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poj 1081 To The Max
To The Max
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 12697 Accepted Submission(s):
6090
Problem Description
Given a two-dimensional array of positive and negative
integers, a sub-rectangle is any contiguous sub-array of size 1 x 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 x 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
题意:二维的矩阵,从中找到一个子矩阵,使得子矩阵的和最大。
思路:可以先考虑一维的情况,一维时即数列,求数列中连续子列的和的最大值,做法就是在线处理,从头到尾一个一个元素考虑并累加过去,记当前累加值为sum,若累加的时候当前sum值小于0了,那么舍弃前面的累加列,sum更新为0,并且从下一个位置
的元素重新开始累加,途中不断的更新sum,找出最大的sum值即可,二维的情况可以看作一维的延伸情况,如果把列固定住(即选取矩阵连续的几列并固定,先算好每一行的这几列的和值),此时纵向的从上到下累加就可以看成是一维情况下的累加,算法类同。
AC代码:
#define _CRT_SECURE_NO_DEPRECATE #include<iostream> #include<algorithm> #include<string> #include<set> #include<map> #include<vector> #include<queue> #include<functional> using namespace std; const int N_MAX= 100+2; int a[N_MAX][N_MAX]; int sum[N_MAX][N_MAX]; int main() { int n; while (scanf("%d", &n) != EOF) { memset(sum,0,sizeof(sum)); memset(a, 0,sizeof(a)); for (int i = 0; i < n; i++) { for (int j = 1; j <= n; j++) { scanf("%d", &a[i][j]); } } for (int i = 0; i < n; i++) { for (int j = 1; j <= n; j++) { sum[i][j] =sum[i][j-1]+ a[i][j]; } } int res = -INT_MAX; for (int i = 0; i < n; i++) {//固定i,j for (int j = i+1; j <= n; j++) { int S = 0; for (int k = 0; k < n; k++) { S += sum[k][j]-sum[k][i-1];//累加上闭区间[i,j]值的和 if (S > res) res = S; if (S < 0)S = 0; } } } printf("%d\n",res); } return 0; }
思路
poj 1081 To The Max
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