[Project Euler]: Question 018

[Project Euler]: Question 018

Zhou yinhui

 

Problem description:

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

3
7 4
2 4 6
8 5 9 3

That is, 3 + 7 + 4 + 9 = 23.

Find the maximum total from top to bottom of the triangle below:

75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23

Note:As there are only 16384 routes, it is possible to solve this problem by trying every route. however, problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method!

 

 

Problem Analysis:

The data in the question seems to be a triangle, but the question requires that a vertex start along its adjacent two points and go down one line, and the two adjacent points in the next line form a binary tree.If a [I, j] indicates the number of J numbers in row I, the adjacent two vertices of a [I, j] are a [I + 1, j] And a [I + 1, J + 1], that is, its left and right subtree.It is easy to change to a binary tree. if best [a] is set, it indicates the calculation result starting from vertex A and meeting the question requirements. The value of node A in the array is (), the left and right subtree of node A are B and C, respectively,So best [a] = (A) + max (best [B], best [c]), huh, recursive

(ReferCodeThe buffer in is a buffer set to avoid repeated recursive operations ) # Include <stdio. h>

# Define SZ 15 # Define end (SZ-1)
Int data [SZ] [SZ] = { {75 }, {95, 64 }, {17, 47, 82 }, {18, 35, 87, 10 }, {20, 4, 82, 47, 65 }, {19, 1, 23, 75, 3, 34 }, {88, 2, 77, 73, 7, 63, 67 }, {99, 65, 4, 28, 6, 16, 70, 92 }, {41, 41, 26, 56, 83, 40, 80, 70, 33 }, {41, 48, 72, 33, 47, 32, 37, 16, 94, 29 }, {53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14 }, {70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57 }, {91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48 }, {63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31 }, {4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23} };
Int buffer [SZ] [SZ];
Int test (int I, Int J) { If (j> I) // J> I is the area in the above array that does not explicitly indicate the number. { Return 0; }
Int sum, sumleft = 0, sumright = 0, Ni, NJ; // Ni: Next I Int currentnode; Currentnode = data [I] [J];
If (I = end) { Return currentnode; }
Ni = I + 1; Nj = J + 1;
If (Ni <sz) { If (buffer [Ni] [J]! = 0) { Sumleft = buffer [Ni] [J]; } Else { Sumleft = test (Ni, J ); Buffer [Ni] [J] = sumleft; } }
If (NJ <sz) { If (buffer [Ni] [NJ]! = 0) { Sumright = buffer [Ni] [NJ]; } Else { Sumright = test (Ni, NJ ); Buffer [Ni] [NJ] = sumright; } }
Sum = currentnode + (sumleft> sumright? Sumleft: sumright ); Buffer [I] [J] = sum;
Return sum; }
Int main () { Printf ("result is % d \ n", test (0, 0 )); Return 0;

} 

 

Speed is good (Intel dual-core 2.4g ):

Real 0m0. 004 s User 0m0. 001 S

Sys 0m0. 003 s