动态规划基础题目之数字三角形
时间: 1ms 内存:64M
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.
示例输入:
5
7
3 8
8 1 0
2 7 4 4
4 5 2 6 5
示例输出:
30
提示:
参考答案(内存最优[1092]):
#include<stdio.h>
#include<malloc.h>
int main()
{
int n,a[100][100],i,j;
scanf("%d",&n);
for(i=0; i<n; ++i)
{
for(j=0; j<=i; ++j)
{
scanf("%d",&a[i][j]);
}
}
for(i=n-1; i>1; --i)
{
for(j=0; j<i; ++j)
{
a[i-1][j]+=(a[i][j]>a[i][j+1])?a[i][j]:a[i][j+1];
}
}
printf("%d",(a[0][0]+((a[1][0]>a[1][1])?a[1][0]:a[1][1])));
return 0;
}
参考答案(时间最优[0]):
#include <iostream>
#include <algorithm>
using namespace std;
#define MAX 101
int D[MAX][MAX];
int n;
int maxSum[MAX][MAX];
int main()
{
int i,j;
cin >> n;
for(i=1; i<=n; i++) for(j=1; j<=i; j++) cin >> D[i][j];
for( int i = 1; i <= n; ++ i )
maxSum[n][i] = D[n][i];
for( int i = n-1; i>= 1; --i )
for( int j = 1; j <= i; ++j )
maxSum[i][j] = max(maxSum[i+1][j],maxSum[i+1][j+1]) + D[i][j] ;
cout << maxSum[1][1] << endl;
}
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