commit 06f304fe22ad367d94adf49080fbfcdfb848f60b
Author: Antoine Amarilli <a3nm@a3nm.net>
Date: Mon, 18 Apr 2022 18:54:24 +0200
initial commit
Diffstat:
| README | | | 4 | ++++ |
| bruteforce.cpp | | | 373 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| common_tetris.cpp | | | 148 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| make_graph.cpp | | | 92 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| minify_graph.py | | | 45 | +++++++++++++++++++++++++++++++++++++++++++++ |
| strategy.txt | | | 5250 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| verify.cpp | | | 88 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
7 files changed, 6000 insertions(+), 0 deletions(-)
diff --git a/README b/README
@@ -0,0 +1,4 @@
+- run bruteforce.cpp to generate "solution", the trace of the winning
+ configurations
+- run make_graph.cpp on "solution" to produce the compressed graph of the strategy
+- run verify.cpp on the compressed graph (versioned as "stategy.txt") to verify correctness
diff --git a/bruteforce.cpp b/bruteforce.cpp
@@ -0,0 +1,373 @@
+/* Compute winning strategy for tetris
+ * Running this code requires around 30GB RAM and a few hours
+ * It writes to file "solution" a strategy to always make a line in the first
+ * MAXHEIGHT rows of a tetris playing field of COLS by LINES */
+
+#include<cstdio>
+#include<iostream>
+#include<unordered_set>
+#include<algorithm>
+#include<cassert>
+#include<queue>
+#include<unordered_map>
+#include "common_tetris.cpp"
+
+// bit sizes when coding configurations
+// a configuration consists of COLS integers over HEIGHTSIZE bits
+// representing the height of the playing field in that column
+// and on the most significant bits a bit vector of SACSIZE bits
+// describing which rows contains holes
+// configurations are 64-bits words so you must have
+// HEIGHTSIZE*COLS+SACSIZE <= 64
+#define HEIGHTSIZE 4
+#define SACSIZE 16
+
+// height of playing field in which to complete lines
+// (you must have SACSIZE >= MAXHEIGHT and 2^HEIGHTSIZE >= MAXHEIGHT+1
+#define MAXHEIGHT 6
+#define TOTALMAXMOVES (MAXHEIGHT*COLS+1)
+
+// search options
+// if JUSTONE is true, the program will run faster to find some winning stategy
+// (without trying to find the shortest paths to a win)
+#define JUSTONE 0
+// if ALPHABETA is true, the program will prune branches using alpha-beta, it
+// should give a strategy with the same performance as when it is not set
+#define ALPHABETA 1
+
+// last played pieces
+int lastpiece[TOTALMAXMOVES];
+
+// file in which to write solution
+FILE *fsol;
+
+using namespace std;
+
+typedef unsigned long long ull;
+typedef pair<int, int> pii;
+typedef pair<int, pii> piii;
+typedef pair<int, ull> piull;
+typedef pair<ull, pii> pullii;
+typedef pair<piull, pii> piullii;
+typedef pair<pii, pii> piiii;
+
+// cache of losing configurations (this takes the most RAM)
+// mapping configurations that were explored and not found to be winning
+// to the maximal maxmoves to which they were explored
+// (-2 for unlimited => always failing)
+// (if ALPHABETA=0, we only care about the set of keys, not the associated
+// values)
+unordered_map<ull, int> mycache0;
+// cache of winning configurations and number of moves to win
+unordered_map<ull, int> mycache1;
+
+bool fits_maxheight(int p, int r, int c, int l) {
+ if (!fits(p, r, c, l))
