joj2511: Number triangle

 2511: Number triangle

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Result	TIME Limit	MEMORY Limit	Run Times	AC Times	JUDGE
	1s	65536K	467	233	Standard

        5
      3   4
    8   1   2
  5   4   3   6
2   1   7   9   8

A number trangle is composed of N(N<=100) line numbers, the i-th line contains i positive integers(<=100). A chess can walk from the top line of the triangle to the bottom line. Suppose the chess is on the k-th number of one line, then it can only move to the k-th number or the (k+1)-th number of the line below in one step. Find a path from the top to the bottom, which can maximize the sum of the integers on the path.

Input

There are multiple test cases.For each test case, there's an integer N representing the size of the triangle, followed by N lines of positive intergers, the first line has 1 integer, next has two integers... the Nth line has N integers.

Output

The maximum sum of the integers on the path.

Sample Input

3
5
7 0
2 4 3
3
2
6 1
2 3 9

Sample Output

16
12

 

Problem Source: xwbsw

 

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This problem is used for contest: 120 

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水DP

倒着推即可

 

#include <stdio.h>
#include <string.h>

int a[105][105];

int main()
{
    //freopen("in.txt", "r", stdin);
    
    int n, i, j;
    
    while (scanf("%d", &n) == 1)
    {
        memset(a, 0, sizeof(a));
        for (i=1; i<=n; ++i)
        {
            for (j=1; j<=i; ++j)
            {
                scanf("%d", &a[i][j]);
            }
        }
        
        for (i=n; i>1; --i)
        {
            for (j=i; j>=1; --j)
            {
                if(a[i][j]+a[i-1][j]>a[i][j+1]+a[i-1][j])
                    a[i-1][j]=a[i][j]+a[i-1][j];
                else
                    a[i-1][j]=a[i][j+1]+a[i-1][j];
            }
        }
        printf("%d\n", a[1][1]);
    }
    
    return 0;
}