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HDU - 2084 数塔 (dp)

题意:在讲述DP算法的时候,一个经典的例子就是数塔问题,它是这样描述的: 有如下所示的数塔,要求从顶层走到底层,若每一步只能走到相邻的结点,则经过的结点的数字之和最大是多少? 

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分析:按照行走路径状态转移即可。

#include<cstdio>#include<cstring>#include<cstdlib>#include<cctype>#include<cmath>#include<iostream>#include<sstream>#include<iterator>#include<algorithm>#include<string>#include<vector>#include<set>#include<map>#include<stack>#include<deque>#include<queue>#include<list>#define lowbit(x) (x & (-x))const double eps = 1e-8;inline int dcmp(double a, double b){    if(fabs(a - b) < eps) return 0;    return a > b ? 1 : -1;}typedef long long LL;typedef unsigned long long ULL;const int INT_INF = 0x3f3f3f3f;const int INT_M_INF = 0x7f7f7f7f;const LL LL_INF = 0x3f3f3f3f3f3f3f3f;const LL LL_M_INF = 0x7f7f7f7f7f7f7f7f;const int dr[] = {0, 0, -1, 1, -1, -1, 1, 1};const int dc[] = {-1, 1, 0, 0, -1, 1, -1, 1};const int MOD = 1e9 + 7;const double pi = acos(-1.0);const int MAXN = 100 + 10;const int MAXT = 250000 + 10;using namespace std;int a[MAXN][MAXN];int dp[MAXN][MAXN];int main(){    int T;    scanf("%d", &T);    while(T--){        memset(dp, 0, sizeof dp);        int N;        scanf("%d", &N);        for(int i = 1; i <= N; ++i){            for(int j = 1; j <= i; ++j){                scanf("%d", &a[i][j]);            }        }        dp[1][1] = a[1][1];        for(int i = 2; i <= N; ++i){            for(int j = 1; j <= i; ++j){                if(j == 1){                    dp[i][j] = max(dp[i][j], dp[i - 1][j] + a[i][j]);                }                else if(j == i){                    dp[i][j] = max(dp[i][j], dp[i - 1][j - 1] + a[i][j]);                }                else{                    dp[i][j] = max(dp[i - 1][j - 1] + a[i][j], dp[i - 1][j] + a[i][j]);                }            }        }        int ans = 0;        for(int i = 1; i <= N; ++i){            ans = max(ans, dp[N][i]);        }        printf("%d\n", ans);    }    return 0;}

  

HDU - 2084 数塔 (dp)