POJ 1163 The Triangle（DP 数塔问题）

The Triangle

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 45125 Accepted: 27270

Description

73   88   1   02   7   4   44   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

573 88 1 0 2 7 4 44 5 2 6 5

Sample Output

30

Source

IOI 1994

很经典的DP问题，数塔问题，从下往上进行动态规划。

下面是AC代码：

#include<cstdio>#include<cstring>#include<algorithm>using namespace std;int a[105][105];int dp[105][105];int main(){    int n;    while(~scanf("%d",&n))    {        for(int i=0; i<n; i++)        {             for(int j=0;j<=i;j++)             {                 scanf("%d",&a[i][j]);             }        }        for(int i=n-1;i>=0;i--)        {            dp[n-1][i]=a[n-1][i];        }        for(int i=n-2;i>=0;i--)        {            for(int j=0;j<=i;j++)            dp[i][j]=a[i][j]+max(dp[i+1][j],dp[i+1][j+1]);        }        printf("%d\n",dp[0][0]);    }    return 0;}