This is to find the smallest area matrix in a matrix, so that its sum is greater than a given K. Because it is to find the optimal solution, it is natural to think of binary search for this value, however, on the premise that the problem does not meet the requirements of binary search, I chose binary search in a hurry, leading to errors. The reason is that when an area is an optimal solution, the Child matrix with an area greater than the optimal solution does not necessarily contain this optimal matrix, for example, a 5*5 matrix, if the optimal matrix is a 2*2 matrix, then the matrix formula with the area of 1*5 is 5 and does not contain the 2*2 matrix, So ......
The Code is as follows:
# Include <cstdlib> # include <cstdio> # include <cstring> # include <algorithm> # define maxn 105 using namespace STD; int n, m, K, G [maxn] [maxn], s [maxn * maxn], Lim; int rec [maxn * maxn], idx, sum [maxn] [maxn]; struct node {int X, Y;} que [maxn]; int front, tail; inline void pre () {int K; Lim = N * m; memset (S, 0, sizeof (s); idx =-1; // getstatus for (INT I = 1; I <= N; ++ I) {k = min (m, lim/I); // select a relatively small value to exclude illegal conditions For (Int J = 1; j <= K; ++ J) {s [I * j] = 1 ;}} for (INT I = 1; I <= lim; ++ I) {If (s [I]) {rec [++ idx] = I ;}// getsum for (INT I = 1; I <= N; ++ I) {for (Int J = 1; j <= m; ++ J) {sum [I] [J] = sum [I-1] [J] + sum [I] [J-1]-sum [I-1] [J-1] + G [I] [J] ;}}} bool judge () {int XX, YY, ZZ, lx, Ly; For (int K = 1; k <= tail; ++ K) {Lx = N-que [K]. X + 1, Ly = m-que [K]. Y + 1; for (INT I = 1; I <= Lx; ++ I) {For (Int J = 1; j <= ly; ++ J) {xx = I + que [K]. x-1, YY = J + que [K]. y-1; If (XX <= N & YY <= m) {ZZ = sum [XX] [YY]-sum [I-1] [YY]-sum [XX] [J-1] + sum [I-1] [J-1]; if (zz> = k) return true ;}}} return false;} bool AC (int x) // ensure that all x values are valid {front = tail = 0; For (INT I = 1; I <= N; ++ I) {If (X % I = 0) {++ tail; que [tail]. X = I, que [tail]. y = x/I ;}/// decomposition of the current area at the processing. If (Judge () {return True;} return false;} int bsearch (int l, int R) {int mid, ret =-1; while (L <= r) {mid = (L + r)> 1; if (AC (REC [Mid]) {ret = rec [Mid]; r = mid-1 ;} else {L = Mid + 1 ;}} return ret ;}int force () {for (INT I = 0; I <= idx; ++ I) {If (AC (REC [I]) {return rec [I] ;}} return-1 ;}int main () {While (scanf ("% d", & N, & M, & K )! = EOF) {for (INT I = 1; I <= N; ++ I) {for (Int J = 1; j <= m; ++ J) {scanf ("% d", & G [I] [J]) ;}} pre (); // printf ("% d \ n", bsearch (0, idx); printf ("% d \ n", force ();} return 0 ;}