+ return false;
+ for (int i = 0; i < 4; i++)
+ for (int j = 0; j < 4; j++)
+ if (piecesr[p][r][i][j]) {
+ // do not put a piece above a column that's already full
+ // the reason is that we do not know how high the column is and so the
+ // effect of lower components of the piece in adjacent columns may be
+ // inaccurate
+ if (field[LINES-MAXHEIGHT][c+j])
+ return false;
+ }
+ return true;
+}
+
+int line_config(ull config) {
+ // test if field contains a line
+ // the argument config is used only for the "SACSIZE" component describing
+ // which rows contain holes
+ ull sac = config >> HEIGHTSIZE*COLS;
+ for (int i = 0; i < LINES; i++) {
+ if (sac & (((ull) 1) << i))
+ continue; // line contains a hole so we shouldn't consider it
+ bool ok = true;
+ for (int j = 0; j < COLS; j++)
+ if (!field[i][j]) {
+ ok = false;
+ break;
+ }
+ if (ok)
+ return true;
+ }
+ return false;
+}
+
+void printfield(int depth, ull config) {
+ // print current status of playing field
+ ull sac = config >> HEIGHTSIZE*COLS;
+ printf("========== MH:%d depth:%d cache0:%ld cache1:%ld\n", MAXHEIGHT, depth, mycache0.size(), mycache1.size());
+ printf("branch %d %d %d %d %d %d\n",
+ lastpiece[0], lastpiece[1], lastpiece[2], lastpiece[3], lastpiece[4], lastpiece[5]);
+ for(int i = 0; i < LINES; i++) {
+ printf("%c", sac & (((ull) 1) << i) ? '!' : ' ');
+ for (int j = 0; j < COLS; j++) {
+ printf("%c", field[i][j] ? '#' : '.');
+ }
+ printf("\n");
+ }
+ printf("==========\n");
+}
+
+void printconfig(ull sig) {
+ // print a configuration
+
+ cout << "sig: " << sig;
+ for (int c = 0; c < 10; c++) {
+ int h = sig & ((((ull) 1) << HEIGHTSIZE)-1);
+ sig >>= HEIGHTSIZE;
+ printf(" %d", h); // height of column c
+ }
+ printf(" ");
+ for (int r = 0; r < LINES; r++)
+ printf("%c", (((ull) 1) << r) & sig ? '!':'.'); // incomplete rows
+ printf("\n");
+}
+
+ull get_config(ull configold) {
+ // compute configuration from field
+ // the argument configold is used only for the "SACSIZE" component describing
+ // which rows contain holes, to account for the fact that they still contain
+ // holes
+ ull sac = configold >> HEIGHTSIZE*COLS;
+ int height[COLS] = {};
+
+ // compute which rows now contain holes, and the maximal height of each line
+ for (int c = 0; c < COLS; c++) {
+ bool seenone = false;
+ for (int r = 0; r < LINES; r++) {
+ if (field[r][c] && !seenone) {
+ seenone = true;
+ height[c] = min(LINES-r, MAXHEIGHT);
+ continue;
+ }
+ if (seenone && !field[r][c]) {
+ if (r >= LINES-MAXHEIGHT)
+ sac |= (((ull) 1) << r); // incomplete row
+ }
+ }
+ if (!seenone)
+ height[c] = 0;
+ }
+
+ // prepare the config
+ ull conf2 = sac;
+ for (int c = COLS-1; c >= 0; c--) {
+ conf2 <<= HEIGHTSIZE;
+ conf2 |= height[c];
+ }
+ return conf2;
+}
+
+
+ull load_config(ull config) {
+ // load configuration into field
+ // return the SACSIZE component with the incomplete lines
+ for (int r = 0; r < LINES; r++)
+ for (int c = 0; c < COLS; c++)
+ field[r][c] = 0;
+ for (int c = 0; c < COLS; c++) {
+ int h = config & ((((ull) 1) << HEIGHTSIZE)-1);
+ config >>= HEIGHTSIZE;
+ for (int r = LINES-1; r > LINES-1-h; r--)
+ field[r][c] = 1;
+ }
+ return config; // remaining sac
+}
+
+int wins(ull sig, int depth, int maxmoves);
+
+piullii winsp(ull config, int depth, int p, int maxmoves) {
+ // do we win at config when playing piece p?
