模拟退火

其实这玩意很好理解,首先看:讲解

做题,luogu 1337,讲解

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#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <cmath>
using namespace std;
const double eps = 1e-14;
const double bei = 0.99;
int n, x[1005], y[1005], w[1005];
double best, bx, by; // 全局最优结果
double calc(double xx, double yy) {
double ret = 0.0;
for (int i = 1; i <= n; i++) {
ret += sqrt((xx-x[i])*(xx-x[i])+(yy-y[i])*(yy-y[i])) * w[i];
}
return ret;
}
int main() {
srand(time(NULL));
cin>>n;
for (int i = 1; i <= n; i++) {
scanf("%d %d %d", &x[i], &y[i], &w[i]);
bx += x[i];
by += y[i];
}
bx /= n;
by /= n;
best = calc(bx, by);
int Times = 5; // 退火五次,每次从全局最优开始退火
while (Times--) {
double ans = best, xx = bx, yy = by;
for (double T = 100000.0; T > eps; T *= bei) {
double dx = xx + (double)T * (2.0 * rand() - RAND_MAX); // 要有正负,但是这个改变量就是玄学
double dy = yy + (double)T * (2.0 * rand() - RAND_MAX);
double ret = calc(dx, dy);
if (best > ret) {
best = ret;
bx = dx;
by = dy;
}
if (ans > ret || (1.0 * rand() / RAND_MAX <= exp((ans-ret)/T))) {
ans = ret;
xx = dx;
yy = dy;
}
}
}
printf("%.3f %.3f\n", bx, by);
return 0;
}

LOJ [BalticOI 2012 Day2]俄罗斯方块

(luogu 的不好使)

模拟退火能调出来五十分的

solver:

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#include "solver.h"
#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
int n, uu;
bool block[15][5][5];
bool board[15][15], tmpb[15][15]; // col 1-9, row 1-9
/*
row
4 0 0 0
3 1 1 0
2 1 0 0
1 0 0 0
1 2 3 col first
col 1, row 2 is always the note block
*/
char fileName[1005];
double zxxd[15]={0, 0.5, 1.0, 0.5, 1.5, 0.5, 1.0, 1.0, 1.0, 0.0}; // 重心相对 note 块 底边的高度
int height[15]={0, 1, 2, 1, 3, 1, 2, 2, 2, 1};// 最高边相对note块底边的高度
// tmp
int canSet(bool tmp[15][15], int col, int bt) { // 可以的话就返回 row
int ret = 0;
for (int row = 10-height[bt]; row >= 1 ; row--) {
// note 希望在 col 列 row 行
bool flag = true;
for (int i = 1; i <= 3; i++)
for (int j = 1; j <= 4; j++)
if (block[bt][i][j]) {
int ri = col + i - 1;
int rj = row + j - 2;
if (!(ri >= 1 && ri <= 9 && rj >= 1 && rj <= 9 && !tmp[ri][rj])) {
flag = false;
}
}
if (flag) ret = row;
else break;
}
return ret;
}

// tmp
void setNotClear(bool tmp[15][15], int col, int row, int bt) {
for (int i = 1; i <= 3; i++)
for (int j = 1; j <= 4; j++)
if (block[bt][i][j])
tmp[col+i-1][row+j-2] = true;
}

// tmp
bool canClear(bool tmp[15][15], int row) {
for (int i = 1; i <= 9; i++)
if (!tmp[i][row])
return false;
return true;
}

// tmp
void clearRow(bool tmp[15][15], int row) {
for (int i = row; i <= 9; i++)
for (int j = 1; j <= 9; j++)
tmp[j][i] = tmp[j][i+1];
}

int colDiffInRow(int row) {
int ret = 0;
for (int i = 2; i <= 9; i++)
if (tmpb[i-1][row] != tmpb[i][row])
ret++;
return ret;
}

int rowDiffInCol(int col) {
int ret = 0;
for (int i = 2; i <= 9; i++)
if (tmpb[col][i-1] != tmpb[col][i])
ret++;
return ret;
}

int getJiao(int bt, int row) {
int ret = 0;
if (row <= 4 && row >= 1)
for (int i = 1; i <= 3; i++)
ret += block[bt][i][row];
return ret;
}

