动态规划

The Triangle
Time Limit: 1000MS Memory Limit: 10000K
Total Submissions: 49826 Accepted: 30089
Description
7
3   8
8   1   0
2   7   4   4
4   5   2   6   5


(Figure 1)
Figure 1 shows a number triangle. Write a program that calculates the highest sum of numbers passed on a route that starts at the top and ends somewhere on the base. Each step can go either diagonally down to the left or diagonally down to the right.
Input
Your program is to read from standard input. The first line contains one integer N: the number of rows in the triangle. The following N lines describe the data of the triangle. The number of rows in the triangle is > 1 but <= 100. The numbers in the triangle, all integers, are between 0 and 99. 
Output
Your program is to write to standard output. The highest sum is written as an integer.
Sample Input
5
7
3 8
8 1 0 
2 7 4 4
4 5 2 6 5
Sample Output
30
Source

IOI 1994

#include <bits/stdc++.h>#include<algorithm>using namespace std;#define MAX 101int D[MAX][MAX];int n;int maxSum[MAX][MAX];int MaxSum(int i,int j){if(maxSum[i][j]!=-1)return maxSum[i][j];if(i==n)   maxSum[i][j]=D[i][j];else {int x=MaxSum(i+1,j);int y=MaxSum(i+1,j+1);maxSum[i][j]=max(x,y)+D[i][j];} return maxSum[i][j];}int main(){int i,j;cin>>n;for(i=1;i<=n;i++)    for(j=1;j<=i;j++){    cin>>D[i][j];    maxSum[i][j]=-1;}cout<<MaxSum(1,1)<<endl;}