+ // depth is the current depth in the tree
+ // last arg is how many moves are allowed
+ // if ALPHABETA=0, last arg is not used
+ // the return value describes the number of moves to win (-1 if losing)
+ // the column and rotation where to put piece p
+ // and the config to which this leads
+
+ // if the configuration is already known to be losing, return
+ if (mycache0.find(config) != mycache0.end()) {
+ int damaxmoves = mycache0[config];
+ if (!ALPHABETA || damaxmoves == -2 || damaxmoves >= maxmoves)
+ return make_pair(make_pair(-1, 0), make_pair(-1, -1));
+ }
+
+ lastpiece[depth] = p;
+ assert(depth < TOTALMAXMOVES);
+
+ load_config(config);
+
+ if (depth < 7) {
+ // show progress info
+ printf("winsp %lld %d %d\n", config, depth, p);
+ cout << "config " << config << endl;
+ printfield(depth, config);
+ }
+
+ // best number of moves to win, and corresponding rotation, column, config
+ int initvbest = (maxmoves == -2 || !ALPHABETA) ? TOTALMAXMOVES : maxmoves;
+ int vbest = initvbest;
+ int rbest = -1, cbest = -1;
+ ull sbest = -1;
+
+ // store options before recursing on them
+ // that way, if there is a win in one move, we won't recurse
+ vector<pullii> opts;
+
+ for (int r = 0; r < 4; r++) {
+ for (int c = -2; c < COLS; c++) {
+ if (fits_maxheight(p, r, c, 0)) {
+ // try to put piece p with rotation r at column c
+ // see where it falls
+ int l = 0;
+ while(fits_maxheight(p, r, c, l))
+ l++;
+ l--;
+ // blit piece at row l
+ blit(p, r, c, l, 0);
+ // check if we won and what is the resulting config
+ bool won = line_config(config);
+ ull config2 = get_config(config);
+ // and reset the field
+ load_config(config);
+
+ if (config2 == config)
+ continue; // no progress when dropping this piece
+ if (won)
+ return make_pair(make_pair(1, config2), make_pair(r, c));
+ if (mycache0.find(config2) != mycache0.end()) {
+ if (!ALPHABETA)
+ continue; // known to be losing
+ // with ALPHABETA, we check how far we explored it
+ int damaxmoves = mycache0[config2];
+ if (damaxmoves == -2 || damaxmoves >= vbest)
+ continue; // known to be losing
+ }
+ ull sac2 = config2 >> HEIGHTSIZE*COLS;
+ if (sac2 == (((ull) 1) << MAXHEIGHT)-1)
+ continue; // no feasible rows remain
+ if (mycache1.find(config2) != mycache1.end()) {
+ // config was already studied and is winning, does it make us win
+ // faster?
+ int vposs = mycache1[config2];
+ if (vposs < vbest) {
+ // it makes us win faster
+ vbest = vposs;
+ rbest = r;
+ cbest = c;
+ sbest = config2;
+ }
+ if (JUSTONE)
+ return make_pair(make_pair(1+vbest, sbest), make_pair(rbest, cbest));
+ continue;
+ }
+ opts.push_back(make_pair(config2, make_pair(r, c)));
+ }
+ }
+ }
+ for (auto opt : opts) {
+ // study the resulting configuration recursively
+ int vposs = wins(opt.first, depth+1, vbest-1);
+ load_config(config); // reset state after recursive call
+ if (vposs >= 0) {
+ if (vposs < vbest) {
+ // resulting configuration makes us win faster
+ vbest = vposs;
+ rbest = opt.second.first;
+ cbest = opt.second.second;
+ sbest = opt.first;
+ }
+ if (JUSTONE)
+ return make_pair(make_pair(1+vbest, sbest), make_pair(rbest, cbest));
+ }
+ }
+ if (vbest < initvbest) {
+ // we found a way to win!