// tmpb
int getHoles() {
int ret = 0;
for (int i = 1; i <= 9; i++) {
bool flag = false;
for (int j = 9; j >= 1; j--) {
flag |= tmpb[i][j];
if (!tmpb[i][j] && flag) ret++;
}
}
return ret;
}

//tmpb
int getWells() {
int ret = 0;
for (int i = 1; i <= 9; i++) {
int jing = 0;
for (int j = 1; j <= 9; j++)
if (tmpb[i][j])
jing = 0;
else {
if ((i==1 && tmpb[2][j]) || (i==9 && tmpb[8][j]) || (i >= 2 && i <= 8 && tmpb[i-1][j] && tmpb[i+1][j])) {
jing++;
ret += jing;
} else {
jing = 0;
}
}
}
//printf("jing %d\n", ret);
return ret;
}

//double chang[6] = {-4.500158825082766,3.4181268101392694, -3.2178882868487753,-9.348695305445199,-7.899265427351652,-3.3855972247263626};
double chang[6]={
-108.1552516822,
93.4515835788,
-33.8268913751,
-36.4696344915,
-165.6161517320,
-34.6613258266
};

double getScore(int col, int row, int bt) { // note 在 col 列 row 行
double landingHeight = row + zxxd[bt];
double rowsEliminated = 0.0;
double rowTransitions = 0.0;
double colTransitions = 0.0;
setNotClear(tmpb, col, row, bt);
int jiao = 0;
for (int i = 1, trueI=1; i <= 9; i++, trueI++)
if (canClear(tmpb, i)) {
rowsEliminated += 1.0;
clearRow(tmpb, i);
i--;
jiao += getJiao(bt, trueI-row+2);
}
if (jiao == 0 && rowsEliminated > 0.1) {
printf("impossible!\n");
}
rowsEliminated *= jiao;
for (int i = 1; i <= 9; i++) {
rowTransitions += colDiffInRow(i);
colTransitions += rowDiffInCol(i);
}
double holeNums = getHoles();
double wells = getWells();
//printf("col %d:\n%.3f\n%.3f\n%.3f\n%.3f\n%.3f\n%.3f\n\n", col, landingHeight, rowsEliminated, rowTransitions, colTransitions, holeNums, wells);
return chang[0] * landingHeight
+ chang[1] * rowsEliminated
+ chang[2] * rowTransitions
+ chang[3] * colTransitions // fixme: 这个行列变化错了!
+ chang[4] * holeNums
+ chang[5] * wells;
}

int setter(int bt) {
int idx = -1, row;
double sco = 0.0, score = 0.0;

for (int i = 1; i <= 9; i++) {
memcpy(tmpb, board, sizeof(board));
row = canSet(tmpb, i, bt);
//printf("col %d, row %d\n", i, row);
if (row) {
score = getScore(i, row, bt);
if (idx == -1 || score > sco) {
sco = score;
idx = i;
}
}
}
return idx;
}

void setBlock(int col, int bt) {
int row = canSet(board, col, bt);
//printf("block %d to %d col, %d row\n", bt, col, row);
setNotClear(board, col, row, bt);
for (int i = 1, trueI=1; i <= 9; i++, trueI++)
if (canClear(board, i)) {
clearRow(board, i);
i--;
}
}

double solve(int number) {
sprintf(fileName, "tiny%d.in", number);
FILE *inFp = fopen(fileName, "r");
sprintf(fileName, "tiny.o%d", number);
FILE *outFp = fopen(fileName, "w");
memset(board, false, sizeof(board));

int solved = 0, ret;
fscanf(inFp, "%d", &n);
//printf("#%d has %d blocks\n", number, n);

for (int i = 1; i <= n; i++) {
fscanf(inFp, "%d", &uu);
ret = setter(uu);

