nyoj18 The Triangle(dp)
The Triangle
时间限制:1000 ms | 内存限制:65535 KB
难度:4
- 描述
-
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.
- 输入
- 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.
- 输出
- Your program is to write to standard output. The highest sum is written as an integer.
- 样例输入
-
5 7 3 8 8 1 0 2 7 4 4 4 5 2 6 5
- 样例输出
-
30
分析:dp[i][j]=max{dp[i-1][j],dp[i-1][j-1]}+a[i][j] ;从上往下更新. -
View Code
#include<iostream> #define N 105 using namespace std; int a[N][N],dp[N][N]; int main() { int n,i,j,min; while(cin>>n) { for(i=1;i<=n;i++) for(j=1;j<=i;j++) { cin>>a[i][j]; dp[i][j]=0; } dp[1][1]=a[1][1]; for(i=2;i<=n;i++) { dp[i][1]=a[i][1]+dp[i-1][1]; for(j=2;j<=i;j++) { min=dp[i-1][j-1]>dp[i-1][j]?dp[i-1][j-1]:dp[i-1][j]; dp[i][j]=a[i][j]+min; } } int ans=0; for(i=1;i<=n;i++) if(ans<dp[n][i]) ans=dp[n][i]; cout<<ans<<endl; } return 0; }