+ return make_pair(make_pair(1+vbest, sbest), make_pair(rbest, cbest));
+ } else {
+ // all moves are losing
+ return make_pair(make_pair(-1, 0), make_pair(-1, -1));
+ }
+}
+
+int wins(ull sig, int depth, int maxmoves) {
+ // what is the minimal number of moves to win from config sig?
+ // maxmoves is the maximal number of allowed moves (-2 for unlimited)
+ // if ALPHABETA=0, last arg is not used
+ if (ALPHABETA && maxmoves != -2 && maxmoves < 0)
+ return -1; // not enough moves remain
+
+ // return values of winsp
+ int mr[7], mc[7], mv[7];
+ ull ms[7];
+
+ if (mycache0.find(sig) != mycache0.end()) {
+ if (!ALPHABETA)
+ return -1; // known to be losing
+ // with ALPHABETA, we check how far we explored it
+ int damaxmoves = mycache0[sig];
+ if (damaxmoves == -2)
+ return -1; // we know it is always losing
+ if (damaxmoves >= maxmoves)
+ return -1; // already explored to this depth and failed
+ }
+ if (mycache1.find(sig) != mycache1.end())
+ return mycache1[sig]; // we know it is winning
+ int longest=-1; // maximal number of moves to win (worse case among all pieces)
+ for (int p = 0; p < 7; p++) {
+ // try each piece
+ piullii nmovespp = winsp(sig, depth, p, maxmoves);
+ mv[p] = nmovespp.first.first;
+ ms[p] = nmovespp.first.second;
+ if (mv[p] == -1) {
+ // piece p is losing, so position is losing
+ if (mycache0.find(sig) == mycache0.end()) {
+ mycache0[sig] = maxmoves; // not known to be losing, store it
+ } else {
+ if (mycache0[sig] >= 0) {
+ if (maxmoves == -2) {
+ mycache0[sig] = -2;
+ } else {
+ mycache0[sig] = max(mycache0[sig], maxmoves); // update depth at which it loses
+ }
+ }
+ }
+ return -1; // losing
+ }
+ mr[p] = nmovespp.second.first;
+ mc[p] = nmovespp.second.second;
+
+ if (mv[p] >= 0) {
+ longest = max(longest, mv[p]);
+ }
+ }
+
+ // if we went so far, this is a winning position
+ mycache1[sig] = longest;
+ // store its details in solution file
+ for (int p = 0; p < 7; p++) {
+ // field 1: the config in question
+ // field 2: the piece to play
+ // field 3: the number of moves to win
+ // fields 4 and 5: the rotation and column where to play it
+ // field 6: the resulting config
+ fprintf(fsol, "%lld %d %d %d %d %lld\n", sig, p, mv[p], mr[p], mc[p], ms[p]);
+ }
+
+ return longest;
+}
+
+int main(int argc, char **argv) {
+ init_pieces();
+ fsol = fopen("solution", "w");
+ int ww = wins(0, 0, -2);
+ assert(ww > 0);
+ fclose(fsol);
+ return 0;
+}
+
diff --git a/common_tetris.cpp b/common_tetris.cpp
@@ -0,0 +1,148 @@
+#include<cassert>
+#include<cstdio>
+
+// dimensions of playing field (LINES should be sufficiently large relative to
+// MAXHEIGHT to have the space to move pieces before dropping them)
+#define COLS 10
+#define LINES 16
+
+// the tetris pieces
+bool pieces[7][4][4] = {
+ {
+ {1, 0, 0, 0},
+ {1, 0, 0, 0},
+ {1, 0, 0, 0},
+ {1, 0, 0, 0}
+ },
+ {
+ {0, 1, 0, 0},
+ {1, 1, 0, 0},
+ {1, 0, 0, 0},
+ {},
+ },
+ {
+ {0, 1, 1, 0},
+ {1, 1, 0, 0},
+ {},
+ {},
+ },
+ {
+ {1, 1, 1, 0},
+ {0, 1, 0, 0},
+ {},
+ {}
+ },
+ {
+ {1, 1, 1, 0},
+ {1, 0, 0, 0},
+ {},
+ {}
+ },
+ {
+ {1, 1, 1, 0},
+ {0, 0, 1, 0},
