.1s=1000ms, open long long
2. The idea of the examination room is to pile up , For each weight , You can choose the pile of the left balance or the pile of the right balance , Or not .
3. Completely forget the laws of math problems , Direct selection as long as 20% Partially divided .
4. In part sort()+cmp
5.dp
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