/*printf("\n");
for (int row = 4; row >= 1; row--) {
for (int col = 1; col <= 3; col++) {
putchar(block[uu][col][row] ? '#' : ' ');
}
printf("\n");
}
printf("\n");
for (int row = 9; row >= 1; row--) {
for (int col = 1; col <= 9; col++) {
putchar(board[col][row] ? '#' : '_');
putchar(' ');
}
printf("\n");
}
getchar();*/
if (ret == -1) {
break;
} else {
setBlock(ret, uu);
solved++;
fprintf(outFp, "%d\n", ret);
}
}

//printf("#%d: solved %d out of %d, rate %.2f\n", number, solved, n, 1.0 * solved / n);
fclose(inFp);
fclose(outFp);
return 1.0*solved/n;
}
double mnthjk(double cchang[]) {
for (int i = 0; i < 6; i++)
chang[i] = cchang[i];
FILE *blockFp = fopen("blocks.txt", "r");
for (int i = 1; i <= 9; i++)
for (int row = 4; row >= 1; row--)
for (int col = 1; col <= 3; col++) {
fscanf(blockFp, "%d", &uu);
block[i][col][row] = uu > 0;
}
double ret = 0.0;
for (int i = 1; i <= 5; i++) ret +=solve(i);
fclose(blockFp);
return ret;
}

int main() {
FILE *blockFp = fopen("blocks.txt", "r");
for (int i = 1; i <= 9; i++)
for (int row = 4; row >= 1; row--)
for (int col = 1; col <= 3; col++) {
fscanf(blockFp, "%d", &uu);
block[i][col][row] = uu > 0;
}
for (int i = 1; i <= 5; i++) solve(i);
fclose(blockFp);
return 0;
}

mnth

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#include "solver.h"
const double eps = 1e-5;
const double bei = 0.97;
extern double mnthjk(double ccss[]);
double css[6] = {
-108.1552516822,
93.4515835788,
-33.8268913751,
-36.4696344915,
-165.6161517320,
-34.6613258266
};

double bcss[6], ecss[6], fcss[6];

int main() {
srand(time(NULL));

for (int i = 0; i < 6; i++)
bcss[i] = css[i];
double best = mnthjk(bcss);
FILE *fp = fopen("best_para.txt", "w");
fprintf(fp, "bret %.3f\n", best);
for (int i = 0; i < 6; i++)
fprintf(fp, "%.10f\n", bcss[i]);
fclose(fp);
int Times = 5; // 退火五次,每次从全局最优开始退火
while (Times--) {
double ans = best;
for (int i = 0; i < 6; i++) {
ecss[i] = bcss[i];
}
int cnt = 0;
for (double T = 100000.0; T > eps; T *= bei) {
for (int i = 0; i < 6; i++) {
fcss[i] = ecss[i] + (double)T * (2.0 * rand() - RAND_MAX)/RAND_MAX/ 5000.0;
}
double ret = mnthjk(fcss);
cnt++;
printf("cnt %d, T %.3f\n ret %.3f, best %.3f\n\n", cnt, T ,ret,best);
if (best < ret) {
best = ret;
for (int i = 0; i < 6; i++)
bcss[i] = fcss[i];
FILE *fp = fopen("best_para.txt", "w");
fprintf(fp, "bret %.3f\n", best);
for (int i = 0; i < 6; i++)
fprintf(fp, "%.10f\n", bcss[i]);
fclose(fp);
}
if (ans < ret || (1.0 * rand() / RAND_MAX <= exp((ret-ans)/T))) {
ans = ret;
for (int i = 0; i < 6; i++)
ecss[i] = fcss[i];
}
}
printf("bret %.3f\n", best);
for (int i = 0; i < 6; i++)
printf("%.10f\n", bcss[i]);
}

return 0;
}
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