POJ--1163 The Triangle(DP)

记录
10:43 2023-5-15

http://poj.org/problem?id=1163

reference:《挑战程序设计竞赛(第2版)》第二章练习题索引 p135

Description

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

30

一鱼俩吃(和之前3176一样 0ms就是用的改进后的方法(dp数组再利用))

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<queue>
using namespace std;
#define MAX_N 100
typedef long long ll;
typedef unsigned int uint;
const int INF = 0x3f3f3f3f;

int dp[MAX_N + 1];  //定义dp[i] = 到这个点的时候得到的最大的值
int N;
// dp[i] = max(dp[i-1], dp[i]) + a; a表示此时读入的值

int main() {
    scanf("%d", &N);
    int a = 0;
    int result = -INF;
    for(int i = 1; i <= N; i++) {
        for(int j = i; j >= 1; j--) {
            scanf("%d", &a);
            dp[j] = max(dp[j-1], dp[j]) + a;
            result = max(result, dp[j]);
        }
    }
    printf("%d\n", result);
}