POJ-1050 To the Max
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To the Max
Time Limit: 1000MS | Memory Limit: 10000K | |
Total Submissions: 56579 | Accepted: 29921 |
Description
Given a two-dimensional array of positive and negative integers, a sub-rectangle is any contiguous sub-array of size 1*1 or greater located within the whole array. The sum of a rectangle is the sum of all the elements in that rectangle. In this problem the sub-rectangle with the largest sum is referred to as the maximal sub-rectangle.
As an example, the maximal sub-rectangle of the array:
0 -2 -7 0
9 2 -6 2
-4 1 -4 1
-1 8 0 -2
is in the lower left corner:
9 2
-4 1
-1 8
and has a sum of 15.
As an example, the maximal sub-rectangle of the array:
0 -2 -7 0
9 2 -6 2
-4 1 -4 1
-1 8 0 -2
is in the lower left corner:
9 2
-4 1
-1 8
and has a sum of 15.
Input
The
input consists of an N * N array of integers. The input begins with a
single positive integer N on a line by itself, indicating the size of
the square two-dimensional array. This is followed by N^2 integers
separated by whitespace (spaces and newlines). These are the N^2
integers of the array, presented in row-major order. That is, all
numbers in the first row, left to right, then all numbers in the second
row, left to right, etc. N may be as large as 100. The numbers in the
array will be in the range [-127,127].
Output
Output the sum of the maximal sub-rectangle.
Sample Input
4 0 -2 -7 0 9 2 -6 2 -4 1 -4 1 -1 8 0 -2
Sample Output
15
Source
OJ-ID:
poj-1050
author:
Caution_X
date of submission:
20191117
tags:
二维数组前缀和
description modelling:
计算二维数组权值和最大的子矩阵
major steps to solve it:
枚举i(i∈[1,n])到j(j∈[i+1,n])行的各列元素之和的一维数组,计算该一维数组连续区间的权值最大和并更新答案
warnings:
将二维数组化成一维数组来处理,减少时间开销
AC code:
#include <stdio.h> #define MAXSIZE 101 //求出一行中最大的子段和 int MaxArray( int n, int arr_[]) { int i, sum_ = 0, max_ = 0; for (i=1; i<=n; i++) { if (sum_>0) { sum_ += arr_[i]; } else { sum_ = arr_[i]; } if (sum_>max_) { max_ = sum_; } } return max_; } //求出最大子矩阵和。 int MaxMatrix( int n, int arr_[][MAXSIZE]) { int max_ = arr_[1][1]; int sum_; int i, j, k; int temp_arr[MAXSIZE]; for (i=1; i<=n; i++) //从第一行开始,直到第n行 { for (j=1; j<=n; j++) //只有起始行改变,temp_arr数组才初始化 { temp_arr[j] = 0; } for (j=i; j<=n; j++) //从i行到第n行 { for (k=1; k<=n; k++) { temp_arr[k] += arr_[j][k]; //temp_arr[k] 表示从第i行到第n行中第k列的总和。 } sum_ = MaxArray(n, temp_arr); //求出该行中最大的子段和 if (sum_ > max_) { max_ = sum_; } } } return max_; } int main() { int n; int i, j; int arr_[MAXSIZE][MAXSIZE]; int max_; while (~scanf("%d", &n)) //多组测试。 相当于 scanf("%d", &n) != EOF { for (i=1; i<=n; i++) { for (j=1; j<=n; j++) { scanf("%d", &arr_[i][j]); } } max_ = MaxMatrix(n, arr_); printf("%d ", max_); } return 0; }
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