Problem 18 Maximum path sum I （dp）

Problem 18 Maximum path sum I （dp）

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.

37 4 2 4 6 8 5 9

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)

题解：dp。dp[i][j]+=max(dp[i-1][j-1],dp[i-1][j])。搞定....

代码：

#include using namespace std;int dp[16][15];int main(){ int maxn=0; memset(dp,0,sizeof(dp)); int dp[15][15] = { {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}, }; for(int i=1;i<=15;i++) { for(int j=1;j<=i;j++) { dp[i][j]+=max(dp[i-1][j-1],dp[i-1][j]); maxn=max(maxn,dp[i][j]); } } cout<

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