POJ-1163 The Triangle（简单dp）

最新推荐文章于 2020-05-03 16:51:48 发布

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本文介绍了一种解决三角形网格中寻找从顶点到底边的最大路径和问题的算法。通过动态规划方法，从底部向上更新每个节点的值，使得每个节点的值变为经过该节点到达底边的所有路径中的最大路径和。

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Description

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.
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

5
7
3 8
8 1 0
2 7 4 4
4 5 2 6 5
Sample Output

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<ctime>
#include<iostream>
#include<algorithm>
#include<map>
#include<stack>
#include<queue>
#include<vector>
#include<set>
#include<string>
#define ll long long
#define dd double
using namespace std;

int main() {
	ios::sync_with_stdio(false);
	ll n;
	cin >> n;
	ll arr[105][105];
	memset(arr, -1, sizeof(arr));
	for (ll i = 0; i < n; i++) {
		for (ll j = 0; j <= i; j++) {
			cin >> arr[i][j];
		}
	}
	for (ll i = n - 2; i >= 0; i--) {
		for (ll j = 0; j <= i; j++) {
			arr[i][j] = max(arr[i][j] + arr[i + 1][j], arr[i][j] + arr[i + 1][j + 1]);
		}
	}
	cout << arr[0][0] << endl;
}