Project Euler Problem 18 Maximum path sum I
2017-03-22 22:54
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Maximum path sum I
Problem 18
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! ;o)
C++:
参考链接:Project Euler Problem 67 Maximum path sum II
Problem 18
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! ;o)
C++:
#include <iostream> #include <cstring> #include <cstdlib> using namespace std; const int MAXN = 15; int grid[MAXN][MAXN]; int max; inline int mymax(int left, int right) { return left > right ? left : right; } int setmax(int n) { for(int i=1; i<n; i++) for(int j=0; j<=i; j++) if(j == 0) grid[i][j] += grid[i-1][j]; else grid[i][j] = mymax(grid[i][j] + grid[i-1][j-1], grid[i][j] + grid[i-1][j]); int max = 0; for(int i=n-1, j=0; j<n; j++) if(grid[i][j] > max) max = grid[i][j]; return max; } int main() { int n; while(cin >> n && n<=MAXN) { memset(grid, 0, sizeof(grid)); for(int i=0; i<n; i++) { for(int j=0; j<=i; j++) cin >> grid[i][j]; } int max = setmax(n); cout << max << endl; } return 0; }
参考链接:Project Euler Problem 67 Maximum path sum II
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