+ {},
+ {}
+ },
+ {
+ {1, 1, 0, 0},
+ {1, 1, 0, 0},
+ {},
+ {}
+ }};
+
+// the rotated tetris pieces
+bool piecesr[7][4][4][4];
+
+// the playing field (global)
+int field[LINES][COLS] = {};
+
+void init_pieces() {
+ // initialize array of rotated pieces
+ for (int p = 0; p < 7; p++)
+ for (int i = 0; i < 4; i++)
+ for (int j = 0; j < 4; j++)
+ piecesr[p][0][i][j] = pieces[p][i][j];
+
+ // do the 3 rotations
+ for (int p = 0; p < 7; p++)
+ for (int r = 1; r < 4; r++)
+ for (int i = 0; i < 4; i++)
+ for (int j = 0; j < 4; j++)
+ piecesr[p][r][i][j] = piecesr[p][r-1][j][3-i];
+}
+
+bool fits(int p, int r, int c, int l) {
+ // does piece p rot r fit at col c line l?
+ for (int i = 0; i < 4; i++)
+ for (int j = 0; j < 4; j++)
+ if (piecesr[p][r][i][j]) {
+ if (c + j < 0)
+ return false;
+ if (c + j >= COLS)
+ return false; // outside the screen right
+ if (l + i >= LINES)
+ return false; // outside the screen bottom
+ if (field[l + i][c + j])
+ return false; // blocked
+ }
+ return true;
+}
+
+bool stopped(int p, int r, int c, int l) {
+ // is piece p rot r at col c line l stopped by something below it?
+ for (int i = 0; i < 4; i++)
+ for (int j = 0; j < 4; j++)
+ if (piecesr[p][r][i][j]) {
+ assert(c + j >= 0);
+ assert(c + j < COLS);
+ assert(l + i < LINES);
+ assert(!field[l + i][c + j]);
+ if (l + i == LINES-1)
+ return true; // screen bottom
+ if (field[l+i+1][c+j])
+ return true; // filled square
+ }
+ return false;
+}
+
+void blit(int p, int r, int c, int l, int x) {
+ // put piece p rot r at col c line l of field
+ // writing it as integer 1+'x' which can be more convenient for printing
+ for (int i = 0; i < 4; i++)
+ for (int j = 0; j < 4; j++)
+ if (piecesr[p][r][i][j]) {
+ assert(c + j < COLS);
+ assert(l + i < LINES);
+ assert(!field[l + i][c + j]);
+ field[l + i][c + j] = 1+x;
+ }
+}
+
+void unblit(int p, int r, int c, int l) {
+ // un piece p rot r at col c line l
+ for (int i = 0; i < 4; i++)
+ for (int j = 0; j < 4; j++)
+ if (piecesr[p][r][i][j]) {
+ assert(c + j < COLS);
+ assert(l + i < LINES);
+ assert(field[l + i][c + j]);
+ field[l + i][c + j] = 0;
+ }
+}
+
+int line() {
+ // check if there is a line in the current configuration
+ for (int i = 0; i < LINES; i++) {
+ bool ok = true;
+ for (int j = 0; j < COLS; j++)
+ if (!field[i][j]) {
+ ok = false; break;
+ }
+ if (ok) {
+ return true;
+ }
+ }
+ return false;
+}
+
diff --git a/make_graph.cpp b/make_graph.cpp
@@ -0,0 +1,92 @@
+#include<cstdio>
+#include<cassert>
+#include<unordered_map>
+#include<vector>
+
+// load trace produced by bruteforce.cpp and produce a graph including only
+// reachable configurations (and renumbering configurations to contiguous
+// ids)
+
+using namespace std;
+
+typedef unsigned long long ull;
+
+vector<ull> n[7]; // the next configuration for each piece in this id
+vector<int> rot[7]; // the rotation with which to play each piece in this id
+vector<int> distwin[7]; // the distance to win for each piece in this id
+vector<int> col[7]; // the column where to play each piece in this id
+vector<bool> fin; // is id in a won state?
