POJ 1163 The Triangle

標籤：acm   algorithm   dp   poj   動態規劃   

來源:http://poj.org/problem?id=1163

The Triangle

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 37660		Accepted: 22611

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

題意:  找一條從頂節點到底部的路徑，使該路徑上點之和最大，求最大值。

題解: 動態規劃解決之

AC代碼:

#include<cstdio>#include<cstring>const int Max=105;int max[Max][Max],sum[Max][Max],n;int DP(int i,int j){if(~sum[i][j])return sum[i][j];if(i==n-1)sum[i][j]=max[i][j];else sum[i][j]=max[i][j]+(DP(i+1,j)>DP(i+1,j+1) ? DP(i+1,j):DP(i+1,j+1));return sum[i][j];}int main(){memset(sum,-1,sizeof(sum));scanf("%d",&n);for(int i=0;i<n;i++)for(int j=0;j<=i;j++)scanf("%d",&max[i][j]);printf("%d\n",DP(0,0));return 0;}