+vector<bool> seen; // have we seen the id?
+unordered_map<ull, int> M; // mapping of configurations to contiguous ids
+
+ull dafind(ull v) {
+ // find config v in M
+ if (M.find(v) == M.end()) {
+ // it does not exist, add it with empty values
+ M[v] = M.size();
+ for (int i = 0 ; i <7; i++)
+ n[i].push_back(0);
+ for (int i = 0 ; i <7; i++)
+ rot[i].push_back(-1);
+ for (int i = 0 ; i <7; i++)
+ col[i].push_back(-1);
+ for (int i = 0 ; i <7; i++)
+ distwin[i].push_back(-1);
+ fin.push_back(true);
+ seen.push_back(false);
+ return M.size()-1;
+ }
+ return M[v];
+}
+
+void explore(int v) {
+ // dfs exploration to find reachable configurations from v
+ if (fin[v])
+ return; // leaf
+ if (seen[v])
+ return; // already seen
+ seen[v] = true;
+ for (int i = 0; i < 7; i++)
+ explore(n[i][v]);
+}
+
+int main() {
+ while (true) {
+ ull f, t;
+ int a, rr, cc, dw;
+
+ int ret = scanf("%lld %d %d %d %d %lld", &f, &a, &dw, &rr, &cc, &t);
+ if (ret != 6)
+ break;
+ // get ids of configs
+ ull ff = dafind(f);
+ ull tt = dafind(t);
+ fin[ff] = false;
+
+ // if already known to be winning with a worse score, ignore
+ if (distwin[a][ff] >= 0 && distwin[a][ff] <= dw)
+ continue;
+
+ // store info
+ distwin[a][ff] = dw;
+ n[a][ff] = tt;
+ rot[a][ff] = rr;
+ col[a][ff] = cc;
+ }
+
+ // explore from the first config
+ explore(M[0]);
+
+ // produce the graph:
+ // field 1: the id
+ // field 2: the piece
+ // fields 3 and 4: the rotation and column
+ // field 5: the resulting id
+ for (ull i = 0; i < seen.size(); i++)
+ if (seen[i] && !fin[i])
+ for (int j = 0; j < 7; j++)
+ printf("%lld %d %d %d %lld\n", i, j, rot[j][i], col[j][i], n[j][i]);
+ return 0;
+
+
+}
diff --git a/minify_graph.py b/minify_graph.py
@@ -0,0 +1,45 @@
+#!/usr/bin/python3
+
+# minify a strategy tree
+
+import sys
+
+T = {}
+M = {}
+cache = {}
+
+last = -1
+
+def minify(v):
+ global T
+ if v not in T.keys():
+ return -1 # leaf
+ if v in cache.keys():
+ return cache[v]
+ # info about this configuration: moves to play and minified resulting config
+ info = tuple([(ip[0], ip[1], minify(ip[2])) for ip in T[v]])
+ if info in M.keys():
+ cache[v] = M[info]
+ return M[info] # node already known
+ # insert the new node and print its outgoing edges
+ idx = len(M.keys())
+ M[info] = idx
+ # idx is not printed because the lines are sequential
+ print(" ".join(" ".join(str(inf) for inf in info[p]) for p in range(7)))
+ cache[v] = idx
+ return idx
+
+for l in sys.stdin.readlines():
+ ff = l.strip().split(' ')
+ f = int(ff[0])
+ p = int(ff[1])
+ r = int(ff[2])
+ c = int(ff[3])
+ t = int(ff[4])
+ if f not in T.keys():
+ T[f] = [-1] * 7
+ T[f][p] = (r, c, t)
+ last = f
+
+assert(last >= 0)
+minify(last)
diff --git a/strategy.txt b/strategy.txt
@@ -0,0 +1,5250 @@
+0 7 -1 0 6 -1 0 6 -1 1 6 -1 3 4 -1 1 6 -1 0 6 -1
+0 7 -1 0 6 -1 1 6 -1 1 6 -1 3 4 -1 2 0 0 0 6 -1
+0 8 -1 1 6 -1 1 7 -1 3 5 -1 1 7 -1 3 5 -1 0 7 -1
+0 8 -1 1 6 -1 1 7 -1 0 6 -1 1 7 -1 0 6 -1 0 7 -1
+0 8 -1 1 6 -1 0 7 -1 3 5 -1 1 7 -1 1 8 -1 0 7 -1
+0 8 0 1 6 -1 1 6 3 1 6 4 0 6 -1 3 5 -1 0 7 -1
+0 8 1 1 6 -1 1 6 2 2 0 5 0 6 -1 3 5 -1 0 7 -1
+0 8 -1 1 3 4 1 7 -1 3 5 -1 3 5 -1 1 8 -1 0 4 4
+1 5 -1 1 6 -1 1 4 5 2 4 7 1 7 -1 3 5 -1 0 7 -1
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diff --git a/verify.cpp b/verify.cpp
@@ -0,0 +1,88 @@
+#include<cstdio>
+#include<iostream>
+#include<cassert>
+#include<vector>
+#include "common_tetris.cpp"
+
+using namespace std;
+
+// the graph information
+vector<int> config[7], rotation[7], column[7];
+vector<int> lastpiece;
+
+using namespace std;
+
+bool wins(int vertex, int depth);
+
+bool winsp(int vertex, int depth, int p) {
+ // check that we win at vertex with piece p
+ int r = rotation[p][vertex];
+ int c = column[p][vertex];
+ int n = config[p][vertex];
+
+ // trace the run
+ for (unsigned int i = 0; i < lastpiece.size(); i++)
+ printf("%d", lastpiece[i]);
+ printf(" vertex %d piece %d => r %d c %d to get to %d\n", vertex, p, r, c, n);
+
+ // check we can actually put the piece
+ assert(fits(p, r, c, 0));
+ int l = 0;
+ while(fits(p, r, c, l))
+ l++;
+ l--;
+ // piece drops at row l
+ blit(p, r, c, l, depth);
+ // recursive call on the result (going at the new vertex)
+ bool win = wins(n, depth+1);
+ assert(win);
+ unblit(p, r, c, l);
+
+ return true;
+}
+
+bool wins(int vertex, int depth) {
+ // check winning strategy at vertex
+
+ // if vertex is winning then check that current board state is winning
+ if (vertex == -1) {
+ assert(line());
+ return true;
+ }
+
+ // otherwise, check that each move has a winning strategy
+ for (int p = 0; p < 7; p++) {
+ lastpiece.push_back(p);
+ bool wins = winsp(vertex, depth, p);
+ lastpiece.pop_back();
+ assert(wins);
+ }
+ return true;
+}
+
+int main(int argc, char **argv) {
+ init_pieces();
+
+ // read strategy from stdin
+ bool reading = true;
+ while (reading) {
+ for (int p = 0; p < 7; p++) {
+ int r, c, t;
+ int ret = scanf("%d%d%d", &r, &c, &t);
+ if (ret != 3) {
+ assert (p == 0);
+ reading = false;
+ break;
+ }
+ column[p].push_back(c);
+ rotation[p].push_back(r);
+ config[p].push_back(t);
+ }
+ }
+ int start = config[0].size()-1;
+
+ bool winn = wins(start, 0);
+ assert(winn);
+ return 0;
+}
+
